The notion of roles and the role use of English nominal as-phrases
Sarah Zobel (University of Tübingen)
In this talk, I argue that natural language is sensitive to the notion of roles and that our
formal system should distinguish (at least) class nouns from role nouns. That is, role
nouns, in contrast to class nouns, are interpreted relative to a domain of roles. The sensitivity to roles can be observed, for instance, for the role use of English nominal as-phrases
(“role as-phrases”): sentences that contain a role as-phrase make statements about a role
structure R, which I add as an additional interpretation parameter.
Class nouns describe properties that are ascribed to individuals independently of any
relation that this individual might bear to other individuals; for example: man, woman,
dog, cat, tree. They denote predicates of individuals, as standardly proposed for nouns
(e.g., Heim & Kratzer 1998; for reasons of simplicity, I assume an extensional system
with individuals, truth values, and eventualities).
(1)
JtreeK = λxe .tree’(x)
In contrast, role nouns describe properties that are ascribed to individuals based on certain
relations that they bear to other individuals: student, lawyer, janitor, pet. I argue that role
nouns denote single roles, i.e., members of a domain Dr containing reified roles.
(2)
JjudgeK = rjudge’
rjudge’ ∈ Dr
Reified roles are independent of their bearers, i.e., two individuals may bear the same role.
They can be individuated through the specific rights and duties that are attached to them,
i.e., the role of a lower ranked judge is distinct from the role of a higher ranked judge, but
both are sub-roles of judge (see Sowa 1984, Steimann 2000). Note, nouns for artifacts,
like peeler, have a dual status: artifacts are created to perform a specific role/function.
De Swart et al. (2007) propose the similar but much more restricted notion of “capacity”.
They aim to account for fact that in some languages that otherwise do not allow singular
nouns to occur bare (e.g., German), bare singular nouns can be used in copular constructions if the noun denotes a capacity but not if it is a class noun, see (3). Nouns denote
capacities if they describe “professions, religions, nationalities or other roles in society”.
(3)
Paul ist (ein) Arzt. (‘Paul is a doctor’) VS . Kitty ist *(eine) Katze. (‘Kitty is a cat’)
Similarly, role as-phrases differentiate between role and class nouns. Sentences containing role as-phrases ascribe the property denoted by the main predicate to the associated
individual of the as-phrase (Paul in (4)) in the role that is given by the complement of as.
(4)
As a doctor, Paul earns 3,000 euros. (≈ Paul earns 3,000 euros in his doctor-role)
The role use is only available if the complement of as denotes a role. In (5), man and
young, talented doctor do not describe roles (note: modification of a role noun may lead
to a nominal expression that does not denote a role), hence the as-phrases do not restrict
predication to a role; instead, they intuitively give reasons for why Paul earns 3,000 euros.
(5)
As a man / as a young, talented doctor, Paul earns 3,000 euros.
This is supported by the observation that only (4) but not (5) can be continued with ‘. . . but
as a janitor, he earns less’ to contrast Paul’s earnings in his janitor- and his judge-role.
Do we need roles AND capacities? We need capacities to exactly delimit the types of
nouns that can occur as bare singulars in copular constructions, as in (3), but the notion
is too strict to capture the behavior of role as-phrases: e.g., in ‘Paul used the book as a
paddle’, the book is said to have served the role of a paddle, but paddle is not a “role in
society” and does not denote a capacity. I propose that capacities are a subclass of roles.
For the behavior of role as-phrases, I account with the role structure R, which is built
on one central idea: for each individual x, there is a set of states and events in which
x participates; associating these states and events with the roles in which x participated
in them creates a structure on this set. Formally, a role structure R is a set of triples
containing an individual, a role, and an eventuality (= a state or event). The following
rules constrain the structure: (I) For each role ri borne by an individual x, R contains at
least one triple hx, ri , ei, where e can be a state or an event. As a consequence, copular
sentences involving role nouns in German and English, as in (6), can be analyzed as
expressing that an individual bears a certain role.
(6)
Paul ist (ein) Richter. (‘Paul is a judge.’)
(∃e[hPaul, rjudge’ , ei ∈ R])
Using this idea, we can formulate a type shifter B. Applying B to a role noun yields the
set of individuals that currently bear that role, i.e., the noun’s traditional denotation.
(7)
B(JjudgeK) = λxe .∃e[hx, rjudge’ , ei ∈ R]
(see CAP in De Swart et al. 2007)
(II) For each individual x and its roles ri , the set of triples contained in R correspond
only to the properties that are ascribed to x in these roles.
Inferences/dependencies between the entries of the role structure R and the individual x
simpliciter (independently of any role) are regulated by the rules in (8), which are sensitive
to the type of eventuality. For any eventuality e and eventuality description P :
(8)
– State e: hPaul, rjudge’ , eP i 6→ P (Paul)(e) AND ∀r[P (Paul)(e) → hPaul, r, eP i]
– Event e: hPaul, rjudge’ , eP i → P (Paul)(e) AND ∀r[P (Paul)(e) 6→ hPaul, r, eP i]
States: From Paul being corrupt as a judge, we may not infer that Paul is corrupt simpliciter. But from Paul being corrupt simpliciter, we may infer that he is corrupt for all
of his roles. Events: From Paul having answered a question as a judge, we may infer
that Paul answered the question simpliciter. But from Paul having answered the question
simpliciter, we may not infer that he answered the question in any of his roles.
I propose that sentences containing a role as-phrase express that the triple built from (i)
the individual associated with the as-phrase, (ii) the role denoted by the complement of
as, and (iii) the eventuality described by the main predicate is a member of R.
(hPaul, rjudge’ , ecorrupt’ i ∈ R)
(9)
Paul as a judge is corrupt.
We may derive this meaning compositionally: the as-phrase first combines with the
main predicate via (generalized) Predicate Modification (see Heim & Kratzer 1998), and
in a second step, the resulting complex predicate combines with the associated individual.
vt
(10)
a. JasK = λr.λx.λe.hx, r, ei ∈ R
he, vti
Paule
b. Jas a judgeK = λx.λe.hx, r judge , ei ∈ R
he, vti
he, vti
(11)
JPaul as a judge is corruptK =
∃e[corrupt’(Paul)(e) & hPaul, r
judge , ei
∈ R]
as a judge het, he, vtii
is
et
corrupt
The analysis based on R can directly account for the central observation in the literature
on role as-phrases (e.g., Landman 1989, Jäger 2003, Szabo 2003, Asher 2011): role asphrases can make otherwise contradictory sentences non-contradictory.
(12)
a. #Paul is corrupt, but he is not corrupt.
b. As a judge, Paul is corrupt, but as a janitor, he is not corrupt.
In (12-a), being corrupt/not corrupt is ascribed to Paul simpliciter. In (12-b), in contrast,
being corrupt is ascribed to Paul only in his judge-role, and being not corrupt is ascribed
to Paul only in his janitor-role. The inferences from (12-b) that Paul simpliciter is (not)
corrupt and that Paul is (not) corrupt in any other role are blocked by the rules in (8).
In sum, the sensitivity to roles found for role as-phrases (and e.g. German copular sentences) can be accounted for by introducing a domain of roles and a role structure R.
References
Asher, N. 2011. Lexical Meaning in Context: A Web of Words. CUP.
De Swart, H, Y Winter, J Zwarts. 2007. Bare nominals and reference to capacities.
Natural Language and Linguistic Theory 25:195–222.
Heim, I & A Kratzer. 1998. Semantics in Generative Grammar. Blackwell.
Landman, F. 1989. Groups II. Linguistics and Philosophy 12:723–744.
Jäger, G. 2003. Towards an explanation of copula effects. Linguistics and Philosophy 26:557–593.
Sowa, JF. 1984. Conceptual Structures: Information Processing in Mind and Machine, Addison-Wesley.
Steimann, F. 2000. On the representation of roles in object-oriented and conceptual
modelling. Data & Knowledge Engineering 35: 83–106.
Szabo, Z. 2003. On qualification. Philosophical Perspectives 17: Language and
Philosophical Linguistics, 409–438.