Quantificational Domains and Recursive Contexts
Barbara H. Partee
University of Massachusetts, Amherst
November 7, 1995
Abstract
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The implicit delimiting or narrowing of the domain of quantification,
e.g. in the case of "unselective quantifiers" such as the adverbs of
quantification _always, usually, mostly_, etc., is a heavily context-dependent
phenomenon that has much in common with anaphora, presupposition projection,
the dynamics of reference time, reference location, etc., and other of the
context-dependent phenomena discussed in Partee (1989). While many non-
linguistic factors clearly play a role in such phenomena, there are
interesting issues at the intersection of discourse processing and sentence
grammar, since in addition to context as constructed at the discourse level,
there are subsentential "local contexts" which have limited lifespans and are
constrained by aspects of sentence grammar, both syntactic and semantic.
So for example in the case of anaphora, while a pronoun can get its
value from an entirely non-linguistic context, if the value of a pronoun is
determined by a linguistic antecedent, there are grammatical contraints
on the possible structural relations that may hold between antecedent and
pronoun, as illustrated by the familiar "precede/command" conditions
known since the early work of Ross and Langacker and illustrated in
(1a-b) below with respect to the possibility of interpreting "some
people" as the antecedent of "they".
(1) (a) Some people complain loudly in the middle of the night and they
make so much noise upstairs that one can't sleep.
(b) They make so much noise upstairs that one can't sleep and some
people complain loudly in the middle of the night.
In examples (2a-b) we see a similar restriction on the possibility of
restricting the domain of the quantifier _usually_ by means of material
accessible in the linguistic context: and the relevant notion of
accessibility turns out to be the same for the wide range of phenomena
mentioned above.
(2) (a) Henrik likes to travel. He goes to France in the summer and he
usually travels by car. He goes to England for the spring holidays and he
usually travels by ferry.
(b) Henrik likes to travel. He usually travels by car and he
goes to France in the summer. He usually travels by ferry and he goes to
England for the spring holidays.
In the discourse (2b), unlike that in (2a), it is impossible to
understand the domain of the quantifier _usually_ to be limited to the
trips to France and the trips to England on its two occurrences, so the
discourse ends up sounding contradictory. This constraint on "backwards
domain restriction" is analogous to constraints on backwards anaphora.
Similar constraints apply to the local satisfaction of presuppositions by
virtue of material that has its source in the local linguistic context. And
Heim has shown in her work on the presupposition projection problem that the
relevant accessibility constraints are fundamentally semantic in nature, as
can be seen from examples with propositional attitude verbs (which will be
reviewed in the lecture) where examples with identical syntactic structure
behave differently because of different presuppositional relationships among
e.g. "belief worlds" and "hope worlds". Of course in many cases the semantic
and syntactic structures are sufficiently parallel that the constraints can
often be described either way.
The notions of topic and focus appear to be among the important
linguistic notions that play a role in structuring these "recursive
contexts"; recent work by Rooth and unpublished work by Von Fintel makes
progress in relating focus structure to anaphoric structure more generally.
As Kempson has demonstrated, the same broad range of inferential
processes that play a role in discourse anaphoric phenomena (e.g. in
licensing the use of a definite article) also play a role in the
corresponding phenomena when they show up in local subsentential
contexts; so the fact that aspects of
sentence grammar play a crucial role in defining accessibility relations for
"antecedent" material in this whole family of phenomena does not mean
that the phenomena themselves are to be described in sentence-grammar
terms. One of the interesting issues, then, is the characterization of
the nature of the interface between the grammatical and the
extragrammatical mechanisms involved. Work by Sidner and Webber
represents one early line of attack on related problems, and recent
developments in dynamic semantics are another.
This talk will focus more on articulating the relationships among the
different phenomena that appear to operate under common "accessibility"
constraints than on choosing a particular formal approach to treating them.
References
Chierchia, G. (1992) "Anaphora and Dynamic Binding", Linguistics and
Philosophy 15, 111-183.
Chierchia, G. (1995). Dynamics of Meaning: Anaphora, Presupposition,
and the Theory of Grammar. Chicago: The University of Chicago Press.
Von Fintel, K. (1994) Conditionals as Quantifier Restrictors. Ph.D.
dissertation, UMass, Amherst.
Groenendijk, J. and M. Stokhof (1991), "Dynamic Predicate Logic", Linguistics
and Philosophy 14.
Hajicova, E.. B. Partee and P. Sgall (ms. 1994), "Topic-Focus Articulation,
Tripartite Structures, and Semantic Content", draft manuscript, Prague
and Amherst.
Heim, I. R. (1982) The Semantics of Definite and Indefinite Noun Phrases,
Ph.D. dissertation, University of Massacusetts, Amherst.
Heim, I.R. (1983) "On the projection problem for presuppositions", WCCFL 2,
Stanford, CA: Stanford Linguistics Association.
Partee, B. (1989) "Binding Implicit Variables in Quantified Contexts, CLS 25
Sgall, P., E. Hajicova, and J. Panevova (1986), The Meaning of the
Sentence in Its Semantic and Pragmatic Aspects, Academia, Prague and Reidel,
Dordrecht.
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