Deriving the typology of aspect neutralization
across tenses
Benjamin Storme
November 21, 2015
Abstract
Patterns of aspect neutralization conditioned by tense are
widespread and show some striking commonalities across languages.
First, in case of neutralization of the perfective/imperfective distinction, languages seem to systematically extend the imperfective form.
Second, the perfective/imperfective distinction is preferentially expressed in the past, then in the future, and finally in the present.
These asymmetries are derived with two main hypotheses. Imperfective morphology is preferred in contexts without aspectual distinction
because it is semantically more expressive than perfective morphology.
All tenses do not behave alike because they are not as informative
about aspectual meanings: aspect neutralization happens preferably
in tenses that are more informative about aspect. The analysis improves on previous analyses by providing an explicit, semanticallyand pragmatically-informed model of aspect syncretism.
1
1.1
Introduction
Aspect neutralization across tenses
English and French have ways to express whether an event occurred (“complete event” interpretation) or whether it was ongoing (“ongoing event” interpretation) at a particular past time. The “complete event” interpretation
is expressed by the simple past in English, illustrated in (1a), and the passé
composé in French, illustrated in (1b). Both sentences describe a complete
event of John making a promise that happened at (or around) 8 pm.
1
(1)
a.
b.
At 8 pm, John promised to come.
A 8 heures, Jean a promis de venir.
The “ongoing event” interpretation is expressed by the past progressive in
English, illustrated in (2a), and by the imperfect in French, illustrated in
(2b). Both sentences can describe an event of John making a promise that
was ongoing at (or around) 8 pm and may have been interrupted.
(2)
a.
b.
At 8 pm, John was promising to come.
A 8 heures, Jean promettait de venir.
The parallel between English and French breaks down in the present tense.
The contrast between the simple verbal form and the progressive form extends to the present tense in English (see (3)), but not the contrast between the passé composé and the imperfect in French (see (4)). The aspect
paradigm has a gap in the present tense in French: only the stem prometfound in the imperfect is available.
(3)
a.
b.
I promise to come.
I am promising to come.
(4)
Je promets de venir.
Patterns of aspect neutralization conditioned by tense are widespread and
show some striking commonalities across languages. For instance, the French
pattern illustrated above is common cross-linguistically whereas the pattern
where there are two forms for the “ongoing event” and “complete event” readings in the present and just one in the past is, to our knowledge, unattested.
Also, as in the French example, languages seem to systematically extend
the form corresponding to the “ongoing event” reading in tenses without
aspectual distinctions.
The goal of this paper is to account for these generalizations and in particular to explain why tense may have an effect on the expression of aspect.
Before introducing in more details the generalizations we aim at accounting
for (section 1.3) and our specific proposal (section 1.4), we introduce our
assumptions about the syntax and semantics of tense and aspect (section
1.2).
2
1.2
The perfective/imperfective distinction
The distinction between (1) and (2) has been well documented in the typological literature and found to exist in many languages (Comrie (1976,
pp. 16-40), Dahl (1985, pp. 69-95), Bybee and Dahl (1989), Bybee, Perkins,
and Pagliuca (1994, pp. 125-175), Dahl and Velupillai (2013a)). Following
Comrie (1976), the morphology expressing the “complete event” interpretation is typically called “perfective” and the morphology expressing the
“ongoing event” interpretation “imperfective.” The English past progressive
and the French imperfect are imperfective morphemes whereas the English
simple past and the French passé composé are perfective morphemes.1 Perfective and imperfective morphemes are common cross-linguistically. In a
sample of 222 languages, Dahl and Velupillai (2013a) found that at least 101
of them have this distinction.2 They also found that this distinction exists in
non-genetically related languages and in different geographical areas. This
suggests that the meanings conveyed by perfective and imperfective morphemes have a universal basis. UG is assumed to contain two operators,
pfv and ipfv, whose meanings are the same across languages.3 Our lexical
1
The fact that perfective and imperfective morphemes might belong to different morphological classes in different languages - e.g. the imperfective morpheme is bound in
French and discontinuous in English and the perfective morpheme is bound in English
and discontinuous in French - is not relevant here, as this typology is based on semantic
factors. It is sometimes assumed that the French equivalent of be -ing in the past is être
en train de rather than the imperfect, based on the fact that both involve a periphrastic
construction with be. However, être en train de has a more constrained distribution than
English be -ing (Copley and Roy, 2014) and is more similar to English to be in the middle
of, both semantically and formally.
2
Dahl and Velupillai (2013a) have a more restrictive view than Comrie (1976) in their
definition of what counts as imperfective. In Comrie (1976), a morpheme is imperfective
if it is compatible with the “ongoing event” reading: both the French imperfect and
the English progressive are imperfective morphemes. In Dahl and Velupillai (2013a),
a morpheme is imperfective if it is compatible both with the “ongoing event” and the
“habitual event” readings: the French imperfect is considered as imperfective but not the
English progressive. This explains why, for Comrie and us, at least 101 languages have
this distinction.
3
The fact that the specific morphemes that instantiate those operators in different languages might have other meanings in addition is ignored. In English, sentences in the
simple past and, to a lesser extent, sentences in the progressive allow for generic/habitual
readings (Krifka et al., 1995). The French imperfect has generic/habitual readings (Comrie, 1976), but not the French passé composé. The French imperfect necessarily occurs in
antecedents of counterfactuals but the English progressive does not (Iatridou, 2000). The
3
entries for pfv and ipfv are couched in the framework of event semantics
(Davidson, 1967), where verbal phrases denote predicates of eventualities
(events or states). The semantic types for eventualities and truth values is
noted v and t respectively. The meanings assumed for pfv and ipfv are
shown below.
(5)
Aspect meanings
a. JpfvK = λPhv, ti .λe.e is a complete P-eventuality
b. JipfvK = λPhv, ti .λe.e is a part of a complete P-eventuality
pfv takes a predicate of eventualities P and a specific eventuality e as arguments and returns true if e is a complete P-event. ipfv returns true if e is
a part of a complete P-event. Among the aspectual operators with semantic
type hhv, ti, hv, tii (e.g. pfv, ipfv, be in the middle of, start, finish, etc.),
pfv and ipfv are assumed to form a paradigm. This syntactic assumption
will allow us to ignore other aspectual morphemes in the remainder of this
paper and just focus on pfv and ipfv.
The meanings of aspect phrases (AspP) are shown below. The eventive
VP Agatha cross the street is used as an example.
(6)
Aspect phrase meanings
a. J[AspP pfv Agatha cross the street]K = λe.e is a complete event of
Agatha crossing the street.
French passé composé has readings corresponding to the English perfect. In Japanese,
the imperfective form -te iru has so-called resultative interpretations in addition with the
ongoing process interpretations (Ogihara, 1998). Romance past imperfectives have plan
readings and allow for so-called narrative uses whereas Slavic past imperfectives do not
(Arregui, Rivero, and Salanova, 2014). In most cases, it is still highly debated whether it
is possible to unify the set of meanings associated with perfective and imperfective morphemes under a single lexical entry in a given language (Ippolito, 2004; Arregui, Rivero,
and Salanova, 2014). The most recurrent case of ambiguity involves “ongoing event” and
“habitual event” readings. It is widespread enough to suggest that it is not a random ambiguity. No consensus has been reached yet on how to analyze this ambiguity (see Ferreira
(2005), Hacquard (2006), Deo (2009) a.o for different proposals). None of the aforementioned accounts requires to posit fundamental differences in the meanings of imperfective
morphemes across languages depending on whether they allow for habitual readings or
not. For instance, in Ferreira (2005), the difference between those two types of languages
amounts to whether imperfectives are allowed to combine with predicates of plural events
or not. This suggests that, despite differences in meanings, it is widely assumed that a
core semantic component is shared by all imperfective morphemes.
4
b.
JAspP ipfv Agatha cross the streetK = λe.e is a part of a complete
event of Agatha crossing the street.
Aspect phrases combine with tense and form a tense phrase (TP), or a sentence. Only three tenses are considered, past, future, and present. The
logical operators pres, past, and fut are assumed to be part of UG and
have the same meanings across languages. We assume the meanings in (7),
based on Parsons (1990). Tense meanings are defined with respect to the
utterance time, noted τ (u). The τ function maps an event, for an instance
an utterance event u, to its run-time.
(7)
Tense meanings
a. JpresKu = λPhv, ti .∃t[t⊆ τ (u) & ∃e[e is a P-eventuality and
τ (e)=t]]
b. JpastKu = λPhv, ti .∃t[t< τ (u) & ∃e[e is a P-eventuality and
τ (e)=t]]
c. JfutKu = λPhv, ti .∃t[t> τ (u) & ∃e[e is a P-eventuality and
τ (e)=t]]
pres takes a predicate of eventualities as complement and returns true if
an eventuality in the extension of this predicate happens at a time interval
equal to or included in the utterance time. With past, the time interval is
before the utterance time. With fut, it is after the utterance time.4
All the ingredients necessary to derive the meanings of perfective and
imperfective sentences are now in place. Consider the English sentences (8a)
and (8b).
(8)
a.
b.
Agatha crossed the street.
Agatha was crossing the street.
These sentences are predicted to have the logical forms and meanings in (9a)
and (9b) respectively.
(9)
4
Tensed phrase meanings
a. J[TP past [pfv [Agatha cross the street]]]Ku = 1 iff
∃t[t< τ (u) & ∃e[e is a complete event of Agatha crossing the
street & τ (e)=t]]
b. J[TP past [ipfv [Agatha cross the street]]]Ku = 1 iff
Future tense is treated as a tense rather than a modal (Klecha, 2014) for simplicity.
5
∃t[t< τ (u) & ∃e[e is a part of a complete event of Agatha crossing
the street & τ (e)=t]]
Sentence (8a) is predicted to entail that a complete event of Agatha crossing
the street happened at a past time. Sentence (8b) is predicted to entail that
a part of a complete event of Agatha crossing the street happened at a past
time. Note that (8b) is not predicted to entail that Agatha finished crossing
the street in the past. This is a welcome prediction as (8b) does not entail
completion of the event, as shown in (10):5 Agatha may have never finished
crossing the street, yet the sentence Agatha was crossing the street can be
uttered truthfully.
(10)
Agatha was crossing the street when she was hit by a bus.
The absence of entailment from an imperfective sentence to its perfective
counterpart is known as the “imperfective paradox” (Dowty, 1979) and is often derived assuming an intensional semantics for ipfv (Dowty, 1979; Landman, 1992; Portner, 1998). Here, the modal component of ipfv is captured
in the “part-of” relation: if a part of a complete event of Agatha crossing
the street happened in the world of evaluation, then it is not necessary that
a complete event of Agatha crossing the street happened in this world.
1.3
Tense-aspect interactions cross-linguistically
It has been noted that whether the “complete event”/“ongoing event” distinction is expressed morphologically depends on tense. The expression
“aspect neutralization” will be used to describe the absence of a perfective/imperfective distinction in a particular tense, i.e. a gap in the paradigm
(as in the French present tense). This expression is used descriptively and
does not commit us to an analysis of the source of this absence.
In French, the perfective/imperfective distinction is neutralized in both
present and future tenses, but not in the past. In Modern Greek, it is neutralized in the present tense, but not in past and future tenses. The French
and Greek verbal paradigms for the first person VP “I promise” are shown
in Table 1.
5
Assume that the when-clause constrains the run-time of the event of Agatha walking
on the street to be just before the event of the bus hitting her.
6
Example
Greek
French
Perfective
iroskhéthika
j’ai promis
Past
Future
Present
Imperfective
Perfective
Imperfective
Perfective Imperfective
iroskhómun tha iroskhethó tha iróskhome
iróskhome
je promettais
je promettrai
je promets
Table 1: Preference for the imperfective in the absence of distinction.
The stem used in the present tense is identical to the imperfective stem
used in the past for French and in the past and in the future for Greek
(see Table 1). In French, the use of the imperfective stem in the present
is visible only with verbs showing stem allomorphy, for instance in second
person plural forms of irregular verbs like promettre and boire in Table 2 (but
not the regular verb chanter, which has the same stem throughout).
Example
sing
promise
drink
Past
Future
Perfective
Imperfective
Perfective Imperfective
avez chanté [Sãt-]
chant-i-ez [Sãt-]
chant-(e)r-ez [Sãt-]
avez promis [pKomi] promett-i-ez [pKomet-] promett-r-ez [pKomet-]
avez bu [by]
buv-i-ez [byv-]
boi-r-ez [bwa-]
Present
Perfective Imperfective
chant-ez [Sãt-]
nous promett-ez [pKomet-]
nous buv-ez [byv-]
Table 2: Verbal stems in regular and irregular conjugations in French
In French, the future of irregular verbs tends to be built on the same
stem as the past imperfective (see promettre in Table 2) but is based on a
stem different from both past perfective and imperfective for other irregular
verbs (see boire in Table 2). Ancient Greek shows additional evidence of the
extension of the imperfective stem in the future tense. In Ancient Greek,
the perfective/imperfective distinction is neutralized in the future (Bary,
2009, p. 3). The verb “show” (see Table 3) seems to show evidence of an
extension of the perfective stem deik- in the future tense. However, this
is confounded by the fact that the perfective stem is the bare verbal stem.
The verb “leave” shows clearer evidence of an extension of the imperfective
stem: the imperfective stem leip- is extended even though it is phonologically
heavier than the perfective stem lip-.
Example
show
leave
Perfective
e-deik-sa
e-lip-on
Past
Imperfective
e-deik-nu-me:n
e-leip-on
Future
Perfective Imperfective
deik-so
leip-so
Present
Perfective Imperfective
deik-nu-mi
leip-o
Table 3: Ancient Greek
As far as we know, this is universally the case. When one of the two
7
forms (perfective or imperfective) is used alone in a given tense without any
clear morphological or phonological reason (e.g. it is not morphologically
or phonologically simpler), the imperfective is always preferred (Malchukov,
2009). In the remainder of this paper, we call this generalization Universal
1. The cross-linguistic preference for imperfective morphology as the default
aspect has also been observed in modal contexts (Iatridou, 2000).
Universal 1. In languages where there are morphemes identified as perfective and imperfective, if in a tense only one of them
is used, it will be the imperfective.
Furthermore, if a language has perfective and imperfective morphemes in
the future, then it also has them in the past, but the reverse is not true. There
are languages with perfective and imperfective morphemes in the past, but no
perfective morpheme in the future, e.g. French and Ancient Greek. However,
as far as we know, there is no language with perfective and imperfective
morphemes in the future and no perfective morpheme in the past (Comrie
(1976, pp. 71-73), Malchukov (2009)). The typology is limited to the three
types in Table 4 instead of the four logically possible types. See Kratzer
(1998) and Reyle, Rossdeutscher, and Kamp (2007, p. 7) on German. In the
remainder of this paper, we call this generalization Universal 2.
Overt distinction
Past
Future
yes
yes
yes
no
no
no
Example
English
French
German
Past
Perfective
Imperfective
I promised I was promising
j’ai promis
je promettais
ich versprach
Future
Perfective
Imperfective
I’ll promise I’ll be promising
je promettrai
ich werde versprechen
Table 4: The perfective/imperfective distinction in the past and in the future.
Universal 2. The presence of a perfective/imperfective distinction in the future asymmetrically entails the presence of this
distinction in the past.
A further asymmetry exists between the present and the future: if a
language has perfective and imperfective morphemes in the present, then
it also has them in the future, but the reverse is not true (Comrie (1976,
pp. 71-73), Malchukov (2009)). There are languages with perfective and
imperfective morphemes in the future, but no perfective morpheme in the
present, e.g. Modern Greek. However, as far as we know, there is no language
8
with perfective and imperfective morphemes in the present and no perfective
morpheme in the future. The typology is limited to the three types in Table
5 instead of the four logically possible types. In the remainder of this paper,
we call this generalization Universal 3.
Overt distinction
Future Present
yes
yes
yes
no
no
no
Example
English
Greek
French
Future
Perfective
Imperfective
I’ll promise
I’ll be promising
tha iroskhethó tha iróskhome
je promettrai
Present
Perfective Imperfective
I promise I’m promising
iróskhome
je promets
Table 5: The perfective/imperfective distinction in the future and in the
present.
Universal 3. The presence of a perfective/imperfective distinction in the present asymmetrically entails the presence of this
distinction in the future.
We stated Universals 1, 2, and 3 in categorical terms. There is to our
knowledge no quantitative study that permits to establish whether these generalizations are absolute, strong, or weak universals, in the sense of Maslova
(2003). In this paper, we will treat them as absolute universals, i.e. as universals without exceptions. Bybee and Dahl (1989) and Dahl and Velupillai (2013b) report that, among languages with the perfective/imperfective
distinction, so-called tripartite systems, i.e. systems with a distinction in
the past and no distinction in the present (like French and Greek), “are
found in many different families, although they are particularly common in
the past-marking part of Eurasia.” Bybee and Dahl (1989, p. 83) report
that languages with full perfective/imperfective distinctions across all three
tenses are rare. The data in Dahl and Velupillai (2013a) suggest that a large
number of languages (more than half of their sample) do not have a perfective/imperfective distinction (like German). To summarize, the typological
literature points to the patterns of preferences shown in (11).
(11)
Preferences among the four attested types
a. Languages with full distinctions (e.g. English) across all tenses
are rare.
b. Tripartite systems (e.g. French, Greek) are common.
c. Languages with no distinction across any tense (e.g. German)
are very common.
9
These preferences must be taken with caution as (i) they are not based on
quantitative data, but on typologists’ intuitions and (ii) some languages with
a perfective/imperfective distinction in some tenses might not be counted as
such if the imperfective morpheme in these languages is not compatible with
habitual/generic readings (see footnote 1).
Universals 1, 2, and 3 are puzzling. There is no obvious reason for why
only the imperfective morpheme should occur in some tenses in some languages. Indeed, it should be possible to assert that a complete event occurs
(as well as “is occurring”) at a particular time no matter when this particular
time is located with respect to the utterance time, as in English. Universals
2 and 3 are puzzling too. Among the eight logically possible patterns of
the expression of aspectual distinctions across tenses, only four are attested:
distinctions across all tenses (English), distinctions everywhere except in the
present (Greek), distinction only in the past (French), and no distinction in
any tense (German). Why is it so? There is again no obvious reason for why
some tenses should favor aspect neutralization more than other.
1.4
Proposal
How should the extension of imperfective morphology to contexts with aspect
neutralization be interpreted? Is the “complete event” reading unavailable
in those contexts? In 2.1, we give evidence for the view that tenses with
aspect neutralization are compatible with both “complete event” and “ongoing event” readings. This motivates a treatment of aspect neutralization
in terms of aspect syncretism: an underlying semantic distinction is unfaithfully represented in the morphology rather than absent (Baerman, Brown,
and Corbett, 2005, p. 2). In 2.2, we present two approaches compatible with
the syncretism hypothesis: the ambiguity and underspecification analyses.
We show that Universal 1 can be derived more straightforwardly under the
underspecification approach. In 2.3., we show that the underspecification
approach can retain some apparent advantages of the ambiguity approach if
underspecified meanings are allowed to be lexically strengthened.
Section 3 is dedicated to Universals 2 and 3. In 3.1, Comrie’s (1976) insight that asymmetric patterns of aspect syncretism correlate with meaning
probability asymmetries is discussed. In 3.2, these probability asymmetries
are interpreted in information-theoretic terms: it is argued that tenses with
larger meaning asymmetries are more informative about aspectual meanings
and therefore should favor aspect neutralization more than tenses with less
10
marked asymmetries. In 3.3, a constraint-based model of the semanticsmorphology interface is proposed that can account for the effect of informativity on morphological patterns. In 3.4, we show how this model derives
Universals 2 and 3. In 3.5, we show how the model is able to derive preferences among the four attested types of aspect syncretism.
Section 4 is dedicated to a discussion of possible extensions of the model
and to a comparison with an alternative analysis where patterns incompatible
with Universals 2 and 3 are filtered out as being harder to learn.
2
2.1
Deriving Universal 1
Aspect neutralization as syncretism
Aspect neutralization can be analyzed in two ways: either the perfective/imperfective distinction is irrelevant semantically in some tenses in some
languages (semantic incompatibility hypothesis) or it is relevant semantically
but not expressed in the morphology (syncretism hypothesis).
The two hypotheses can be illustrated with gender distinctions in pronouns. Mixed-gender pronouns exist in the plural, for instance in Vanimo, a
language spoken in North Guinea (Plank and Schellinger, 1997, p. 76), but
not in the singular. This is arguably because the mixed-gender predicate is
semantically incompatible with singular number. However, the absence of
gender distinctions in plural pronouns in English (English has only they) is
not due to any semantic incompatibility between gender and plural number:
they can denote only-female groups, only-male groups, and mixed groups.
The distinction is semantically relevant but not expressed in English.
The two hypotheses are formulated in (12) for the case of aspect neutralization in a tense t.
(12)
Aspect neutralization in a tense t.
a. Semantic incompatibility. The meaning of the perfective morpheme is incompatible with the meaning of tense t.
b. Syncretism. The perfective/imperfective distinction is relevant
semantically in t but not expressed morphologically.
It has been argued that present tense and perfective morphology are semantically incompatible (Taylor, 1977; Dowty, 1979; Kamp and Reyle, 1993;
Giorgi and Pianesi, 1997; Ogihara, 2007) and that this explains why present
11
tense tends to associate with imperfective aspect cross-linguistically. We first
show that this position is not tenable for languages that do allow perfective
aspect and present tense to combine.
A present perfective sentence should entail that an event in the denotation
of the complement VP happens exactly at the moment of utterance or its runtime is strictly contained in the utterance time. These truth conditions are
exactly the truth conditions desired for sentences with explicit performative
verbs like (13). Assuming the meaning in (14a) for the VP I promise to come,
sentence (13) should have the meaning in (14b).
(13)
I promise to come.
(14)
a.
b.
JI promise to comeKu = λe. e is an event of the speaker of u
promising to come
J[pres [pfv [I promise to come]]]Ku = 1 iff
∃t[t⊆ τ (u) & ∃e[e is a complete event of the speaker of u promising to come & τ (e)=t]]
The meaning in (14b) is compatible with the event of promising happening
exactly at the moment of utterance of u. Sentence (13) is interpreted performatively, i.e. it is interpreted as being true by virtue of being uttered.
The performative effect can be derived using the meaning in (14b) and a
pragmatic theory of performativity, as proposed by Condoravdi and Lauer
(2011) and Lauer (2013) for instance.
Present perfective sentences also occur in special conversational contexts,
with the sportscaster present tense as in (15a) and in so-called historical
present sentences as in (15b) (e.g. Bennett and Partee (1978, p. 10), Parsons
(1990, p. 30), Bertinetto and Bianchi (2003, p. 588)). Assume that in 49 BC
is an AspP modifier and has the meaning in (16). The meanings predicted
for those sentences are shown in (17a) and (17b) respectively.
(15)
a.
b.
(16)
J[in 49 BC]K = λe.τ (e)⊆49 BC
(17)
a.
b.
Jones passes the ball to Smith.
In 49 BC, Caesar crosses the Rubicon.
J[pres [pfv [Jones pass the ball to Smith]]]Ku = 1 iff
∃t[t⊆ τ (u) & ∃e[e is a complete event of John passing the ball
to Smith & τ (e)=t]]
J[pres [[in 49 BC] [pfv [Caesar crosses the Rubicon]]]]Ku = 1 iff
12
∃t[t⊆ τ (u) & ∃e[e is a complete event of Caesar crossing the
Rubicon & τ (e)⊆49 BC & τ (e)=t]]
These sentences are predicted to be literally false in the contexts where they
are typically uttered. Sentence (15a) is false because the event has already
happened when it is described by the sportscaster commentator. Sentence
(15b), assumed to be uttered in the 21st century AD, is false because it
entails than an event can happen in the 21st century AD and in 49 BC.
The fact that those sentences are predicted to be false is actually a desirable
result. Sentences (15a) and (15b) are used figuratively: they are perceived
as literally false and conveying something about the affect of the speaker.
The speaker does as if the event he describes happens at the same time he
is describing it, even though it is false. See Kao et al. (2014) for a treatment
of figurative language in truth-conditional semantics.
These uses of present perfective sentences are not limited to English but
found across a number of languages (Dahl, 1985, pp. 71-72). This suggests that the hypothesis that present tense and perfective aspect are semantically incompatible cannot hold for languages that maintain the perfective/imperfective distinction in the present tense. What about languages
that do not? We show that the French sentences in (18) are compatible with
“complete event” readings, even though they are morphologically imperfective and thus could be expected to be only compatible with “ongoing event”
readings (see also Schaden (2011)).
(18)
a.
b.
c.
Je promets
de venir.
I promise.pres.ipfv.1sg of come.inf
I promise to come.
Jones passe la balle à Smith.
Jones passe.pres.ipfv.3sg the ball to Smith
Jones passes the ball to Smith.
En 49 avant J.-C., César traverse le Rubicon.
in 49 before Jesus-Christ Caesar cross.pres.ipfv.3sg the Rubicon
In 49 BC, Caesar crosses the Rubicon.
Generally, simple present sentences interpreted with “ongoing event” readings can be used interchangeably with être en train de sentences in the present
(Comrie, 1976). This is illustrated by the pair in (19).
13
(19)
a.
b.
Jean
I
Jean
Jean
Jean
Jean
fait
ses devoirs.
promise.ipfv.pres.3sg of come.inf
is doing his homework.
est en
train de faire ses devoirs.
is in-the middle of do.inf his homework
is in the middle of doing his homework.
If the “ongoing event” reading were the only episodic reading available for
sentences in (18), we would expect them to be able to be used interchangeably
with their en train de variants in (20).
(20)
a.
b.
c.
Je suis en
train de promettre de venir.
I am in-the middle of promise.inf of come.inf
I am in the middle of promising to come.
Jones est en
train de passer la balle à Smith.
Jones is in-the middle of passe.inf the ball to Smith
Jones est en train de passer la balle à Smith.
En 49 avant J.-C.,
César est en
train de
in 49 before Jesus-Christ Caesar is in-the middle of
traverser le Rubicon.
cross.inf the Rubicon
In 49 BC, Caesar is in the middle of crossing the Rubicon.
However, this is not the case. Only sentences (18) are compatible with the
episodic “complete event” reading. We take this as evidence that imperfective
morphology in the present tense in French is compatible with “complete
event” readings whereas en train de is not. The “complete event” reading
is not available for sentence (19a) because it is highly unlikely that an event
of someone doing one’s homework has the same as or shorter duration than
the utterance of a sentence like (19a). These facts support the syncretism
hypothesis against the semantic incompatibility hypothesis.
The present imperfective behaves similarly in many other languages without a present perfective.6 Bary (2012) shows that the imperfective in Ancient
Greek is compatible with “complete event” readings with explicit performative verbs. Historical present sentences with imperfective morphology allow
6
We consider that Russian does not have a present perfective morphologically since
present tense is necessarily interpreted with a future reference when combining with perfective morphology: the meaning of the present tense morpheme combining with perfective
is not correctly modeled by the lexical entry for pres proposed above.
14
for “complete event” readings in many languages, including Modern Greek
and Ancient Greek (Bary, 2009), Slavic languages (Stunovà, 1994), and Classical Arabic (Brustad, 2000, pp. 186-187).
To our knowledge, no argument has been made that future tense is semantically incompatible with “complete event” readings. In French, future
sentences with episodic readings are compatible with “complete event” as
well as “ongoing event” readings, even though the verbal stem is morphologically imperfective (see Table 1). This is illustrated in sentence (21).
(21)
Demain à 8h, Jean promettra
de venir.
Tomorrow at 8 Jean promise.ipfv.fut of come.inf
Tomorrow at 8, Jean will promise to come/be promising to come.
This sentence has two readings. The most salient reading is the “complete
event” reading, where Jean is predicted by the speaker to make a promise,
at 8 on the following day, to come. Under the second reading, Jean is predicted by the speaker to be in the middle of making a promise, at 8 on the
following day, to come. The speaker’s prediction is compatible with Jean
never finishing making his promise: Jean may be interrupted. This reading can be paraphrased using the progressive periphrase être en train de in
(22) whereas the “complete event” reading cannot. The availability of both
“complete event” and “ongoing readings” for French future tense sentences
supports the syncretism hypothesis against the semantic incompatibility hypothesis.
(22)
Demain à 8h, Jean sera en
train de promettre de
Tomorrow at 8 Jean be.fut in-the middle of promise.inf of
venir.
come.inf
Tomorrow at 8, John will be promising to come/John will be in the
middle of promising to come.
We end this section with languages without any perfective/imperfective distinction in any tense. German is such a language, yet it allows for both
“complete event” and “ongoing event” readings of sentences (Kratzer, 1998;
Csirmaz, 2004; Reyle, Rossdeutscher, and Kamp, 2007), as can be seen in
(23) (from Csirmaz (2004)). The “complete event” reading is highlighted by
the use of the adverb sofort and the “ongoing event” reading by the use of
gerade. Csirmaz (2004) also cites Hungarian as behaving in a parallel way
15
as German.
(23)
Als wir ankamen, telefonierte Julia (sofort/gerade).
as we arrived phoned
Julia (just/then)
When we arrived, Julia phoned straight away/ was talking on the
phone.
To sum up, the data presented in this section speaks in favor of the syncretism
hypothesis: the perfective/imperfective distinction is relevant semantically,
but not expressed morphologically in some tenses in some languages.
2.2
Syncretism: ambiguity or semantic underspecification?
Two analytical approaches are compatible with aspect syncretism: the imperfective form used in a context with aspect syncretism could be ambiguous
or its meaning could be underspecified. The ambiguity approach has been
proposed by Hacquard (2006) for French, among others. The underspecification approach is implicit in Malchukov (2009)’s treatment of Universal
1 and is proposed explicitly by Bar-El, Davis, and Matthewson (2005) for
St’át’imcets and Skwxwú7mesh. 7
Under the ambiguity analysis, perfective and imperfective operators are
mapped to the same morpheme in contexts with aspect syncretism. The
relationship between logical form (LF) and phonetic form (PF) is rendered
non-transparent, as many-to-one mappings are permitted. The ambiguity
analysis is pictured in (24), with {pfv, ipfv} ⊆ LF structures, {α, β} ⊆
PF structures. We call the morphemes that are mapped from an operator
“exponents” of these operators. Hence, α is the exponent of pfv and β the
exponent of ipfv in non-syncretic contexts.
(24)
Ambiguity analysis of aspect syncretism:
a. Non-syncretic context
(i) pfv → α
(ii) ipfv → β
b. Syncretic context
(i) pfv → β
7
Reyle, Rossdeutscher, and Kamp (2007, p. 614) also adopt an underspecification approach for German, formulated in Discourse Representation Theory.
16
(ii)
ipfv → β
Under the underspecification analysis, only the imperfective operator is morphologically available in contexts with aspect syncretism. Imperfective and
perfective meanings are assumed to be in a relation of asymmetric entailment,
with the imperfective having a more general meaning than the perfective
(JpfvK ⇒ JipfvK). The “ongoing event” reading that arises for morphologically imperfective sentences in contexts where there is a perfective competitor
available (e.g. the past tense in English and French) results from an implicature. In this analysis, the relationship between LF and PF is transparent.
The underspecification analysis is pictured in (25).
(25)
Underspecification analysis of aspect syncretism:
a. Non-syncretic context
(i) pfv → α
(ii) ipfv → β
b. Syncretic context
(i) pfv unavailable
(ii) ipfv → β
The two hypotheses are summarized in (26).
(26)
Syncretism in tense t is due to:
a. Ambiguity. The perfective and imperfective operators are
mapped to a single morpheme in tense t.
b. Underspecification. Only the imperfective operator is morphologically available in tense t.
In this section, we focus on an explanatory argument: how can each theory justify the non-existence of the pattern ruled out by Universal 1, where
perfective rather than imperfective morphology is extended to contexts with
aspect syncretism? In the ambiguity analysis of syncretism, the pattern ruled
out by Universal 1 is analyzed as in (27).
(27)
Ambiguity analysis of the Universal 1-incompatible syncretism pattern:
a. Non-syncretic context
(i) pfv → α
(ii) ipfv → β
17
b.
Syncretic context
(i) pfv → α
(ii) ipfv → α
Two hypotheses could be entertained to explain the preference for the pattern in (24) over (27). (H1) In languages where imperfective morphology is
used in contexts with aspect syncretism, imperfective morphology is simpler
than perfective morphology: the choice of the form is motivated by morphological or phonological simplicity. (H2) The “ongoing event” reading is more
frequent in contexts with aspect syncretism: the choice of the imperfective
form corresponds to an extension of the morpheme conveying the most likely
reading. The use of the imperfective stem in the present tense is compatible
with H2, as “complete event” readings of present tense sentences are arguably
infrequent (see section 3 on meaning probabilities). However, this is not the
case for the future tense: “ongoing event” readings are not more likely in the
future than “complete event” readings (see section 3). The only hypothesis
that could explain the preference for imperfective morphology in the future is
H1. However, Ancient Greek is problematic for H1: imperfective morphology
is extended to the future tense even in cases where it is more complex than
perfective morphology. The future form leip-so “I will leave” (transitive)
based on the imperfective stem leip- and not on the simpler, perfective stem
lip-. To sum up, the preference for imperfective morphology cannot be easily
explained under the ambiguity hypothesis.
In the underspecification analysis of syncretism, the pattern incompatible with Universal 1 is analyzed as in (28): the imperfective operator is
morphologically unavailable in syncretic contexts.
(28)
Underspecification analysis of the Universal 1-incompatible syncretism pattern:
a. Non-syncretic context
(i) pfv → α
(ii) ipfv → β
b. Syncretic context
(i) pfv → α
(ii) ipfv unavailable
We can explain why this pattern is unattested under the under-specification
analysis if we can show that pfv asymmetrically entails ipfv. Extending
18
ipfv to syncretic contexts should not necessarily result in a loss of expressive
power whereas extending pfv should. We show that this asymmetry follows
from the lexical entries for pfv and ipfv repeated below, if we assume in
addition that the part-of relation in the meaning of ipfv is reflexive.
(29)
a.
b.
JpfvK = λPhv, ti .λe.e is a complete P-eventuality
JipfvK = λPhv, ti .λe.e is a part of a complete P-eventuality
For any predicate of eventualities P, if e is a complete P-eventuality, then e
is part of a complete P-eventuality by reflexivity of the part-of relation. The
entailment relation is asymmetric. See Szabó (2004) for the same observation.
One typically infers from hearing a sentence like (30) that only a part of
a complete event of John baking the cake happened between 2 and 3 pm.
(30)
John was baking the cake between 2 and 3 pm.
Under the underspecification story, this inference is predicted to be an implicature and therefore to be suspendable. This prediction is borne out: (31b)
would not qualify as a coherent answer to the question in (31a) if a positive
answer to (31a) entailed that only a strict part of the event happened between
2 and 3 pm. This suggests that the underspecification analysis makes correct
predictions also for contexts where a perfective competitor is morphologically
available.
(31)
a.
b.
Was John baking the cake between 2 and 3 pm?
Yes, indeed, he baked it from 2:30 to 2:50.
In other words, in a syncretic context, imperfective morphology is compatible
with both “complete event” and “ongoing event” readings whereas perfective morphology would be compatible with the “complete event” reading
only. Extending perfective morphology would result in loss of expressive
power, i.e. the impossibility to convey the “ongoing event” reading, whereas
extending imperfective morphology does not. To sum up, the underspecification hypothesis is explanatorily superior to the ambiguity hypothesis as it can
account for why the imperfective might be extended whereas the ambiguity
hypothesis cannot.
19
2.3
Refining the underspecification analysis
In tenses with aspect syncretism, sentences with an imperfective morpheme
license stronger inferences than what is allowed by the underspecification
approach as presented so far.8 Consider the French sentence in the future
tense in (32). The meaning for this sentence is shown in (33), where the
part-of relation is reflexive.
(32)
Jean grimpera
la montagne entre
6h00 et 7h00.
Jean climb.ipfv.fut.3sg the mountain between 6am and 7am
Jean will climb/be climbing the mountain between 6 am and 7 am.
(33)
J[fut [[pfv [Jean grimper la montagne]] [entre 6h00 et 7h00]]]Ku =
1 iff
∃t[t> τ (u) & ∃e[e is a part of a complete event of Jean climbing the
mountain & τ (e)⊆[6 am, 7 am] & τ (e)=t]]
Based on (33), it is predicted that only a weak belief should be attributed to
the speaker of (32) by the hearer, i.e. the belief in (34).
(34)
Bspeaker (Jean will finish climbing the mountain before or after 7 am)
However, stronger beliefs might be attributed to the speaker by the hearer,
as suggested by possible comments a hearer hearing (32) might make.
(35)
a.
b.
c.
So, Jean will have finished climbing the mountain by 7.
So, Jean will finish climbing the mountain after 7.
So, you don’t know whether he will finish climbing the mountain
before or after 7.
The comment in (35a) corresponds to the speaker belief state in (36a), etc.
All these belief states are refinements of the belief state in (34).
(36)
a.
Bspeaker (Jean will have finished climbing the mountain by 7 am)
b.
Bspeaker (Jean will finish climbing the mountain after 7 am)
8
Only upward entailing contexts are considered here. In downward entailing contexts,
weaker inferences are licensed than predicted under the underspecification approach as
presented so far. The proposal presented in this section can also account for downward
entailing contexts.
20
c.
The speaker does not know whether Jean will have finished
climbing the mountain by 7 am or will finish climbing it after 7
am
How do these refinements come about in the absence of a perfective competitor? The ambiguity analysis seems better armed to deal with these facts,
as it assumes that a perfective operator is available in contexts with aspect
syncretism: the belief state in (36a) is inferred if the imperfective morphology is disambiguated as expressing a perfective operator, and the two belief
states in (36b) and (36c) are inferred if the disambiguation is in favor the
imperfective operator. However, the ambiguity analysis is not desirable for
reasons discussed in the previous section. What is needed is a mechanism
that strengthens the meaning of a semantically underspecified morpheme
without resorting to pragmatic competition between two morphemes. The
lexical uncertainty model of implicatures proposed by Bergen, Goodman, and
Levy (2012) and the “semantic free variables” model of positive adjectives
proposed by Lassiter and Goodman (2013) do exactly that: these approaches
allow for a competition between the underspecified meaning of a morpheme
α and stronger alternative meanings for α. For concreteness, we adopt Lassiter & Goodman’s (2013) proposal. Meaning competitors are generated as
follows: (i) an abstracted version of a lexical entry with meaning λy.C(y)
is obtained by conjoining a free predicate variable to it, λF.λy.C(y)&F (y),
where the variable F represents the enriched semantic content the lexical
entry will denote, and (ii) the meaning obtained by filling the F argument
may compete with the basic meaning λy.C(y). F is inferred from the context
in which the sentence is uttered.
The abstracted versions of the meanings of imperfective and perfective
morphemes are shown in (37).
(37)
a.
b.
Jipfvabstract K = λQhhv, ti, hv, tii .λPhv, ti .λe.e is a part of a complete
P-eventuality & Q(P)(e)
Jpfvabstract K = λQhhv, ti, hv, tii .λPhv, ti .λe.e is a complete Peventuality & Q(P)(e)
Assuming that only ipfv and pfv can be arguments of ipfvabstract and
pfvabstract , the only refinements available are obtained by feeding JipfvK
and JpfvK as arguments to Jipfvabstract K and Jpfvabstract K. Among the four
refined meanings obtained by this operation, only ipfvabstract (pfv) results in
a meaning stronger than the basic meaning. This meaning is equivalent to
21
that of pfv.
(38)
Jipfvabstract (pfv)K = λPhv, ti .λe.e is a part of a complete Peventuality & e is a complete P-eventuality = JpfvK
Effectively, this system amounts to making a strictly perfective reading available in contexts with aspect neutralization. The inferences in (35) can now
be explained as follows: the belief state in (36a) is inferred when the speaker
is inferred to use the refined lexical entry for imperfective and the belief
states in (36b) and (36a) are inferred when the speaker is inferred to use the
basic lexical entry. This approach allows us to retain advantages of both the
underspecification and the ambiguity analyses. It explains why ipfv is used
rather than pfv in a tense with aspect syncretism and how ipfv can be used
with the meaning of pfv in this tense. In tenses without aspect syncretism,
ipfv does not get the strengthened “complete event” meaning because pfv
is available. From the perspective of the hearer, the difference between tenses
with and without aspect syncretism can now be characterized as follows: (i)
in tenses with syncretism aspect, the hearer must use the context to guess
whether the speaker intended an LF with the refined or with the basic meaning for ipfv and (ii) in contexts without aspect syncretism, the hearer does
not have to guess because the refined meaning for ipfv must be expressed
by a different morpheme, the exponent of pfv.
3
Deriving Universals 2 and 3
The difference between the four attested types of patterns (English, Greek,
French, and German) can be characterized as follows: all grammars share
the same rule for TP and AspP in (39) but differ in the derivation of the Asp
node, as shown in (40).
(39)
TP → T AspP
AspP → Asp VP
(40)
a.
b.
English grammar (context-free)
Asp → pfv|ipfv
Greek grammar (context-sensitive)
Asp → pfv|ipfv/T → past|T → fut
Asp → ipfv /T → pres
22
c.
d.
French grammar (context-sensitive)
Asp → pfv|ipfv/T → past
Asp → ipfv/T → pres|T → fut
German grammar (context-free)
Asp → ipfv
In this section, we tackle the question of why only those four types of languages are attested among the eight logically possible ones.
3.1
Meaning probability asymmetries
To our knowledge, Comrie (1976) was the first to observe that the typology of aspect neutralization across tenses correlates with frequency asymmetries between perfective and imperfective morphologies across tenses (see also
Malchukov (2009)). His observation was based (i) on the frequency of use of
perfective and imperfective aspects in the future and in the past in a corpus
of Russian dialogs, shown in Table (43)9 and (ii) on the rarity of contexts
allowing for “complete event” readings of English present tense sentences.
These contexts - performative sentences, sportcaster present tense, historical present - are rare enough that many authors have considered present
perfective sentences to be ungrammatical.
Past
Future
Perfective
0.70
0.94
Imperfective
0.30
0.06
Figure 1: Frequency of use of perfective and imperfective in the past and in
the future (Josselson, 1953).
Assuming that the frequency of perfective presents is smaller than the
frequency of imperfective futures, we get the following ordering of the contexts, from the one with the largest asymmetry to the one with the smallest
9
We use Josselson’s (1953) data to estimate P(T|pfv), P(T|ipfv), P(ipfv), and P(pfv)
and, from those, we compute P(pfv|T) and P(ipfv|T) using the equations below.
(
(T |pf v)P (pf v)
= PP(T
|ipf v)P (ipf v)
P (pf v|T ) + P (ipf v|T ) = 1
P (pf v|T )
P (ipf v|T )
23
asymmetry: present > future > past. This ordering mirrors the order in
which aspectual distinctions are neutralized: first in the present, then in the
future, and finally in the past.
How reliable are Josselson’s estimates? One has to be cautious in using
Josselson’s (1953) data to infer the frequency of “complete event” readings
and “ongoing event” readings, as morphemes labelled as perfective and imperfective in Russian may have additional readings. In particular, sentences
in the imperfective in Russian are also compatible with habitual/generic
readings and, for some verbal phrases, with “complete event” readings. Using the imperfective morpheme frequency in Russian as an estimate of the
probability of the “ongoing event” meaning will necessarily yield to an overestimation. The question is whether this overestimation is uniform across
past and future tenses. Mathew and Katz (2009) showed that the proportion of habitual readings is larger in the present than in the past in English.
There is no data to our knowledge about the difference between past and
future tenses. To control for this, one should use a corpus where habitual,
“complete event” and “ongoing event” readings are distinguished. To our
knowledge, there is no such corpus available now. See Mathew and Katz
(2009) and Friedrich and Pinkal (2015) for developments to disambiguate
habitual and episodic readings of English sentences using machine learning
methods.
As far as we know, there is no numerical data to support the intuition
that the asymmetry is the largest in the present tense. The difficulty here
is due to the fact that (i) perfective morphemes are rarely attested in the
present tense across languages and (ii) in languages where they are (as in
English), they have additional readings (e.g. habitual readings in English),
making it hard to estimate the probability of “complete event” readings.
Assuming those asymmetries are real, where do they come from? It is
intuitive to see why present perfective sentences may rarely occur. For a
perfective present LF to be true, it must be the case that an event in the
denotation of the VP happens exactly at the same time as the speaker utters the sentence or at a subinterval of the utterance time. Arguably, this
can happen only in a very limited set of contexts, for instance when the VP
denotes a property of events that can be predicated of the utterance event
itself, as with performative verbs, or when in a conversational context that
allows for literally false sentences to be uttered felicitously, e.g. in the relating of sports events with the sportscaster present and of past events with
the historical present. Why should “complete event” readings of sentences
24
be more probable in the future than in the past? The reason is less obvious,
as time intervals qualifying as past or future intervals are not subject to the
same kind of time constraints as the present. We tentatively propose that it
is because the relating of past events tends to be more detailed than predictions about future events in human conversations: intuitively, past narratives
typically involve reports of more intricate situations than predictions about
the future.
3.2
Informativity
In tenses with aspect syncretism, only ipfv is available. A hearer will have to
guess whether the speaker intended the refined lexical entry for ipfv (equivalent to the meaning of pfv) or the basic lexical entry. If he chooses the
former option, then he will infer that the speaker expresses a belief about
a complete event. If he chooses the latter one, then he will infer that the
speaker either expresses a belief about a part of complete event or is ignorant
about whether the event is a part of a complete event or a complete event
(see section 2.3). These two choices are exhaustive and mutually-exclusive.
Therefore, their probabilities sum to one. Different guessing strategies might
be considered. (a) The hearer might choose randomly one of the two options.
(b) He might choose one of the two options according to their probabilities
in a given context. (c) He might choose to default to the most likely option
in a given context. The hearer’s guess will be correct if the lexical entry intended by the speaker and the lexical entry guessed by the hearer match and
incorrect if they don’t. The probability of correct and incorrect guesses will
depend on the strategy adopted by the hearer, as shown in (41). We call m1
and m2 two exhaustive and mutually-exclusive meanings the hearer is trying
to guess. The probabilities of correct and incorrect guesses are relativized to
a context ci .
(41)
Potential hearer strategies
a. Random choice
(i) P (error|ci ) = P (m1 |ci ) ∗ 0.5 + P (m2 |ci ) ∗ 0.5 = 0.5
(ii) P (correct|ci ) = P (m1 |ci ) ∗ 0.5 + P (m2 |ci ) ∗ 0.5 = 0.5
b. Choice according to underlying probabilities
(i) P (error|ci ) = P (m1 |ci ) ∗ P (m2 |ci ) + P (m2 |ci ) ∗ P (m1 |ci ) =
2P (m1 |ci )P (m2 |ci )
(ii) P (correct|ci ) = P (m1 |ci )2 + P (m2 |ci )2
25
c.
Choice of the most likely meaning
(i) P (error|ci ) = min{P (m1 |ci ), P (m2 |ci )}
(ii) P (correct|ci ) = max{P (m1 |ci ), P (m2 |ci )}
The strategy that mimimizes the probability of error is the “default to the
most likely meaning” strategy in (41c). The graph in Figure (41) shows that
the probablity of error is smaller with this strategy than with the two other
strategies for any probability assigned to m1 . We assume that hearers are
rational agents and therefore adopt the “default to the most likely meaning”
strategy.
Figure 2: Probability of incorrect guesses under the three hearer strategies
in (41)
Because the probability of incorrect guesses in a given context is equal
to the smallest meaning probability in this context under the “default to the
most likely meaning” strategy, the larger the asymmetry in a context, the
smaller the error. Based on the data in the previous section, it is predicted
that, for a given verbal phrase, the probability of incorrect aspect guesses
26
should be larger in the past than in the future, and larger in the future
than in the present. In other words, present tense is the most informative
about aspect whereas past tense is the least informative. Instead of using the
probability of error as a measure of informativity, we could use Shannon’s
entropy, as is done in Piantadosi, Tily, and Gibson (2011). The same predictions would follow. The entropy of a binary random variable increases, i.e.
predicting its outcome (success or failure) on a given trial becomes harder,
as the probability of success gets closer to 0.5 (MacKay, 2003, p. 2).
3.3
A model for syncretism
In this section, we propose a model relating informativity and patterns of
syncretism. In this model, two pressures are in conflict: the pressure to minimize misinterpretation on part of the hearer and the pressure to minimize
the effort involved in processing rich morphology (see Jäger (2007) for a similar proposal to derive the typology of case marking). Not marking a semantic
distinction morphologically incurs a cost, called the ambiguity cost. Marking
a semantic distinction morphologically also incurs a cost, called the processing cost. Lexicons with varying degrees of syncretism in the expression of two
(exhaustive and mutually-exclusive) meanings m1 and m2 across n contexts
will be evaluated with respect to a weighted sum of the ambiguity cost and
the processing cost. These costs contain (i) a language-universal component
(the definitions of the cost) and (ii) a language-specific component (represented by language-specific, positive weights wA and wP for ambiguity and
processing respectively). We show (i) how the language-universal component
predicts that languages should display asymmetric patterns of syncretism if
the meanings and contexts have asymmetric probabilities universally and
(ii) how the language-specific component predicts that varying degrees of
syncretism should exist across languages.
Informally, languages with overt aspectual distinctions minimize the risk
of ambiguity. Formally, the ambiguity cost of having two exhaustive and
mutually-exclusive meanings m1 and m2 mapped to the same morphological
expression ei in a context ci is assumed to be proportional to the probability of misinterpretation on part of the hearer. We note this probability
P(error & ci ), with P(error & ci )=P(error|ci )P(ci ). P(error|ci ) is defined in
the preceding section. The ambiguity cost of having two meanings m1 and
m2 mapped to two different morphological expressions e1 and e2 in a context
ci is assumed to be equal to 0. This is because, if the two meanings are distin27
guished morphologically, a hearer can deterministically recover the meaning
intended by the speaker (we leave aside the possibility of mishearing).
We further assume that languages may vary in the importance attributed
to minimizing misinterpretation. This is implemented by multiplying the
probabilities of misidentification in syncretic and non-syncretic contexts by
a language-specific, positive weight wA , where A stands for ambiguity. Note
that this assumption does not entail that a language as a whole will be more
ambiguous than another language: other sets of meanings might have different weights. For instance, French has more syncretism than English in
the aspectual domain under discussion, but less syncretism in the domain of
gendered pronouns: gender distinctions are available in the plural in French
(ils/elles) but not in English (they). In our framework, this difference is
interpreted as follows: English has a larger ambiguity weight for aspectual
meanings than French (wA,English,aspect > wA,F rench,aspect ) but a smaller ambiguity weight for gender meanings (wA,F rench,gender > wA,English,gender ).
In sum, the ambiguity cost for syncretic and non-syncretic expressions
of two meanings m1 and m2 in a context ci and a language with ambiguity
weight wA can be written as follows:
costA (ci ) = 0
costA (ci ) = min{P (m1 |ci ), P (m2 |ci )}P (ci )wA
if no syncretism
if syncretism
Intuitively, having two words available in a context ci should be costlier
than having just one. It seems unlikely that it is just because of lexicon or
grammar size, as memory is cheap. Following Wasow, Perfors, and Beaver
(2005), Piantadosi, Tily, and Gibson (2011), and Wasow (2015), we assume
that the cost of having more morphological distinctions available in a context
ci should be understood in terms of processing efficiency: the hearer must allocate attention resources to identify which word among a set of possibilities
was uttered. It is well-known in the processing literature that frequent morphemes are easier to process than less frequent ones (Jaeger and Tily, 2011).
However, there is also evidence that only the processing of open class items
is influenced by frequency (Bradley, 1978). Because we are dealing with the
meanings of closed class items in this paper, we do not allow for a role of
frequency in the processing cost of words e1 and e2 with meanings m1 and
m2 . This means that, as far as the processing cost is concerned, syncretism
should be equally good in any context. The processing cost of having two
meanings m1 and m2 mapped to the same morphological expression ei in a
28
context ci is assumed to be equal to 0. This is because the hearer does not
have to pay attention to which word was uttered in a syncretic context as
there is just a single option (here, we ignore the fact that morphemes’ sizes
may vary across languages).
We further assume that languages may vary in the importance attributed
to the processing cost. This is implemented by multiplying the processing
cost in syncretic and non-syncretic contexts by a language-specific, positive
weight wP , where P stands for processing. Here again, this assumption does
not entail that a language as a whole will be less complex morphologically
than another language: other sets of meanings might have different processing weights. Going back to the difference between French and English,
English may be analyzed as having a smaller processing weight for aspectual meanings than French (wP,English,aspect < wP,F rench,aspect ) but a larger
processing weight for gender meanings (wA,English,gender < wA,F rench,gender ).
In sum, the processing cost for syncretic and non-syncretic expressions
of two meanings m1 and m2 in a context ci and a language with processing
weight wP can be written as follows:
costP (ci ) = wP
costP (ci ) = 0
if no syncretism
if syncretism
For a given context ci , it will be preferable to have syncretism or no
syncretism depending on which of the two costs is larger. If costA (ci ) >
costP (ci ), it is preferable to have a non-syncretic expression of meanings m1
and m2 in ci . If costA (ci ) < costP (ci ), it is preferable to have a syncretic
expression of meanings m1 and m2 in ci . These relations can be rewritten in
terms of the probabilities of meanings and contexts using our definitions of
the ambiguity and processing costs. It is equally good to have syncretism or
no syncretism if the following holds:
min{P (m1 |ci ), P (m2 |ci )}P (ci )wA = wP
(1)
Equation (1) is equivalent to:
min{P (m1 |ci ), P (m2 |ci )} =
wP
1
∗
P (ci ) wA
29
(2)
Note that what matters is the ratio wP /wA rather than the individual
values of wA and wP . Assuming that none of the probabilities are equal to
zero, we can take the natural logarithm of both sides of equation (2) and we
obtain equation (3):
log(min{P (m1 |ci ), P (m2 |ci )}) = −log(P (ci )) + (log(wP ) − log(wA )) (3)
Equation (3) is the equation of a line with slope −1 and intercept
log(wP ) − log(wA ). This line is graphically represented in Figure 3.3,
for arbitrarily chosen weights. P (ci ) takes values between 0 and 1 and
min{P (m1 |ci ), P (m2 |ci )} takes values between 0 and 0.5. The intercept will
vary as a function of wP and wA : the larger the ratio wP /wA , the larger the
intercept; the smaller this ratio, the smaller the intercept.
The region above the line corresponds to contexts where it is less costly to
have syncretism than no syncretism (costA (ci ) < costP (ci )), i.e. where syncretism is desirable. The region under the line corresponds to contexts where
it is less costly to have no syncretism than syncretism (costA (ci ) > costP (ci )),
30
i.e. where syncretism is undesirable. We assume that, for a given context ci ,
the probabilities P(m1 |ci ), P(m2 |ci ), and P(ci ) are drawn from the same probability distribution for all languages. This means that languages only vary in
their weights. Because the slope is the same across languages, it is predicted
that the presence of syncretism in some contexts will always asymmetrically
entail the presence of syncretism in other contexts. For instance, syncretism
in a context with a larger probability and a smaller asymmetry between the
meaning probabilities entails syncretism in a context with a smaller probability and a larger asymmetry between the meaning probabilities. Absence
of syncretism in a context with a smaller probability and a larger asymmetry
between the meaning probabilities entails absence of syncretism in a context with a larger probability and a smaller asymmetry between the meaning
probabilities. This can be reformulated graphically. For any line with equation (3), (i) if a point in the north-east region of the graph is under it (i.e. is
a syncretic context), then any point in the south-west region of the graph is
also under it (i.e. is a syncretic context) and (ii) if a point in the south-west
region of the graph is above it (i.e. is a non-syncretic context), then any point
in the north-east region of the graph is also above it (i.e. is a non-syncretic
context). Because the intercept of the line varies across languages, it is predicted that some languages will have more syncretism than others, and will
also neutralize distinctions in the south-west region before distinctions in the
north-east region.
3.4
Universals 2 and 3
We apply the model of syncretism to the case of aspect syncretism across
tenses. We make two simplifying assumptions. First, tense is assumed to be
always conveyed unambiguously. We do not allow for tense syncretism, even
though it exists in some languages (Ultan, 1978), for instance in Japanese,
where the morpheme defined as present has a non-past meaning (Ogihara,
2007), and in Murrinh-Patha, where the morpheme defined as present has a
non-future meaning (Nordlinger and Caudal, 2012). We assume that there
are always other cues available in the context for the temporal interpretation
of a sentence in case of syncretism. See section 4 for more discussion.
Second, the probability of a speaker intending a “complete event” or
an “ongoing event” interpretation is assumed to be independent from the
VP. Doing so, we ignore well-known preferences for grammatical and lexical aspect combinations. In English, Achievement VPs, as win the race,
31
with imperfective aspect sound more marked than activity VPs, as run,
with imperfective aspect (see Dowty (1979, p. 60)). In some languages,
sentences with achievement verbs do not allow for imperfective readings
(Csirmaz (2004) on Hungarian and Kratzer (2002, pp. 31-32) and Reyle,
Rossdeutscher, and Kamp (2007, p. 7) on German). Also, languages show
evidence for aspect syncretism conditioned by verbs. For instance, English
does not distinguish perfective and imperfective interpretations of sentences
with be whereas French does in the past. Sentence (42) is ambiguous between
a perfective reading and an imperfective readings. Those two readings are
morphologically distinguished in French, as can be seen in (43).10
(42)
Yesterday I was sick.
(43)
a.
b.
Hier
j’ étais
malade.
yesterday I be.ipfv.past sick
I was sick throughout yesterday.
Hier
j’ ai été
malade.
yesterday I pfv be.past sick
I was sick at some period of time yesterday.
We leave the question of aspect syncretism conditioned by verb type aside,
as it has not been investigated in a systematic manner in the typological
literature and it is not clear what the attested patterns are. See section 4 for
more discussion.
We now need estimates for the probabilities of pfv and ipfv given a tense,
noted P(Asp|T), and the probabilities of tenses, noted P(T). We use tense
and aspect token frequencies in corpora of oral speech, as recommended by
Croft (2003, p. 87). For P(Asp|T), we use (Josselson, 1953). Because only the
imperfective morphology occurs in the Russian present tense, P(pfv|pres)
10
The verb be can co-occur with the imperfective morpheme be -ing with some adjectives
in English, e.g. be silly can occur both in the simple past and with the imperfective, in
(ia) and (ib) respectively (see Comrie (1976, p. 36)). We analyze cases like (ib) as a
recategorization of a stative verb as an activity verb: sentence (ib) is paraphrasable as
John was acting in a silly manner. Sentence (ia) remains compatible with an episodic
perfective reading (scenario: John was just silly at the moment of the call) and an episodic
imperfective reading (scenario: John was silly for a period of time that includes the time
of the call and may extend after the call).
(i)
a.
b.
When I called him, John was silly. episodic perfective/episodic imperfective
When I called him, John was being silly.
32
cannot be estimated using this source. We assume P(pfv|pres)=0.01.11
Perfective
Past
0.70
Future
0.94
Present
0.01
Imperfective
0.30
0.06
0.99
Figure 3: Estimates for P(pfv|T) and P(ipfv|T).
For P(T), we use tense frequencies in an English oral corpus from Szagun
(1978). They are frequencies of use of semantic tenses rather than morphological tenses. For instance, present tense sentences with future meaning are
counted as futures. German tenses have very similar probabilities according
to Szagun (1978).
Past
Future
Pres
0.44
0.16
0.42
Figure 4: Estimates for P(T).
The model predictions for 4 different values for wA are plotted on the
graph below (wP = 1). Each tense ci is represented with two coordinates: (i)
on the x-axis, the log value of the smallest of the two meaning probabilities
in ci , and (ii) on the y-axis, the log probability of ci . The lines represent
values for x and y for which the cost of having a morphological distinction is
equal to the cost of having aspect syncretism.
11
Crucially, it must be smaller than P(ipfv|past) and P(ipfv|fut).
33
Figure 5: Predictions
The asymmetry between pfv and ipfv being larger in the present tense
than in the future tense, it is predicted that no language should have aspect
syncretism in the future and not in the present. The probability of present
perfective sentences is small enough compared to the probability of future
tense to ensure that syncretism should be preferred in the present than in
the future. The asymmetry between pfv and ipfv being larger in the future
tense than in the past tense and the probability of past being larger than
the probability of future, it is predicted that no language should have aspect
syncretism in the past and not in the future. Universals 2 and 3 are derived.
3.5
Deriving preferences among language types
There are preferences among the four attested types of languages, at least
based on typologists’ intuitions (see introduction). Languages with fewer
morphological distinctions are favored. This can be derived by our model
assuming an overall preference for minimizing processing complexity over
misinterpretation. Lexicons with varying degrees of syncretism across n contexts are represented as vectors of length n, as in (44).
(44)
A lexicon x is a vector of length n where:
34
x[j] = 0 if j is a context with aspect syncretism
x[j] = 1 if j is a context without aspect syncretism
Lexicon probabilities are calculated based on the costs and the weights. The
calculation proceeds in several steps. To begin, we find what we will call the
score or harmony of each lexicon. This is the weighted sum of the lexicon
processing and ambiguity costs, as defined in (45) (Smolensky and Legendre,
2006).
(45)
The score of a lexicon x, denoted h(x), is
n
P
h(x) =
wP ∗ costP ∗ x[i] + wA ∗ costA ∗ abs(x[i] − 1)
i=1
where
n
P
denotes summation over all contexts c1 , ..., cn
i=1
abs(x[i] − 1) is equal to 0 if there is a distinction in ci , and to 1 if
there is none
Then, we set wP = 1 and vary only wA . This is possible as what matters for
the model predictions is the ratio wP /wA . Values for wA are generated in
two steps: (i) 1000 numbers are generated from an exponential probability
distribution with parameter λ = 0.5 and (ii) values for wA are generated by
raising e to these numbers. The first operation ensures that smaller values
of wA are more probable than larger values. The second operation is our
attempt to undo the preference for minimizing processing cost that was built
in the formulation of the model. The presence of a morphological distinction
is associated with a processing cost of 1 whereas the absence of morphological
distinction is always associated with an ambiguity cost smaller than 1. By
obtaining wA via exponentiation, we aim at generating larger values for wA
and counterbalancing the built-in preference for syncretism.
The probability of each lexicon type x among the eight possible types
is obtained by counting the number of times x is the winner (i.e. has the
highest score) for the 1000 values of wA and dividing this number by 1000.
The lexicon probabilities predicted by the model are shown in Figure 6.
35
Figure 6: Predicted lexicon probabilities. 1: aspectual distinctions across
all tenses; 2: only the present has no aspectual distinction; 3: aspectual
distinctions in the past only; 4: no aspectual distinction in any tense
With the assumption that there is an overall preference for minimizing
processing cost over ambiguity cost, the model predicts that patterns without perfective/imperfective distinction in any tense (type 4) should be most
probable, followed by patterns with a distinction in the past and none in the
present (types 2 and 3), and finally by patterns with full aspectual distinctions across tenses (type 1). These predictions are in line with typologists’
intuitions about cross-linguistic preferences.
4
Discussion
In this section, we discuss the need to get better data in order to put our
model to a more stringent test, we mention possible extensions of the model
and compare it to an alternative, learnability-based model of syncretism.
36
4.1
Quality of the data
The model helps understand the typology of aspect neutralization across
tenses as it is reported in the literature in a way that was never done before.
However, the data the model relies on could be improved.
First, more typological work is needed in order to make sure that the
observed asymmetries are real and not too dependent on languages where
data and analyses are available, i.e. Indo-European languages. Quantitative
data should be collected about the frequency of aspect neutralization patterns
in order to get a more reliable picture than what is now available.
Second, better corpora are needed to obtain better estimates of aspect
and tense probabilities. One major obstacle has to do with aspectual and
temporal morphemes being highly ambiguous across languages. Both the estimates of aspectual meaning based on Josselson (1953) and temporal meanings based on Szagun (1978) are not perfect, in particular because habitual
readings of sentences are not factored out. To remedy this problem, manually
or automatically annotated corpora should be used. Recent efforts towards
developing algorithms to distinguish habitual and episodic readings of sentences (Mathew and Katz, 2009; Friedrich and Pinkal, 2015) could be very
useful in helping get better meaning probability estimates.
4.2
Extensions
We assumed in the model that tense is always expressed and is used in order to disambiguate the aspectual interpretation of a sentence. However,
as noted earlier, tense syncretism is found in a number of languages (Ultan,
1978). Note that, given the asymmetries in the probabilities of aspects across
tenses, it is expected that aspect is also informative about tense. In particular, in the absence of temporal marking, a perfective form is more likely to
have a non-present interpretation and an imperfective form to have a present
interpretation. On this basis, one can imagine a linguistic system that would
use massive tense syncretism and use aspectual distinctions to disambiguate
temporal reference. As the question of how the typology of tense syncretism
and aspect syncretism interact remains unclear now, we leave this question
for further research.
We assumed in the model that lexical aspect is not relevant to grammatical aspect disambiguation. This was mainly for practical purposes, as
the question of how aspect neutralization interacts with lexical aspect cross37
linguistically was never addressed in a systematic way in the literature. We
could integrate verb types in the context and see what predictions it makes
regarding aspect syncretism. We would need data on the probability of “complete event” and “ongoing event” readings for each type. If achievements
are typically more probable with “complete event” interpretations, statives
with “ongoing event” interpretations, and activities have more balanced interpretations, we expect that aspect syncretism with actitivity verbs should
asymmetrically entail aspect syncretism with achievement and stative verbs.
The fact that English shows some degree of syncretism with stative verbs is
consistent with this picture.
Aspect neutralization also happens in modal contexts, the most famous
case being counterfactuals (Iatridou, 2000). According to Comrie (1976),
modals have the same position as the future tense in the typology of aspect
neutralization. The model proposed here cannot directly extend to modal
contexts, as they involve additional syntax and more complex semantics.
Other factors than informativity might play a role in explaining why aspectual distinctions are preferably neutralized in modal contexts than in the past
tense, for instance. Not expressing aspectual distinctions under modals could
be a way to compensate for the morphological cost of expressing modality.
However, it is likely that informativity still plays a role, as aspect neutralization with modals entails aspect neutralization in the present tense, a nonmodal context. If only complexity mattered, one might expect neutralization
in modal contexts to be preferred over neutralization in the present and in
the past in some languages. However, this does not seem to happen.
4.3
Alternative model
The hypothesis that frequency asymmetries and syncretism asymmetries are
related has been developed for other cases of syncretism (e.g. Haspelmath
(2006) on gender syncretism across numbers). A popular way of accounting
for frequency-based syncretism is to say that rarer morphological combinations are harder to learn and therefore are the first to be lost in language
change (Haspelmath, 2006, p. 48):
“Syncretism is generally found to a greater extent in rarer
inflectional categories (and more generally in rarer words/word
types) because it is more difficult to remember the distinct forms
when they do not occur often.”
38
This hypothesis predicts that, in case of syncretism in a context ci , the
morpheme associated with the most likely meaning in ci should be used. The
reason is the following: if one of the two morphemes conveying meanings m1
and m2 is not learnt in ci , this morpheme will be the one with the smallest
probability in ci . In the specific case under study, it is correctly predicted
that the imperfective should be used alone in the present tense in case of
syncretism and it is wrongly predicted that the perfective should be used
alone in the future tense in case of syncretism. In contrast, our proposal does
not predict that the morpheme that should be used in case of neutralization
in a context ci is the one corresponding to the most likely meaning in ci .
5
Conclusion
Asymmetries in the typology of aspect neutralization across tenses were derived with two main hypotheses. Imperfective morphology is preferred in
contexts with aspect neutralization because it allows for more expressivity
than perfective morphology. All tenses do not behave alike with respect to
aspect neutralization because they are not as informative about aspectual
meanings: syncretism happens preferably in tenses that are more informative about aspect. The analysis improves on previous analyses, in particular Comrie (1976) and Malchukov (2009), by providing an explicit model
of syncretism and a reason for the preference for imperfective morphology
in syncretic contexts. The ultimate success of the analysis depends on the
quality of the typological and corpus data. It is hoped that future work will
dig further into these areas and make it possible to put the model to a more
stringent test.
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