eALIS:
An Interpretation System which is Reciprocal and Lifelong
eALIS, REciprocal And Lifelong Interpretation System, is
a new “post-Montagovian” [3] theory concerning the formal interpretation of sentences constituting coherent discourses [1], with
a lifelong model of lexical, interpersonal and cultural
/encyclopedic knowledge of interpreters in its center including
their reciprocal knowledge on each other.
The decisive theoretical feature of eALIS lies in a peculiar
reconciliation of three objectives which are all worth accomplishing
in formal semantics but could not be reconciled so far.
The first aim concerns the exact formal basis itself, which is
often mentioned as Montague’s Thesis: human languages can be
described as interpreted formal systems.
The second aim concerns compositionality, practically postulating the existence of a homomorphism from syntax to semantics.
In Montague’s interpretation systems a traditional logical
representation played the role of an intermediate level between
the syntactic representation and the world model, but Montague
argued that this intermediate level of representation can, and
should, be eliminated. The post-Montagovian history of formal
semantics [3] [1], however, seems to have proven the opposite,
some principle of “discourse representationalism”: “some level of
[intermediate] representation is indispensable in modeling the interpretation of natural language” [2].
The Thesis of eALIS is that the two fundamental Montagovian objectives can be reconciled with the principle of “discourse
representationalism” – by embedding discourse representations in
the world model, getting rid of an intermediate level of representation in this way while preserving its content and relevant structural
characteristics. This idea can be carried out in the larger-scale
framework of embedding discourse representations in the world
model not directly but as parts of the representations of interpreters’
minds, i.e. that of their (permanently changing) information states.
Definition I: the world model of eALIS
[1]
[2]
[3]
2
Asher – Lascarides 2003: Logics of Conversation, Cambridge Univ. Press.
Dekker 2000: Coreference and Representationalism, in vHeusinger – Egli eds.:
Reference and Anaphoric Relations.
Kamp – vGenabith – Reyle 2005: Discourse Representation Theory, ...,
http://www.ims.uni-stuttgart.de/~hans.
Definition I:
the world model of eALIS
The WORLD MODEL of eALIS is defined as a triplet  = U, W0, W
where
 U is a countably infinite set: the UNIVERSE
 W0 = U0, T, S, I, D, , A: the EXTERNAL WORLD
 W is a partial function from the Cartesian product ITm, where
W[i,t] is a quintuple U[i], [i,t], [i,t], [i,t], [i,t]: the
INTERNAL-WORLD FUNCTION
 and all the stipulations listed in subsections 1.1-1.2 hold.
1.1
The external world
W0 = U0, T, S, I, D, , A: the EXTERNAL WORLD, where
 U0 is (called) the EXTERNAL UNIVERSE
 T = T,  is the structured set of (TEMPORAL) INTERVALS
 S = S,  is the structured set of SPATIAL ENTITIES
 I = I,  is the structured set of INTERPRETERS
 D = D,  is the structured set of PHONETIC FORMS
   TU0* is the set of CORE RELATIONS
 A is the INFORMATION STRUCTURE of the external world
 T, S, I and D are pairwise disjoint, infinite, real subsets of the
basic set U0 of the external universe
 and all the stipulations listed in subsections 1.1.1-1.1.7 hold.
Definition I: the world model of eALIS
3
1.1.1 The external universe
The external universe U0  U is an infinite subset of universe U, whose
elements will be referred to as the (EXTERNAL) ENTITIES.
1.1.2 The time
We regard the infinite structured set T = T,  of (temporal) intervals
(TU0) as isomorphic to the set of intervals over the set of rational numbers. Set  contains the relations typically interpreted here and can be extended freely depending on our descriptive aims. We list below a few unconditionally necessary elements of :
 Moment: a one-argument relation on the set of intervals
which selects the point-like elements; the sum of elements like
this (tMoment) is denoted by Tm and called MOMENTS
 Startp: a two-argument relation; t’, tStartp expresses that
(the point-like) t’ is the (single) STARTING-POINT of interval t
 Endp: a two-argument relation; t”, tEndp expresses that
(the point-like) t” is the (single) ENDPOINT of interval t
 Intp: a two-argument relation; t*, tIntp expresses that (the
point-like) t* is an INTERNAL POINT of interval t
 Prec: a two-argument relation, too; t’, t”Prec expresses that
interval t’ PRECEDES interval t” (in the sense that the startingpoint of t” does not precede the endpoint of t’)
1.1.3 The space
The infinite structured set S = S,  of spatial entities (SU0) is supposed
to be isomorphic to the space defined by the three-dimensional coordinate
system Q3. Set  contains the relations typically interpreted here and can
be extended freely depending on our descriptive aims.
1.1.4 Az interpretálók
The relation set  over the infinite structured set I = I,  of interpreters
(I  U0) can be decided freely depending on our descriptive aims.
1.1.5 The performed discourse and its components
Over the infinite structured set D = D,  of phonetic forms (D  U0) the
set  of relations will be referred to as PHONETIC-FORM RELATIONS can be
decided depending on our descriptive aims. Below we mention a few distinguished elements of the set  of relations:
4
Definition I: the world model of eALIS
Dis: a one-argument relation over the elements in D, which contains
the sequences of sounds (or parts of writings) that can be regarded as the
performed form of discourses; the total sum of elements like this is denoted
by Ddis (dDis) and is called DISCOURSE ENTITIES.
Morph: a two-argument relation over D which serves the purpose of
deciding the smallest pieces of discourse entities bearing some meaning; if
dDdis holds, what d’,dMorph expresses is that d’ is a MORPH of discourse (entity) d. Morphs of a given discourse d are supposed to constitute
a linearly ordered (<) finite set, which is intended to capture the CHRONOLOGY OF THEIR PERFORMANCE.
Sequence  = d1, d2,..., dN is called the SEGMENTATION of discourse
d if it is the listing of the morphs in d linearly ordered in the way mentioned above. Under the segmentation formulated above a morph di is
called to be NEXT to morphs di-1 and di+1 (if they exist), and exclusively to
them. Element d1 is called the FIRST morph of the discourse, and dN is
called its LAST morph.
Further relations in  concern intonational features of morphs, classifying
sound intensity, height and tempo to the grammatically relevant extent.
1.1.6 Relations of the external world
Elements of the infinite set   TU0* of core relations can be decided
depending on our descriptive aims, but it is to contain the distinguished
core relation PERCEIVE.
1.1.7 Events of the external world decomposed as infons
The information structure A of the external world is the isomorphic reformulation of relation structure U0,  into a standard simple information
structure, as is defined in Seligman és Moss (1997: 245); its infons will be
mentioned as the INFONS OF THE EXTERNAL WORLD.
Let  denote the set of infons. It is also necessary to introduce a partial function 0 : N  U0, to be called the INFON-STRUCTURAL FUNCTION, which assigns a positive integer k (k2) and an infon  the k-th element of the infon (as a linearly ordered N-tuple), which is an entity; and
this function is such that number 1 is assigned a core relation (an element
of ), and number 2 is assigned an interval (an element of T).
Definition I: the world model of eALIS
1.2
5
Internal worlds, that is, information states
INTERNAL-WORLD FUNCTION W is a partial function from domain
ITm, where W[i,t] can be defined as a quintuple U[i], [i,t], [i,t],
[i,t], [i,t] with components satisfying the requirements below:
 The relational structure W[i,t] will be referred to as interpreter
i’s INTERNAL WORLD at moment t, or her INFORMATION STATE
 U[i]  U is an infinite set: interpreter i’s INTERNAL UNIVERSE, or
the set of her REFERENTS; or U[i] can also be called the set of i’s
INTERNAL ENTITIES
 [i,t] : U[i]  U[i] is a partial function: the EVENTUAL(ITY) FUNCTION
 [i,t] : U[i]  U[i]U0 is another partial function: the
ANCHORING FUNCTION
 [i,t] : U[i]  U[i] is also a partial function: the
LEVEL
FUNCTION
 [i,t] :   U[i] is a fourth partial function: the CURSOR
(FUNCTION)
 These four partial functions will be referred to as the interpreter’s INTERNAL FUNCTIONS
 It is also required that the stipulations below in 1.2.1-1.2.5 be met.
1.2.1 An interpreter’s life
Internal-world function W is partial in the way that, relative to an arbitrary
information state W[i,], there is to exist a single PRECEDING information
state W[i,’] (thus ’<, but function W is not interpreted at a mediate moment ” (which would mean that <”<)).
For each interpreter i, there is a moment t’ of her BIRTH and a moment t” of her DEATH, t’t”, which also meet the requirements that <t’,
and if >t” the internal functions belonging to the internal world W[i,] are
all empty. Otherwise, the factual domains of interpretation and values of all
the four partial functions are finite sets.
The internal universe U[i], for a fixed interpreter i,is the same at
each moment t, but for arbitrary two interpreters i’ and i”, U[i’] and U[i”]
are disjoint sets.
6
Definition I: the world model of eALIS
1.2.2 The (function) structure of event(ualitie)s
We refer to the referents occupying the second argument position of the
eventual(ity) function [i,t] : U[i]  U[i] as EVENTUAL REFERENTS,
and elements of  as EVENTUAL LABELS.
The set  of eventual labels consist of ordered pairs whose first
member comes from a finite set EVE={Pred, Temp, Arg, Spat,...} of labels
(which can be extended freely depending on their linguistic aims) – let us
call them EVENTUAL MAIN PARAMETERS. The second member can be chosen, depending on the first member, from label sets Pred, Temp, Arg, Spat
etc., also depending on our linguistic aims; elements of these sets will be
referred to as follows, respectively.
1.2.2.1 The event structure
Pred: SUBPARAMETERS OF EVENT STRUCTURE; some event-typological classification of predicates (chiefly verbs) of language (e.g. an extended version of Vendler classes). The referent that appears next to the main parameter Pred in the argument position of function [i,t] is called the PREDICATE (REFERENT).
1.2.2.2 Time – from the internal perspective (aspect)
Temp: TEMPORAL SUBPARAMETERS; they are intended to express different
relations of reference time  to the event structure. We mention a few important relations referred to by temporal subparameters:
 InPre: “ is a point of the preparatory phase of the event”
 AtSta: “ coincides with the starting-point of the event”
 InCum: “ is an (internal) point of the cumulative phase”
 AtCum: “ coincides with the cumulative point of the event”
 InRes: “ is a point of the result phase”
If we intend to express also the relation of the reference time to the
speech time by means of temporal subparameters (past: , present: ,
future: ), we need, instead of 5 subparameters, three times five (i.e. 15)
ones (e.g. ’InRes’ is suitable for capturing the English Past Perfect).
The referent that appears next to the main parameter Temp in the argument position of function [i,t] is called the TIME REFERENT.
1.2.2.3 The arguments
Arg: ARGUMENT-MARKING SUBPARAMETERS; this label set practically consists of the case-marking morphemes of a language. The referent that appears next to the main parameter Arg in the argument position of function
[i,t] is called the ARGUMENT REFERENT.
7
Definition I: the world model of eALIS
1.2.2.4 The space from the internal perspective
Spat: SPATIAL SUBPARAMETERS; they are intended to express the relation of
spatial referent s to the spatial structure of the event:
 AtSta: “s coincides with the spatial point at the moment at the
starting-point of the event”
 InCum: “an internal point of the path of the event”
 AtCum: “s coincides with the place of the event at the cumulative point of the event”
1.2.2.5 Different representations of the structure of event(ualitie)s
Function  is a method easy to handle in mathematical definitions, which
clearly elucidates details of eventuality structures; in the logical / linguistic
literature, however, a reduced formula type is used, demonstrated in iv. below. We show its relation to the richer description of eventualities based on
function , illustrated in i. below.
Thus what is described by method i. is that there is an eventuality e
predicating about referents r1, ..., rK and moment t that they stand in the relation expressed by predicate p. Formula ii. below provides exactly the
same information, with function  having hidden; only the labels say which
referent plays what role in the event(uality) described. Method iii. is already a simplified description, in which only the order of referents provides some information on their roles in the event. Finally, in iv, even the
eventuality and the time are ignored. We can afford this method if these
two factors are either irrelevant or can be reconstructed from somewhere
else.
i. The FUNCTION-STRUCTURAL representation of event(ualitie)s:
(Pred, , e) = p
(Temp, , e) = t
(Arg, 1, e)= r1
...
(Arg, K, e)= rK
((Spat, , e)= s, if there is a spatial referent)
ii. The EVENTUALITY-CENTERED representation of event(ualitie)s:
e:: Pred,: p, Temp,: t, Arg,1, e)= r1, ..., Arg,K, e)= rK...
iii. The SIMPLIFIED EVENTUALITY-CENTERED representation:
e: p t r1 ... rK
iv. The SIMPLIFIED TIMELESS PREDICATE-CENTERED representation:
p(r1, ..., rK)
8
Definition I: the world model of eALIS
1.2.3 Identificational anchoring of referents
The referents occupying the first argument position of the anchoring function [i,t] : U[i]  U[i]U0 – i.e., elements of : are the ANCHORING
LABELS.
 is a set consisting of ordered pairs. The first member of a pair like
this is a set ANCH={Arg, Pred, Adj, Ana, Out,...} of labels (potentially
freely extendable depending on our linguistic aims), which refer to the
grammatic / pragmatic way of anchoring a referent to another referent, to
be called the ANCHORING TYPE. The second member is an ordered N-tuple
(where 0 is also a permitted value of N) which provides the DIMENSIONS OF
ANCHORING (or the ANCHORING CABLES), depending on the anchoring type,
in a language-specific way to a certain extent. We show some typical cables in the correspondig anchoring types:
 Arg: ARGUMENT ANCHORING; typical cables: category (Cat),
word order (Ord), (expected) case (Case)
 Pred: PREDICATE ANCHORING; cables: category (Cat), word order (Ord), agreement (Agr)
 Adj: BASE-OF-ADJUNCTION ANCHORING; cables: category (Cat),
word order (Ord), agreement (Agr) ground
 Ant: ANTECEDENT ANCHORING; cables: e.g. agreement (Agr),
retaining topic (Top)
 Out: ANCHORING-OUT; cables: e.g. some information referring
to gender (Gen), number (Num), human character (Hum), gesticulation (Gest)
The value of anchoring-out is necessarily an external entity (an element of U0). The value of the other anchoring types should be a referent
(i.e. an element of U[i,t]); these types are all called INTERNAL ANCHORINGS.
1.2.4 Internal levels of referents
The referents occupying the first argument position of the level function
[i,t] : U[i]  U[i] – elements of : are the LEVEL LABELS.
Each element of U[i] is either assigned to another referent, accompanied with a certain level label – these are the FICTIVE referents –or assigned to nothing: – these are the ROOT REFERENTS. A characteristic property of root referents is that only this group of referents can be anchored-out
(by function ).
The set  of level labels consists of ordered quadruples.
9
Definition I: the world model of eALIS
1.2.4.1 Modal labels to capture scope relations, propositional attitudes
and rhetorical relations
The first member of a level label is a set modal = {.supp, .cons, .neg,
.beln, .desn, !intn, .dream, .see, .hear, .touch, .sme, .tas,
.elab, ?elab, .exp, .cor, .nar, .back, ?nar, ?back, .conj,
.disj, .alt, .res, .contr, .par, !cons*,...} (which can be extended
freely depending on our linguistic aims): the MODAL LABELS. Each modal
label is itself an ordered triplet, with the following components, respectively:
 LEVEL-RAISING / LEVEL-RETAINING FEATURE:  / 
 MODE FEATURE, with the following values: declaration, exclamation, interrogation (. / ! / ?)
 MODAL CONTENT (e.g. assumption, consequence, negation, belief (of rank n), dream, information acquired by seeing / hearing / ..., elaboration, disjunction, alternation, result, etc.)
1.2.4.2 The other three components of level labels
The second element of a level label is a moment  (Tm): the MOMENT of
the level label.
The third element of a level label is an element of U[i] which – if it is
anchored out in the external universe – it is anchored to an entity who is an
interpreter (including interpreter i herself): this interpreter is called the DIRECT HOST of the anchored-out referent.
The fourth element of a level label is an element of set {+, 0, -}: the
POLARITY of the level label (positive / neutral / negative).
1.2.4.3 The interpreter’s worldlets
The system of level labels is defined so that, from each referent r, it is possible to get to the root referent i*, the referent anchored to i herself, by applying function  finite times, and exactly in a single possible way:
i* = (1,1,i1,1, ...(k-1,k-1,ik-1,k-1, (k,k,ik,k, r)), ... ).
Let  denote the series of labels in the formula above. It is called the
WORLDLET INDEX of referent r. The sum of referents of worldlet index  is
called interpreter i’s WORLDLET of index . We also define the LEVEL of the
worldlet, which is a positive integer: the number of level-raising () modal
labels in the index of the worldlet. We regard the empty series  as the INDEX of root referents; and we call the sum of referents of index  interpreter i’s ROOT WORLDLET.
10
Definition I: the world model of eALIS
1.2.5 The cursor (What is the interpreter concentrating on?)
The labels occurring in the argument position of the cursor (function)
[i,t] :   U[i] form a finite set ={Now, Here, Me, Then, There, You,
Eve,...}, the set of CURSOR LABELS (which is freely extendable depending
on our linguistic aims), with the following fixed elements:
 [i,t](Now) = t, which is anchored-out to t: the NOW
 [i,t](Here) = s, which is anchored-out to a spatial entity: the
HERE





[i,t](Ego) = i, which is anchored-out to interpreter i: the EGO
[i,t](Then) = t’,: the THEN (REFERENCE TIME)
[i,t](There) = s’,: the THERE (REFERENCE SPACE)
[i,t](You) = j,: the YOU
[i,t](Eve) = e,: the REFERENCE EVENTUALITY
Definition II:
the interpretation in
eALIS
We are defining STATIC and DYNAMIC DISCOURSE INTERPRETATION in
a eALIS world model.
We base this definition on the world model  = U, W0, W as it was
defined in Definition I, retaining all notations.
Subsection 2.1 is devoted to the preparation of the definitions directly concerning interpretation. Then in 2.2 dynamic interpretation is defined
(and a few supplementary concepts), and in 2.3 we provide the definition
system of static interpretation.
Definition II. interpretation in eALIS
2.1
12
Some supplementary concepts to the interpretation concept of eALIS
The following infon of the external world is required to be in the information structure of the given world model, that is, :
 =  PERCEIVE, t, i, j, d, s,
where i and j are interpreters (i, j  I), t is a moment (tTm), s is a spatial
entity (sS), d is a discourse (entity) (dDis), and PERCEIVE is a distinguished core relation, that is, an element of  (1.1.6). We are defining the
interpretation of this discourse d, relative to the external world W0 and the
momentary internal world W[i,t].
2.1.1 Putting a new referent to use
First of all, we need the concept of a new referent. We call a referent r of an
information state W[i,] a NEW REFERENT (at moment ) if it is an argument
or value of neither function [i,’], nor [i,’], nor [i,’], where W[i,’] is
the preceding information state. If the above mentioned new referent r becomes an argument or a value of one of the internal functions [i,], [i,t],
[i,] in information state W[i,], we say that the referent has been PUT TO
USE.
2.1.2 The external grammar of the discourse
Remember that we are defining the interpretation of a discourse d appearing in an infon =PERCEIVE, t, i, j, d, s relative to the external world W0
and the internal world W[i,t]; this subsection is devoted to the preparation
of this definition system. Remember, further, that we have defined in the
external world the relational structure D = D,  of phonetic forms, where
 denotes the set of phonetic-form relations, and that there is a segmentation  = d1, d2,..., dN belonging to d, which makes a list of its morphs in
the chronology of their performance (1.1.5).
We define, in this point, a relational structure D = D, , to be
called the EXTERNAL GRAMMAR of discourse d, which, relative to the total
relational structure D = D,  of phonetic forms, can be constructed by the
following method based on “restrictions”:
2.1.2.1 The set D of entities related to discourse d
In addition to discourse entity d and the morphs appearing in its segmentation, the basic set D is defined so that it is to contain elements of D, and
only such elements of D, that stands in some -relation with d, or with the
13
Definition II. interpretation in eALIS
phonetic forms related to d, or with these latter entities, etc. (the basic set
D, thus, can be constructed by a recursive method).
2.1.2.2 The relations related to discourse d
Now let us consider the relations which are elements of the set  and delete
from them all the n-tuples containing (one or more) elements that are not
contained by D; in this way we obtain a set ’ of relations.
2.1.2.3 The external grammar of discourse d embedded in the external world
The set  of relations itself is defined as the following Cartesian product:
 = {t}’.
This last technical step is useful because in this way the phoneticform relations which play some role in the given interpretation (  )
can be construed as core relations and decomposed into infons.
2.1.3 Extending (monotonously increasing) information states in the
course of dynamic interpretation
We need to define, relative to an arbitrary information state W[i,], the concept of a POTENTIAL EXTENDED information state. An arbitrary information
state W[i,’], ’>, can be considered a potential extended information state
which belongs to an arbitrary eALIS world model ’ if
 ’ ~  (the two world models COINCIDES UNTIL moment ,
that is, their external worlds are the same, and the internal
worlds belonging to each moment ”, ”, are the same for
each interpreters
 and [i,’]  [i,], [i,’]  [i,], [i,’]  [i,] in world
model ’.
All types of dynamic interpretation taking place in an information
state W[i,] will be defined as a mapping that assigns W[i,] a potential extended information state (with restrictions depending on the above mentioned
types).
2.1.4 Perceiving an infon: the impact of the external world upon the interpreter’s information state
In this subsection the concept of infon perception is defined. We can also
decide here the basic step of static and dynamic interpretation.
Suppose interpreter i, in an arbitrary information state W[i,], gets in
touch with the infon 1 specified in i. below (ii. provides an equivalent formulation) :
i.
1 =  P1, T1, U1,1, U1,2, ..., U1,K, where T1
ii.
Definition II. interpretation in eALIS
0(1,1)= (P1)
0(2,1)=T1
0(3,1)= U1,1
...
0(K+2,1)= U1,K
14
2.1.4.1 Internal mappings of the infon perceived
PERCEIVING infon 1 is defined as an elementary dynamic interpretation in the course of which information state W[i,] is mapped to the potential extended information state W* specified in iii.-vii. below.1
iii.
*  [i,]
*(Pred,1,e1)= p1,
*(Temp,InCum,e1)=t1,
*(Arg,Case1,e1)= r1,1,
...
*(Arg,CaseK,e1)= r1,K
iv. *  [i,], and instead of modal label .SEE, other sorts of perception can also be applied, depending on the factual way of infon perception
(remember i* is the root referent anchored-out to i):
*(.SEE,,i,+,e1) = i*
*(.SEE,,i,+,p1) = i*
*(.SEE,,i,+,t1) = i*
*(.SEE,,i,+,r1,1) = i*
...
*(.SEE,,i,+,r1,K) = i*
v.
1
*  [i,]
*(Ant,,e1)=e1* (by putting a root referent e1* into use)
*(Ant,,p1)=p1* (root referent p1* is typically not new,
but it is not excluded that it is a new referent)
*(Ant,,t1)=t* (t* is the root referent anchored or to be
anchored to )
*(Ant,,r1,1)=r1,1*
In the course of deciding the extension of the four partial internal functions (now as
well as in what follows) we provide the values defined at the new arguments, and the
definition should be understood in the way that there is no extension elsewhere (i.e., at
potential argument places that have not been mentioned explicitly).
Definition II. interpretation in eALIS
... (referents r1,k* are either already in the root worldlet, in
which case the novelty lies in the connection carried
out by *, or they are to be put into use in this step)
*(Ant,,r1,K)=r1,K*
15
*  [i,]
*(Out,,e1*)=1 (the eventuality referent is to be anchored out in this step)
*(Out,,p1*)=P1 (if p1* is not new, it has already been
anchored out to the core relation mentioned)
*(Out,,t*)= (remember: T1)
*(Out,,r1,1*)=U1,1,
... (if a referent r1,k* is not new, it has already been anchored out to the entity mentioned)
*(Out,,r1,K*)=U1,K.
vi.
vii.
*  [i,]
*(Pred,1,e1*)= p1*
*(Temp,InCum, e1*)=t1*
*(Arg,Case1, e1*)= r1,1*
...
*(Arg,CaseK, e1*)= r1,K*
vii’. the simplified eventuality-centered representation:
e1* : p1* t1* r1,1* ... r1,K*
vii”. the predicate-centered representation: p1*(,r1,1*, ..., r1,K*)
viii. values of *, where it is interpreted:
*(Now) = t* (which is anchored out to )
*(Here) = S* (which is anchored out to a spatial entity,
where i can be found)
*(Ego) = i* (which is anchored out to i)
*(Then) = t*
*(There) = s1* (some root referent anchored out to the
perception place of infon 1).
*(Eve) = e1*
It is specified in iii. above how the “acting” of the infon-structural
function is copied by the eventuality function in the interpreter’s internal
world, making -connections among new referents e1, p1, t1, r1,1, r1,2,..., r1,K
(where K may be 0, too), under the given eventual parameters (which depend on the predicate).
16
Definition II. interpretation in eALIS
According to iv. above, the level function is extended so that the new
referents are located on the first level (and not the root level) of the internal
world, with a modal label depending on the way of infon perception (deciding their position relative to referent i, which is necessarily a root referent).
If more organs of sense inform of the infon, counterparts of the infon copy
specified in iii. above will appear in more fictive worldlets, putting further
referents into use. Identification of these referents, i.e., those corresponding
to each other, is specified in v. above.
What is specified in this point (iv.) is that referents e1, p1, t1, r1,1,
r1,2,..., r1,K are anchored to root referents. If the interpreter recognizes the
core relation or one or more external entities, then this fact means that the
root referents in question are not new and, hence, have been anchored out
to the core relation / corresponding external entities; but this situation already makes us turn to point vi. above. In the case of new root referents, the
anchoring-out takes place in the course of the infon perception. In both
ways, the final result specified in vi. concerning the extension of the anchoring function will come about.
In vii. we demonstrate the final steps of constructing the eventual
function *, which also build the eventuality structure for e1*. Points vii’
and vii” are devoted to equivalent representations of e1*, which are worth
comparing to the infon demonstrated in i. in order to observe the (almost)
isomorphic relation of an infon to the eventuality coming from its perception.
Finally, viii. shows the set of the cursor values coming about in the
new information state. We mention the value of reference eventuality: the
cursor points to the root referent e1* corresponding to the infon.
2.1.4.2 Infon perception as an elementary dynamic interpretation and as
the verification of a static step of interpretation
We regard the infon perception, defined above, as a sort of DYNAMIC INTERPRETATION: called ELEMENTARY dynamic interpretation; whose important
outcome is the appearance, in the resulting potential extended information
state W*, of a root referent e1*, which has been anchored out to just the perceived infon. We say (under the conditions specified above) that infon 1
(and each group of infons containg this infon in the given world model), under anchoring *, VERIFIES eventuality e1*, on the basis of which we can also say that e1* is TRUE; which is the STATIC INTERPRETTION of e1*.
2.1.4.3 A referent and several “twins”
In a given information state, for an arbitrary referent r, we can construct
ANCHORING SERIES r, (’,r), (”,(’,r)), ...) (which are necessarily
17
Definition II. interpretation in eALIS
finite due to the structure of information states). The last member in an anchoring series which still belongs to the internal world is called the PRIMARY COPY of r. If there is a further member belonging to the external
world, it is called the EXTERNAL COPY of referent r. If a primary copy is a
root referent, it can also be referred to as the ROOT COPY of r!2
2.1.4.4 The internal universe cut into identity classes and the representatives
The ANCHORING / IDENTITY CLASS of an interpretert i’s arbitrary referent r is
the subset [r] of the internal universe U[i] which contains, in addition to r
itself, its primary copy r*, and all members of all anchoring series from referent r to r*, and all further anchoring series leading to r*, but nothing else.
The identity classes in information state W[i,t] generate a partition
over universe U[i], which we call the IDENTITY PARTITION of the universe at
moment t.
The following stipulation pertains to eALIS world models: an identity class contains exactly one primary copy; which is called the PRIMARY
REPRESENTATIVE of the identity class in question.
If referents that can be found in the same identity class are anchored
out to exactly one external entity, then this entity is called the EXTERNAL
REPRESENTATIVE of the identity class as well as of its each referent.
We say that an identity class LACKS AN EXTERNAL REPRESENTATIVE if
no referent belonging to it is anchored out.
If a referent r has an entity u as its external representative, we can also say that referent r is an INTERNAL REPRESENTATIVE of entity u.
2.1.4.5 The partial perception of the Evening Star and the false perception of twins
If an entity u is such that its internal representatives in an information state
W[i,t] form a single identity class, this situation is called the TRUE PERCEPTION of entity u. If an entity u’s internal representatives belong to more
identity classes, this situation is called the PARTIAL PERCEPTION of entity u.
If two different entities u’ and u” have internal representatives belonging to
the same identity class, this situation is called an instance of FALSE PERCEPTION
2
In v. above, the referent p1* which has been assigned to predicate (referent) p1 by
anchoring, and the referents denoted by r1,i*, which „anchor” argument referents ri,1 in a
similar way, hence, are primary copies, as well as root copies, of the referents anchored to
them.
18
Definition II. interpretation in eALIS
2.1.4.6 Reduced eventuality representations
If we replace the referents in any of the representation types of eventualities demonstrated in 1.2.2.5 with their primary representatives, we obtain a
(SYSTEMATICALLY) REDUCED eventuality representation. If referents are
replaced with arbitrary members of their identity classes, what we obtain
can be called an ARBITRARILY REDUCED version of the input eventuality
representation.
Definition II. interpretation in eALIS
2.2
19
The dynamic interpretation as it is defined in eALIS
Consider the external grammar D = D, , specified in subsection 2.1.2,
in which the phonetic-form relations taking part in the given process of interpretation (  ) can be construed as core relations and can also be
decomposed into infons. Remember our unvarying aim is to define the interpretation of the discourse d appearing in infon =PERCEIVE, t, i, j, d, s
(whose segmentation is  = d1, d2,..., dN), relative to the external world
W0 and the internal world W[i,t].
The first step of interpretation requires that interpreter i perceive (in
the sense specified in 2.1.4) the phonetic-form relational infons relevant to
her mother-tongue grammar (which she bears as an acquired competence),
getting, in this way, to a potential extended information state W*. Remember: perception is nothing else but eventual referents’ (and their dependents’) building into the information state. In the eALIS approach the
system of requirements coming from grammatical relations are also considered to be a part of information state (hence, word orders, categories, cases, agreements should be checked in a certain period of interpretation), so
grammatical relations are registered by representations based on eventual
referents and their dependents. Referents like this should be brought into a
“verificational” connection with eventual referents coming from perceived
infons.
We define three kinds of their combinations on the basis of the following distinguished predicates:  (conjunction),  (disjunction),  (conditional). These predicate referents are assumed to be represented by nonanchored-out root referents.
2.2.1 Constructing indirect perceptions from (indirect) perceptions
2.2.1.1 The conjunction of perceptions (and indirect perceptions)
Suppose that in the information state W* (under the anchoring function *)
the infon group  verifies the eventualities e’ and e” specified in i. below.
Then it can be claimed about the eventuality e1 which has been constructed
by putting the new referents also mentioned in i. into use and forming the
given **- and **-connections among them that in the new information
state W**, under anchoring **, the infon group  VERIFIES it (e1), so its
static semantic value is TRUE. We can also say that we INDIRECTLY PERCEIVE the information content carried by e1 on the basis of the infon group
.
i.
New referents: e1, p1, t1, r1,1, r1,2
Definition II. interpretation in eALIS
**(Pred,Logical,e1)= p1, where **(Ant,,p1) = 
**(Temp,InCum,e1)=t1, where **(Ant,,t1) = t*
(t* is the root referent anchored out or to be anchored out to t)
**(Arg,Left,e1)= r1,1, where **(Ant,,r1,1) = e’, where
e’ is an eventual root referent
**(Arg,Right,e1)= r1,2, where **(Ant,,r1,2) = e”, where
e” is an eventual root referent
**(Eve) = e1
20
2.2.1.2 The disjunction of perceptions (and indirect perceptions)
Suppose, in a similar way, that in the information state W* (under the anchoring function *) the infon group  verifies at least one of the eventualities e’ and e” specified in ii. below. Then it can be claimed about the
eventuality e1 which has been constructed by putting the new referents also
mentioned in ii. into use and forming the given **- and **-connections
among them that in the new information state W**, under anchoring **,
the infon group  VERIFIES it (e1), so its static semantic value is TRUE. We
can also say that we INDIRECTLY PERCEIVE the information content carried
by e1 on the basis of the infon group .
ii.
New referents: e1, p1, t1, r1,1, r1,2
**(Pred,Logical,e1)= p1, where **(Ant,,p1) = 
**(Temp,InCum,e1)=t1, where **(Ant,,t1) = t*
(t* is the root referent anchored out or to be anchored out to t)
**(Arg,Left,e1)= r1,1, where **(Ant,,r1,1) = e’, where
e’ is an eventual root referent
**(Arg,Right,e1)= r1,2, where **(Ant,,r1,2) = e”, where
e” is an eventual root referent
**(Eve) = e1
2.2.1.3 Indirect perception due to Modus Ponens
We would like to start by confessing that the definition concerning conditional is much more complicated. Now our starting-point is that the information state W* contains the rule-describing eventuality specified in iii.
below (which expresses a general inference). As this eventuality is a root
referent, its static semantic value (by definition) is TRUE. We should also
suppose that the anchoring function * has an extension + that would map
the closure [e’] of the eventuality e’ also specified in iii. below to a root
referent e+ whose being true is verified by the infon group .
iii.
Definition II. interpretation in eALIS
*(Pred,Logical,e1)= p1, where *(Ant,,p1) = 
*(Temp,InCum,e1)=t1, where *(Ant,,t1) = t*
(t* is the root referent anchored out or to be anchored out to t)
*(Arg,Left,e1)= e’, where *(.SUPP,t,i,+,e’) = e1, where
e1 is an eventual root referent
*(Arg,Right,e1)= e”, where *(.CONS,t,i,+,e”) = e’
21
Under these conditions we say that an appropriately constructed **copy of the closure [e”] of eventuality e” – let it be denoted by e” – is TRUE
in an appropriately constructed information state W**: the infon group 
VERIFIES it (e”) under the given anchoring **; or we can also say that we
INDIRECTLY PERCEIVE it on the basis of  due to the information expressed
by the above mentioned rule-describing eventuality; see 2.2.1.4-2.2.1.5 below. The value of **(Eve) – a root referent – will be nothing else but the
copy e” (which belongs to e”).
2.2.1.4 Closure according to the anchoring and the level function
Our first task is to define the CLOSURE [e’], or more precisely, the closure
according to an eventual function * and an anchoring *. This means a
sub-relational-structure, to be defined recursively, of relational structure
U*, {*,*,*}: a relational structure U’, {’,’,’}, where each
“primed” set is a subset of the corresponding “starred” set. In the basis of
the recursive definition of set U’ we can found referent e’ itself. Set U’ also
contains each referent mapped to e’ by * or * (in the case of some label).
Then we should set in U’ all *-images and *-images of these latter referents; and so on... The external entities resulting in this way, however,
should be deleted from the final version of U’. The functions ’ and ’ will
also result from the algorythm constructing U’: together with a new referent whose introduction has been legitimized by * or *, the developing
functions (hence, sets) ’ and ’ should also be enriched with the legitimizing *- or *-connection. Finally, ’ results from the following method:
we set in this relational set to be constructed the (total) *-connections existing between elements of U’ (and nothing else).
Végül a ’ úgy adódik, hogy az U’ elemei között meglévő (teljes) *kapcsolatokat vesszük be a felépítendő ’ relációs halmazba. A eALISmodell olyan kell, hogy legyen, hogy az eljárás egyértelmű eredményt ad.
We stipulate that a well-formed eALIS model is such that the procedure discussed above yields an unambiguous result.
For referent e”, the same procedure is to be applied in order to produce its closure [e”] according to * and *.
22
Definition II. interpretation in eALIS
2.2.1.5 Copying of a referent set structured by internal functions
We decide now how it is possible, relative to the potential anchoring function +, to construct the anchoring ** (as an extension of *) and the required copy of [e”]. Note that ** will not be an extension of +, although
** and + are both extensions of *; nevertheless, ** is to be constructed on the basis of +. Let us consider the method!
The definition of COPYING is that we should put into use the same
number of new referents as many elements the closure [e”] has; by means
of an arbitrary bijective “copying function” , the elements of [e”] should
be mapped onto the new referents; then all internal-function relations
among elements of [e”] should be constructed among the set ([e”]) of new
referents in a relation- and label-PRESERVING way regarding all internal
functions *, * and *, applying, as a starting-point of the method, the
root referent e”, recently put into use, which corresponds to the eventual
referent e”3:
if * : ,x  y, then ** : ,(x)  (y)
if * : ,x  y, then ** : ,(x)  (y)
if * : ,x  y, then ** : ,(x)  (y)
The connection system among the referents in the copy set ([e”])
should also be completed with a few anchoring connections: copies (”)
of certain elements ” in the closure [e”] should be anchored. Such referents ” are concerned which + (and practically already * itself) maps to
an element ’ of [e’] where ’ has a * primary copy (according to +) outside the referent set [e’]. Well, the copy in question should be anchored to
this *: **(Ant,,(”)):=*.
By completely executing all these operations (i.e., what has been
written above should be applied to each possible ”), we will obtain the
internal world W** structured by the appropriate internal functions, in
which the reference eventuality e” will be qualified as TRUE (VERIFIED by
infon group  under the given anchoring **).
Referent e” will be a root referent because the world model of eALIS is such that
function * assigns no value to the original e”, and hence ** will not take the copy as
its argument either.
3
23
Definition II. interpretation in eALIS
2.2.2 The interpreter perceives morphs, words and sentences (indirectly), and the external grammar among them, and then the implied
internal grammar
As a crucial part of the phylosophy behind eALIS, we have the following
substantial and restrictive hypothesis concerning Universal Grammar: the
above discussed three distinguished predicates (, , ), constructing relations among eventualities, and the eventualities relying on them which can
be verified on the basis of  (registering the external connection system of
phonetic forms in discourse d) are sufficient for what is discussed below in
the following paragraphs. What is at our disposal is essentially the capacity
of a standard, classical Prolog language – to provide a data-base-like description of the properties of phonetic forms of morphs as well as their
word order and intonation in given discourses, and to frame, in the form of
inference rules, “environmental requirements” of these morphs, that is,
with which other morphs they “intend” to enter into some anchoring relations:
The interpreter (indirectly) perceives the morphs of discourse d (i.e.,
she can identify them with ones that occurred earlier), and by this way she
(indirectly) perceives their segmentation  = d1, d2,..., dN on the basis of
their external phonetic properties (registered by ), be means of the internal rule-describing eventualities, demonstrated in 2.2.1.3.
The interpreter (indirectly) perceives such important relations that
certain morphs can be found “in the same word” or “in the same sentence”,
chiefly on the basis of intonational characteristics, too (!), relying on the
morphotactic and syntactic connections typical of the given language. The
human competence concerning the knowledge of a language is assumed to
be carried chiefly by the rule-describing eventuality type, shown in
(2.2.1.3.iii) above. The sentence is a relevant component of the discourse
because essentially sentences can undergo static interpretation (or more
precisely, the eventualities constructed via the indirect perception of sentences). The STATIC EVALUATION OF A DISCOURSE is defined as the sequence
of evaluations of their sentences.
The interpreter (indirectly) perceives the anchoring connections
among morphs. Due to this perception, she can create relations among certain lexical items (to be discussed in the following subsection) becoming
able and entitled to merge their semantic content (represented by DRS-like
constructions, which can undergo the operation of unification). Our hypothesis behind this approach is that lexical items standing in some grammatical relation co-predicate: they predicate something (different things, of
course) of the same referent.
24
Definition II. interpretation in eALIS
2.2.3 The interpreter’s grammatical knowledge
Returning to an intermediate information state W* of the process of interpretation of discourse d, interpreter i’s GRAMMATICAL KNOWLEDGE (at a
given moment t) is assumed to be carried by a sub-relational-structure
Ugr = Ugr, {gr, gr, gr} of the relational structure U*, {*,*,*}. This
special relational structure contains, on the one hand, rule-describing eventualities (belonging to the root worldlet), whose structure is like that of e 1
in 2.2.1.3.iii, and whose content is such that they can support the indirect
grammatical perceptions, discussed in 2.2.2. On the other hand, it contains
lexical items. Now we define them.
2.2.3.1 The lexical item
The LEXICAL ITEM of a predicate (referent) p is a pair Lex(p)=Up,p where
Up = Up, {p, p, p} is a sub-relational-structure of the relational structure Ugr = Ugr, {gr, gr, gr}; which practically means that predicate p is
characterized via a few eventualities containing it, including the phonetic
characterization of the phonetic form belonging to it (this latter task, too, is
essentially to be done by the often mentioned rule-describing eventualities:
e.g. „if this and this hold of a certain morph, then it must be the word honey”). Symbol ’p’ pertains to elements of the domain of the cursor function
which have not been defined so far, which appear in temporary information
states. An information state is TEMPORARY, by definition, just because in
this information state cursor  is defined at the argument places to be decided below. Consequently, the temporary character finishes when the concerned argument–value pairs have been deleted from the function relation
expressed by the cursor, as from some store, as a result of the successful
execution of certain operations.
2.2.3.2 Finding the lexical copy
First of all, the process of LEXICAL RETRIEVAL should be discussed; which
can be captured as a transition from an information state to a temporary
information state. Its first step is that the interpreter recognizes, in an (indirectly) perceived morph, its LEXICAL COPY (see i. below): this connection is
to be marked as an instance of -anchoring (with a label Lex, which refers
to “lexical anchoring”). If the interpreter hears (or assumes to hear) a
morph for the first time, special lexical-item constructing operations initiate
(we do not enter into its details, but note that they can be defined in
eALIS).
Note that the lexical copy necessarily differs from the primary or root
copy, because this latter one is typically an anchored-out referent (as a default, the interpreter’s first perception of a kind of achievement, accom-
25
Definition II. interpretation in eALIS
plishment, activity or state), whilst the lexical copy is a fictive predicate
referent, to be used by her to link all grammatical properties of the given
predicate to this copy (note here that the whole amount of information associated with arbitrary members of the identity class represented by the
root copy is potentially available in the course of the development of the
lexical item).
As is illustrated in ii. below by a simplified predicate-centered representation, the lexical item contains the connection between a morph q and
the predicate p expressing the meaning carried by the morph. The parameters are intended to suggest our approach that we regard, as variants of the
same predicate, aspectual alterations (), event-type versions (), argumentstructure versions ().
Then the interpreter introduces a new referent (p*) and links it to the
lexical copy p (iii.). It is worth noting that in the course of direct infon perception (2.1.4) she carries out just the opposite of this step (see the third
row of v. below): she perceives an event (action / state) in the world and
anchors the predicate referent expressing it to a lexical copy if she recognizes in the eventuality the recurrence of an event / state / action she had
already perceived.
i.
*(Ant,Lex,q*)=q
ii.
phonf(q, p, , , 1, ..., K)
iii.
*(Ant,Lex,p*)=p
2.2.3.3 Grammatical description in the lexical item: the cursor as a
“parsing motor”
Thus the lexical retrieval has taken place, and the interpreter has attained
the lexical item p. It necessarily contains a fictive eventuality to which p
belongs as a predicate referent. Its general form is illustrated below in iv.,
which is completed with alternative notations for the sake of understanding; see v.-vii. The bold referents all belong to a fictive worldlet (providing
a sample of grammatical description), in which the interpreter can store and -connections as well.4
iv.
*(Pred, , ) = p
The meaning of mosakodik ’wash oneself’ (in Hungarian), for instance, can appear in
the lexical item belonging to mos ’wash’, with the object referent -anchored to the
subject referent. The description of keres ’look for’ illustrates the case where the object
referent is linked to the corresponding subject or eventuality referent by a -connection
of label .BELn (de dicto reading). The default case is where each argument referent
belongs to the same worldlet as the eventuality referent (see viii.).
4
Definition II. interpretation in eALIS
*(Temp, , ep) =
*(Arg, 1, ep)=
...
*(Arg, K, ep)= rKp
v.
eventuality-centered representation:
ep:: Pred,: p, Temp,: tp, Arg,1: r1p,..., Arg,K: rKp
vi.
simplified eventuality-centered representation:
ep: p tp r1p ... rKp
vii.
predicate-centered representation: p(r1p, ..., rKp)
26
Besides introducing the new predicate referent p*, the interpreter
should put further referents into use, which are to play the “roles” of ep, tp
and rkp below, requiring an appropriate relation-preserving copying 
(2.2.1.5).
viii. *(Antec,, r2p) = r1p
*(.BELn,i,,+, rkp)= ep
*( , rkp)= ep
ix.
*(Pred, , e*) = p*
*(Temp, , e*) = t*
*(Arg, 1, e*)= r1*
...
*(Arg, K, e*)= rK*
x.
eventuality-centered representation:
e*:: Pred,: p*, Temp,: t*, Arg,1: r1*,..., Arg,K: rK*
Within the lexical item Lex(p)=Up,p, the grammatical information
peculiar to the given language is located in the sector of the domain of the
cursor function  whose being interpreted makes the information state temporary. The lexical item specifies (in its part related to ) that, if one of its
copies gets in a sentence, there the referent copies belonging to it (and possible further referents whose appearance is due to accommodation) are to
enter into (primarily anchoring) connections. This kind of operation of the
cursor is illustrated in xi. below. The concerned referent (copy) will serve
as a cursor value, and it is registered at the cursor argument into which
connection the given argument referent is allowed to enter (LEXICAL ENVIRONMENTAL DESCRIPTION). Although the cursor is “formally” a oneargument function in eALIS, the argument place accepts a quite intricate
label structure, namely an ordered quintuple.
xi.
27
Definition II. interpretation in eALIS
p
p
 (133, ↑, , Arg, Ord,-7,Nei, Cat,+2,N, Case,+2,) = ri
p(134, ↓, , Pred, Cat,0,V+rA, Agr,0,3Sg) = rip
p’(755, ↓, , Arg, Cat,0,Prop, Case,0,) = rip
p’(756, ↑, , Pred, Cat,+2,X, Agr,+2,3Sg) = rip
p”(1214, ↑, ,  ) = ep
The first element of a lexical environmental description is a natural
number: its SERIAL NUMBER. Its second element provides the nature of the
description, which has five variants: DEMAND (↑) / OFFER (↓) / OPTIONAL
DEMAND (┴) / OPTIONAL OFFER (┬), PRESUPPOSITION (╩). Its third element
specifies which internal function plays some role in bringing certain referents into connections; thus the options here are:  /  / . The fourth and
fifth factor of the lexical environmental description depend on the third factor, of course. In the case of anchoring, for instance, the fourth position
accepts anchoring types, and then comes in the fifth position a series of ordered triplets whose each member (a triplet) starts with reference to a cable/dimension, followed by a rank parameter, which is followed by the
specification of the grammatical features / relations “streaming” through
the given cable. If the third member of the lexical environmental description is , a level label is permitted to appear in the fourth position. If no
level label is specified, an arbitrary -connection can be developed, but
some kind of -connection must be created. If  is the third element of the
lexical environmental description, the fourth element should be an eventstructural main parameter, followed by a compatible subparameter in the
fifth position (a quadruple like this plays some role in capturing the phenomenon of bridging in the course if interpretation).
Illustration xii. shows (the structure of) a simplified and reduced lexical environmental description of a Hungarian word (hasonlít ‘resemble’):
xii.
hasonlít(r’↑:: Arg: Ord,-7,Nei, Cat,+2,N, Case,+2,,
↓:: Pred: Cat,+2,V+SUBL, Agr,0,3Sg,
r” ↑:: Arg: Ord,+7,Nei, Cat,+2,N, Case,+2,SUBL
↓:: Pred: Cat,+2, V+SUBL, Agr,0,3)
2.2.3.4 Mediating demands and offers by the cursor
The discussed cursor settings makes the information state temporary because they express well-formedness requirements to be satisfied. A demand
(or presuppostion) registered at serial number n’ should be associated with
an offer of a serial number n”. If there is a sufficient amount of compatibility (which will be discussed in the following subsection), the connection in
question should be formed and the discussed cursor settings of serial num-
28
Definition II. interpretation in eALIS
bers n’ and n” can be deleted. The interpreter gets out of her temporary information state when she has deleted all her cursor settings of some serial
number. Optional demands and offers, obviously, can be deleted freely,
without any satisfying matching unless they have been exploited. Their importance lies in the fact that they can satisfy an obligatory offer or demand.
Beyond the elegant handling of optional arguments, they are also suitable
for capturing bridging phenomena: in a case like this such predicates appear in the process of interpretation which correspond to no phonetic forms
in the segmentation  of discourse d.
2.2.3.5 The cost of interpretation, and the principle of Maximizing Discourse Coherence
A consumed optional offer, obviously, is deleted via satisfying an offer. Its
certain types, however, mean some cost to the interpretation, involving
some uncertainty. The more bridgings have been applied, for instance, the
more dubious it is whether the speaker had intended to associate the series
of sounds of the performed discourse with the resulting interpretation. It
seems to be worth, however, taking the anchoring of an optional argument
to be “cheap” or just free, depending on our linguistic aims.
Presuppositions that have not been satisfied also differ from demands, at least to a certain extent. It is a hot linguistic problem to describe
systematically which presuppositions are easy to accommodate (these ones
should be assigned a low cost) and which are not. The accommodated presupposition can already be deleted, so it can be removed from the domain
of the cursor .
To recapitulate, the sum of optional demands consumed and presuppositions accommodated is to be defined as the COST of the given interpretation, which is nothing else but a collection of -, - and -connections
among referents; that is, a sub-rls; that is, a sub-relational-structure U° =
U°, {°, °, °} of the relational structure U*, {*,*,*}. It is then a
linguistic task to express this cost by numbers or having recourse to some
partial order, on the basis of which the cheapest dynamic interpretation will
coincide with the reading speakers consider to be the best, including the
association of discourses judged to be ambiguous with more equivalent interpretations (of an equal and low cost).
By this approach the principle (type) of Maximize Discourse Coherence could be built into the eALIS theory.
2.2.3.6 Available referents
Let us return to a problem (primarily) concerning presuppositions: Where
should the information required to satisfy demands be looked for? So far
29
Definition II. interpretation in eALIS
we have discussed only that kind of filling up the temporary zone of the
cursor which pertains to pieces of information coming from the sentence or
discourse just being interpreted, whilst certain linguistic elements make it
obligatory or at least strongly prefer that they be linked to information
coming from earlier sentences or discourses, or the context. We would like
to integrate in the eALIS interpretation, for instance, the thesis of SDRT
according to which each sentence has a “main eventuality”, which requires
some connection with an eventuality not coming from its own sentence (see
the last row of xi.).
What is required, thus, is having recourse to steps of accommodation
in the course of which certain referents of the sub-relational-structure
Ur, {r,r,r} of relational structure U*, {*,*,*}, the sum of referents available from r, get in the temporary zone of the cursor. Such availability laws as the principle of “right boundaries”, applied in SDRT, or the
DRT rule “to the left or upward” can be reformulated in eALIS relying
on the system of -connections of information state W*. To referent r in
the worldlet whose index is specified in xiii. below, the AVAILABLE referents are those belonging to the worldlets given in xiv., which can be approached trough elementary -connections. To certain anaphoric elements
(e.g. pronouns), less worldlets are available: this STRONG AVAILABILITY is
valid, out of the available worldlets, for the own worldlet and for the
worldlets following a worldlet with a level-raising level label (see xv. below); this rule corresponds to the above mentioned principle of “right
boundaries”).
xiii. 1,1,i1,1, 2,2,i2,3, 3,3,i3,3, 4,4,i4,4, 5,5,i5,5,
6,6,i6,6, 7,7,i7,7, 8,8,i8,8,..., M,M,iM,M
xiv. 1,1,i1,1, ,..., M,M,iM,M
2,2,i2,2, ,..., M,M,iM,M
3,3,i3,3, ,..., M,M,iM,M
...
M,M,iM,M
 (the root worldlet)
xv.
1,1,i1,1,2,2,i2,3,3,3,i3,3,4,4,i4,4,5,5,i5,5,
6,6,i6,6,7,7,i7,7,8,8,i8,8,9,9,i9,9,10,10,i10,10,...
2.2.4 Grammatical compatibility
Instances of the kind of compatibility mentioned in 2.2.3.4 can be verified
indirectly by means of rule-describing eventualities.
30
Definition II. interpretation in eALIS
A real rank parameter occurs only in the three sorts of demands concerning anchoring (demand, optional demand, presupposition). In formulas
expressing anchoring offers, the rank parameter is ‘0’ (and its appearance is
due to exclusively technical reasons).
Now let us recall the structure of the cursor setting typical of anchoring demands. The relevant fifth argument place is occupied by a series of
triplets whose each member  starts with an anchoring type’s (see 1.2.3:
ANCH={Arg, Pred, Adj, Ana, Out,...}) cable (an element of Arg / Pred /...,
followed by a rank parameter, and then the specification of the grammatical features streaming through the cable. We recall an earlier example (xi.)
renumbered as i. below; the underlined triplets specify anchoring demands:
i.
p(133, ↑, , Arg, Ord,-7,Nei, Cat,+2,N, Case,+2,) = rip
p(134, ↓, , Pred, Cat,0,V,SUBL, Agr,0,3Sg) = rip
p’(755, ↓, , Arg, Cat,0,Prop, Case,0,) = rip
p’(756, ↑, , Pred, Cat,+2,X, Agr,+2,3Sg) = rip
2.2.4.1 Direct satisfaction, on the basis of partial ordering of feature
specifications
Suppose feature specifications form partially ordered relational structures:
e.g. Cat = Cat, , Agr = Agr, , Case = Case, ; which can be regarded, in the worst case, as trivial, depending on our linguistic aims (‘trivial’
means: each element in the partial ordering is both minimal and maximal).
Relying on these partial orderings, we can define the INDIRECT SATISFACTION of a demand ’ by an offer ” through a given cable simply as follows: ’” (that is, the specification of ’ is weaker than that of ”).5
2.2.4.2 Indirect satisfaction, on the basis of satisfaction by rank parameters
It is decided for each demand how it can be satisfied directly; in this
case, thus, the rank parameters attached to feature specifications remain
irrelevant. If, however, a demand ’ of rank parameter n’ cannot be satisfied directly by an offer ” through a cable, it is still possible that grammar
Ugr supplies a rule-describing eventuality (containing reference also to the
rank parameter) which declares that if a demand ’” of a stronger rank n’”
5
Demand 133, for instance, pertains to a noun as the category of the required element.
The proper noun in offer 755 can satisfy this demand. Relational structure Agr is taken
to be a structured set of agreement bundles where the „structure” means a subset
relation over the total set of agreement features relevant in the given language. The
Hungarian verb látlak ’I see you’, for instance, requires a ’second person’ feature ({2})
for its object argument, which can be satisfied by the more specific agreement-feature
bundle {Pl, 2}, contained by the lexical description of titeket ’you.Pl.Acc’.
31
Definition II. interpretation in eALIS
(n’”<n’ or n’”n’; both conditions can be applied, depending on our linguistic aims) is satisfied, then demand ↑,n’,’ by offer ↓,0,” is to be
considered INDIRECTLY SATISFIED due to (direct or indirect) satisfation of
demand ↑’”,n’”,’” by offer ↓’”,0,””.
2.2.4.3 The syntax of eALIS: generative but not phrase-structure generating
Working out rule descriptions concerning indirect satisfaction relying on
ranks (and distinguishing its language-specific elements from universal
ones) is an enormous linguistic task which forms an inherent part of the
eALIS theory. The syntax of eALIS is a generative grammar but not a
transformational one; what is more, this syntax builds no phrase structures
at all. The tasks completed by transformations and phrases (e.g. in decision
of word order) are executed by the ranked rules in eALIS, which is an
idea strongly related to the idea Optimality Theories rely on. eALIS syntax, nevertheless, is definitely generative: the sentence set of a natural language is identified with the set of constructions which can be built from
lexical items of the given language by means of combination rules concerning well-formedness. However, as this “combination” is controlled exclusively by lexical environmental descriptions (built in lexical items),
eALIS has a totally lexicalist (morpho-) syntax. It is also monostratal in
the sense that sentences are regarded as built directly from morphemes. The
(standard) two-level alternative is regarding sentences as built from words
(by means of a grammar), which are built from morphemes (by means of
another grammar). This does not mean, nevertheless, that word level is totally ignored in our monostratal grammar. In our lexical descriptions there
are two kinds of demands concerning the adjacency of two morphemes:
they are to be either adjacent morphemes within the same word, or located
in two adjacent words within the sentence.
2.2.5 The dynamic interpretation of the discourse: a monotonous information-state extension in the course of which come about the
eventuality representing the discourse in question
We have already almost finished providing the dynamic semantic interpretation of discourse d (at least its part to be specified “mathematically”, and
not “linguistically”). We argue that the definition is sufficiently general: for
an arbitrary information state, it can be given what other information state
comes about. Dynamic interpretation, thus, is a partial function Dyn which
assigns a discourse entity d, to be located in an arbitrary eALIS world
model  = U, W0, W, and an interpreter i’s arbitrary information state
W[i,t] a potential extended information state (i.e., ‘potential’: one coming
32
Definition II. interpretation in eALIS
about not necessarily in the same eALIS world model) at a cost U° (decided in 2.2.3.5); it is also worth emphasizing in the function-output the
cursor’ final reference eventuality value (e° below) because this referent is
the EVENTUALITY REPRESENTING the discourse d:
Dyn(d) : ,W[i,t]  W°, e°, U°
Function Dyn(d) is partial, that is, certain inputs are assigned no
output. In cases like this discourse d is ill-formed in the given context. Due
to the introduction of cost, ill-formedness is a gradual category: a high cost
refers to an “almost unacceptable” qualification (in the given context).
The fact that the output W° is an extension of the input W[i,t] by definition means that we assume the interpreter to have increased its
knowledge at all times (in a monotonous way). We consider this consequence favorable, at least from our linguistic point of view: it is not a question of linguistics how the interpreter utilizes the new information coming
from a discourse; whether she deletes, for instance, certain pieces of information incompatible with the new pieces (which is not a monotonous
method). The linguistic part of interpretation pertains to the fact that the
interpreter has learned what the speaker thinks, or rather, what the speaker
intends to convey, or what the speaker intends to make her believe... The
world model of eALIS, due to its worldlet system, is suitable for storing
(potentially contradicting) pieces of information coming from different
places and times. Consistency is required only within single worldlets.
Beyond linguistic aims, however, the interpretation model of
eALIS offers an excellent basis for capturing human processes of information management, in the course of which, for instance, the interpreter
“makes order” in certain sectors of her information state: she makes a comparison between pieces of information stored as others’ beliefs, and either
considers them incompatible and deletes certain parts, or considers them
corroborating each other and moving them in worldlet with modal labels
expressing an increased reliability of the pieces of information in question.
Definition II. interpretation in eALIS
2.3
33
Static interpretation
In this subsection we define STATIC INTERPRETATION in a recursive way, in
an information state W[i,], applied to its eventual referent e; and then we
provide an immense generalization. If e is the eventuality representing discourse d (2.2.5), we define the STATIC INTERPRETATION of the discourse as
the static interpretation of the eventuality.
We have already discussed the basic phases of static interpretation in
the course of discussing dynamic interpretation as the two sorts of interpretation are multiply interwoven. On the one hand, only a discourse understood, and not a flow of sounds, may undergo static interpretation; which
seems to suggest that dynamic interpretation feeds static interpretation
(DynSta). For the interpreter to develop hypotheses concerning the anchoring of phonetic-form relations of the discourse and to check presuppositions,
however, is the task of static interpretation, whose completing the continuation of the process of dynamic interpretation, at certain points, seems to require (StaDyn). Consequently, both types of interpretation are required.
Their defining, nevertheless, will not run into a vicious circle, but starts from
infon perception (2.1.4) as a common root, and then come about so that static
interpretation and dynamic interpretation is being defined independently of
each other. As a matter of fact, the constructions to undergo static interpretation are quite simple: eventualities directly coming from infon perception,
further eventualities that can be traced back to these, and logical combinations
of eventualities (, , , Q), in addition to eventualities “organized by”
modal predicates but this latter group can be evaluated via the simplest way of
pattern matching, due to the advantageous worldlet structure of internal
worlds.
2.3.1 Truth, relying on infon perception (but interpreters are not infallible, of course)
Let us rephrase and generalize infon perception (see 2.1.4). Suppose that, in
interpreter i’s information state W[i,], the eventuality e specified in ii. below is anchored-out to the infon  specified in i., together with all of its referents (iii.) (typically due to some indirect perception):
i.
 =  P, T, U1, U2, ..., UK, where T
ii.
e:: Pred,: p, Temp,InCum: t, Arg,1: r1,..., Arg,K: rK
iii.
(Out,,e) = 
(Out,,p) = P
Definition II. interpretation in eALIS
(Out,,t) =  (remember: T)
(Out,,r1) = U1
...
(Out,,rK) = UK
34
The temporal dimension is the only one where there is no isomorphic
connection between the external and the internal entities: the time referent
is obligatorily regarded as point-like whilst the external time is taken to be
interval-like. That is why in formula ii. above the InCum subparameter of
the temporal parameter can be found, as what can be perceived is (primarily) a homogeneous process which is just coming about.6 If any other temporal subparameter appears as the label of the time referent of an eventuality, the static interpretation of this eventuality requires the indirect method
of evaluation, to be discussed later, usually involving intensional means.
We say, under the conditions specified in this subsection, that eventuality e is VERIFIED UNDER ANCHORING  due to infon  if the perception is ideal;7 on the basis of which we can also say that e is TRUE; which is eventuality
e’s STATIC INTERPRETATION IN THE EXTERNAL WORLD. The eventuality is
FALSE if it differs from the ideal perception.
2.3.2 Truth coming from potential extension of the anchoring function
Suppose now that in interpreter i’s information state W[i,] the eventuality
e is such that its closure according to  and  (see 2.2.1.4) is verified under
an extension + of the interpreter’s momentary anchoring function 
(+). In this case we say that eventuality e is VERIFIED UNDER ANCHORING
; on the basis of which we can also say that e is TRUE; which is eventuality
e’s STATIC INTERPRETATION IN THE EXTERNAL WORLD. The eventuality is
FALSE if anchoring  has no extension under which e would be verified.
The extension + is allowed to be anchored to points of time different
from the “momentary” time, and it is not necessarily the interpreter’s factual perception but only a potential. As a matter of fact, what the interpreter
herself supplies is the anchoring of only argument referents.
6
We consider homogeneous processes also in order to avoid the Imperfective Paradox.
It is not a mathematical, but a linguistic question when a given predicate is to be
judged to be the ideal perception of a state or process in the given world. Certain
phenomena suggest, unfortunately, that anchoring-out belongs to an individual
interpreter (who is „then” „there”) whilst predicate selection should be judged „from
outside”. This operation can be modeled so that the ideal decision (concerning predicate
selection) is the decision that the speakers’ (language / dialect) community would make
in the given context (according to which truth evaluation of a sentence seems to be
community-dependent).
7
35
Definition II. interpretation in eALIS
2.3.3 Truth evaluation on the basis of generalized logical functions
Now let us consider two eventualities, denoted by e’ and e”, in interpreter
i’s information state W[i,], and recall that [e’] and [e’,e”] denote the corresponding closures according to  and . Let us introduce, then, for an arbitrary anchoring function , the following two three-argument functions,
which assigns  a finite set of its extensions:
i.
ii.
+ : , e’, e”  {+ : + verifies[e’] and has an extension ++
(+++) that verifies [e’,e”]}8
- : , e’, e”  {+ : + verifies [e’] and has no extension ++
(+++) that verifies [e’,e”]}
By means of these two functions we are already in a position to define the static interpretation of eventualities coming from logical combinations of the types listed below:
iii.
e:: Pred,Logical: p, Temp,InCum: t, Arg,Left: e’, Arg,Right: e”
The same conjunctive eventuality is shown in iv.1 below, applying a
simplified notation and omitting references to time. Then we keep on using
the simplified notation, concentrating on the logical essence. As for connections: in the first three examples (iv.1-3) e’ and e” belong to the
worldlet of e itself, and then in iv.6-10, e’ and e” is -linked to e in the way
specified in iv.5.
iv.1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
e:  e’ e”
e
e:  e’ e”
e:  e’ ((.NEG,,i,+,e’) = e)
e:  e’ e” ((.SUPP,,i,+,e’) = e; (.CONS,t,i,+,e”) = e’)
e:  e’ e”
e: Q e’ e”
e: G e’ e”
e: G e’ e”
e: Q e1’ e2’... eK’ e”
v.
Eventuality e is VERIFIED UNDER ANCHORING  (due to its extensions), so we can also say that e is TRUE – and otherwise FALSE (which is
its STATIC INTERPRETATION IN THE EXTERNAL WORLD) if...
1.
+(, e’, e” is not empty
8
A possible extension of  should be such that implies no false perception (see 2.1.4.5).
2.
3.
4.
5.
6.
7.
8.
9.
10.
36
Definition II. interpretation in eALIS
+
 (, e’, e’ is not empty
+(, e’, e’ or +(, e”, e” is not empty (or neither is empty)
+(, e’, e’ is empty
-(, e’, e” is empty
+(, e’, e” is not empty
The STATIC INTERPRETATION of a generalized quantifier determiner
Q is provided by a characteristic function StaQ, which has three
argument places to be occupied by sets of -extensions as follows:
StaQ (+, e’, e’, +, e’, e”, -, e’, e”) = TRUE/FALSE.
The STATIC INTERPRETATION of a generalized existential quantifier
determiner G is provided by a characteristic function StaG,
which has one argument place to be occupied by sets of extensions as follows:
Sta G (+, e’, e”) = TRUE/FALSE.
The STATIC INTERPRETATION of a generalized universal quantifier
determiner G is provided by a characteristic function StaG,
which has one argument place to be occupied by sets of extensions as follows:
Sta G (-, e’, e”) = TRUE/FALSE.
The STATIC INTERPRETATION of a polyadic generalized quantifier
determiner Q is provided by a characteristic function StaQ, which
has argument places to be occupied by sets of -extensions as follows:
StaQ (+,e1’,e1’, ..., +,eK’,eK’, +,e”,e”,
+,e1’,e”, ..., +,eK’,e”, -,e1’,e”, ..., -,eK’,e”) =
TRUE/FALSE.
Default inference, specified in vi. below, can be evaluated depending
on our linguistic aims. It can be construed so that at a certain point of the
process of interpretation the eventual referent of the default inference
should be anchored to a particular type of inference (depending on the context or other circumstances).9 It can also be construed as deferred: it is to be
applied again and again when the following situation emerges: the truth of
e” should be estimated, e’ is unquestionably true, and there is no special
reason to think that e” is false.
vi.
9
e: Default e’ e” ((.SUPP,,i,+,e’) = e; (.CONS,t,i,+,e”) = e’)
The typical candidate is some generalized universal quantifier (G), but the problem
of the „parking meter” suggests that even an existential reading () may emerge.
37
Definition II. interpretation in eALIS
2.3.4 Truth-conditional evaluation of modal eventualities
In this subsection we decide the calculation of the static interpretation of
an eventuality e which a modal predicate referent p belongs to, as is specified below in i. Beyond the -connection of e’ with e (see i.), what plays a
crucial role is the worldlet index of e (see 1.2.4.3), which can also be the
empty index  (if e happens to be a root referent). By definition, MODAL
predicates cannot be anchored to an external core relation, so their static
interpretation cannot be traced back to anchoring-out by the method applied so far.
At this instant the interpretation will be based upon a special extension A of interpreter i’s anchoring function , which can be called a TRANSANCHORING: a partial function U  U, where it is allowed to connect
even different interpreters’ referents.
e:: Pred,Modal: p, Temp,InCum: t’, Arg,1: i’, Arg,2: e’,...
(’,t’,i’,’, e’) = e
the worldlet index of e: 
A(Trans,, e) = el
A(Trans,, i’) = i’l, ahol l(Out,, i’l) = l
A is relation-preserving (including the labels as well as worldlet index )
i.
ii.
We suppose that there is an interpreter l, who has an eventual referent e , and i’s anchoring  has a trans-anchoring extension A (capital )
such that A maps the closure [e] of e (according to  and ) to el in a relation-preserving way. Eventuality e expresses a propositional attitude of referent i’. Trans-anchoring A leads to a worldlet whose host is the interpreter
l to which i’ is anchored out; let us call this worldlet the TARGET of the
modal eventuality denoted by e. It is also worth mentioning that the anchoring function l in ii. above belongs to interpreter l, and not i.
In this case (if the appropriate trans-anchoring -extension exists),
we say that eventuality e is VERIFIED UNDER ANCHORING  (due to the transanchoring extension); on the basis of which we can also say that e is TRUE;
which is eventuality e’s STATIC INTERPRETATION IN THE EXTERNAL WORLD.
The above mentioned relation-preserving unconditionally pertains to
the -connections; trans-anchoring A thus maps, to referents in U[l], the
predicate referents and argument referents belonging to eventualities e and
e’ – as well as further eventualities, if an argument of e’ happens to be anchored to an eventuality (which might, again, have an argument anchored
to an eventuality; and so on...); all this comes from the definition of closure.
l
38
Definition II. interpretation in eALIS
The application of relation-preserving to internal anchoring is
straightforward: the A-image of i’s identified referents will be identified
referents in l’s internal universe. As for anchoring-out, relation-preserving
seems to be worth to define as follows:
iii.
If (Out,, ri) = u,
and A(Trans,, ri) = rl, then
l(Out,, rl) = A(Trans,, u) = u.
Finally we make some comments on the application of relationpreserving to the level function . Level labels contain elements of U; such
elements will correspond to their A-images. Other elements in level labels
will correspond to themselves. The A-image of the modal predicate is an
appropriate modal label  (whose perception should be ideal; see 2.3.1). As
[e] is a closure (only) according to  and , it does not contain its -image,
but we make the following extra stipulation: the worldlet index  of eventuality e corresponds to a worldlet index A(Trans,,).
2.3.5 Generalizing static interpretation – in more directions
Trans-anchoring provides an interesting possibility for the GENERALIZATION OF STATIC INTERPRETATION. Contrary to 2.3.4.i, in i. below we have
no special stipulations concerning the structure of eventuality e; the predicate, for instance, is not (necessarily) modal. Nor is it stipulated that the
worldlet index of e should be inherited as a result of trans-anchoring. Thus
we look for the information carried by the closure [e] of e in an arbitrary
interpreter’s arbitrary worldlet, even in the case of an opposite label polarity.
i.
ii.
e:: Pred,: p, Temp,: t’, Arg,1: r1, ..., Arg,K: rK
A(Trans,, e) = el, and A is relation-preserving
Suppose a trans-anchoring -extension A maps, in a bijective relation-preserving way, the {,}-closure [e] of e to an eventuality el of an
interpreter l, where interpreter l does not necessarily differ from interpreter i. If an A like this exists, we say that a trans-anchoring -extension
forms a PATTERN MATCHING between eventuality e (of worldlet index )
and eventuality el (of worldlet index l).
Depending on the pair ,l of worldlet indices, the above discussed
pattern matching is suitable for basing some PRAGMATIC EVALUATION upon
it: such concepts can be captured in this way as mistake, misunderstanding,
bluff, telling a lie, misleading, blurting out a secret, etc. This pragmatic
evaluation can also be regarded as a generalization of static interpretation:
39
Definition II. interpretation in eALIS
the GENERALIZED STATIC INTERPRETATION of eventuality e in a worldlet of
index l from a worldlet of index . A special form of accommodation can
also be explained on the basis of this generalization of static interpretation:
eventualities expressing the pragmatic relation of such (external and internal) entities as discourse d, eventualities e and el, and interpreters i and l
can be accommodated in certain information states; e.g. “the speaker wants
to mislead the listener by saying that...”
Let us turn to another way of generalizing static interpretation. If the
mode feature in a modal level label  is exclamation or interrogation (see
1.2.4.1) and the target of static interpretation is the external world, then,
instead of the true/false pair, the static semantic value will be
+COMPLETED / –COMPLETED in the case of an exclamation, and
+ANSWERED / –ANSWERED in the case of an interrogation. As a matter of
fact, answering a question is a special case of completing a request; a request whose peculiar property is that it does not pertain to the external
world (e.g. “do the room!”), but it pertains to an interpreter’s internal
world, somehow in this way: “reveal a certain sector of your information
state in order to give me some relevant information!” We mention that the
completion of this latter request can be evaluated in eALIS, due to the
rich worldlet system of interpreters’ information states.
2.3.6 Truth-conditional evaluation on the basis of meaning postulates
Besides modal predicates, numerous other kinds of predicates are also such
that cannot be anchored out (directly), as no core relations (1.1) correspond
to them in the external world. To avoid several theoretical and technical
problems, infons expressing heterogeneous events have been precluded
from the external world of the eALIS model. We argue that heterogeneous eventualities are constructed by interpreters via combining elementary
eventualities coming from direct infon perception by logical means (and
usually by having recourse to modal embedding, too).
In ii. below we have specified the eventuality e” from which a
general statement e’ result whose predicate can be anchored to p. The rule
description itself is the task of a special eventuality emea, which supplies the
MEANING POSTULATE of the predicate:
i.
ii.
10
e:: Pred,: p, Temp,: t’, Arg,1: r1, ..., Arg,K: rK, ahol (Ant,e)=e’
emea:  e” e’ ((.SUPP,,i,+,e’) = e; (.CONS,t,i,+,e”) = e’)10
Symbol ‘’ can be substituted for the symbol of default inference (’Default’).
40
Definition II. interpretation in eALIS
The static interpretation of e (in i.) is to be decided under anchoring
. Note that it is typical that it is not the predicate itself that needs some
meaning postulate but its variant of a special temporal subparameter .
As a first step, we should apply a  bijective relation-preserving
function that maps the {,}-closure [e’] of e’ to the eventuality e, which
should be evaluated. Then we should apply a (bijective relation-preserving)
extension + of  whose task is to copy the “new” elements of the closure
[e”,e’] (relative to [e’]) on new referents (to be put into use). Observe that
closure [e”,e’] is not the same as closure [emea] because the former lacks the
conditional connection; but it retains the -anchors since it is an -closure.
The hypothetical construction thus yields a new potential W+ information
state with an + extension of  as its anchoring function.
If in this information state W+ the group ([e”]) of eventualities is
verified under an +-extension ++, then we say that eventuality e is VERIFIED under the original anchoring  in information state W[i,], by means
of meaning postulate emea; we can also say that e is TRUE; which is eventuality e’s STATIC INTERPRETATION IN THE EXTERNAL WORLD. The eventuality is
FALSE if anchoring  has no appropriate extension + under which e would be
verified by means of meaning postulate emea or some other meaning postulate.
2.3.7 “Accommodating” classical logic in an interpreter’s mind
If during the static interpretation of a modal eventuality e we cannot find an
appropriate target worldlet for the pattern matching discussed in 2.3.4, then
e should be qualified as false, at least formally. It is possible, however, that
what is required is that the host of the target worldlet draw some very simple conclusion in order to reach the verification of e. We can say in a situation like this that e is TRUE AT THE COST OF ACCOMMODATING CERTAIN
PIECES OF INFORMATION VIA USING CERTAIN INFERENCE RULES.
The classical laws of inference and rules of standard predicate logics
can all be reformulated in eALIS, and it can be assumed that more or less
out of them are present in interpreters’ grammatical knowledge in the form
of rule-describing eventualities (2.2.3).