We present Logical Description Grammar (LDG), a model ofgrammar and the syntax-semantics interface based on descriptions inelementary logic. A description may simultaneously describe the syntacticstructure and the semantics of a natural language expression, i.e., thedescribing logic talks about the trees and about the truth-conditionsof the language described. Logical Description Grammars offer a naturalway of dealing with underspecification in natural language syntax andsemantics. If a logical description (up to isomorphism) has exactly onetree plus truth-conditions as a model, it completely specifies thatgrammatical (...) object. More common is the situation, corresponding tounderspecification, in which there is more than one model. A situation inwhich there are no models corresponds to an ungrammatical input. (shrink)

There are two kinds of semantic theories of anaphora. Some, such as Heim’s File Change Semantics, Groenendijk and Stokhof’s Dynamic Predicate Logic, or Muskens’ Compositional DRT (CDRT), seem to require full coindexing of anaphora and their antecedents prior to interpretation. Others, such as Kamp’s Discourse Representation Theory (DRT), do not require this coindexing and seem to have an important advantage here. In this squib I will sketch a procedure that the first group of theories may help themselves to so that (...) they can interleave interpretation and coindexing in DRT’s way. (shrink)

The concept of a dialogue is considered in general terms from the standpoint of its referential presuppositions. The semantics of dialogue implies that dialogue participants must generally have a collective intentionality of agreed-upon references that is minimally sufficient for them to be able to disagree about other things, and ideally for outstanding disagreements to become clearer at successive stages of the dialogue. These points are detailed and illustrated in a fictional dialogue, in which precisely these kinds of referential confusions impede (...) progress in shared understanding. It is only through a continuous exchange of question and answer in this dialogue case study that the meanings of key terms and anaphorical references are disambiguated, and a relevantly complete collective intentionality of shared meaning between dialogue participants is achieved. The importance of a minimally shared referential semantics for the terms entering into reasoning and argument in dialogue contexts broadly construed cannot be over-estimated. Where to draw the line between referential agreement and disagreement within any chosen dialogue, as participants work toward better mutual understanding in clearing up referential incongruities, is sometimes among the dialogue’s main points of dispute. (shrink)

This paper presents the Constraint Language for Lambda Structures(CLLS), a first-order language for semantic underspecification thatconservatively extends dominance constraints. It is interpreted overlambda structures, tree-like structures that encode -terms. Based onCLLS, we present an underspecified, uniform analysis of scope,ellipsis, anaphora, and their interactions. CLLS solves a variablecapturing problem that is omnipresent in scope underspecification andcan be processed efficiently.

This paper gives a simple method for providing categorial brands of feature-based unification grammars with a model-theoretic semantics. The key idea is to apply the paradigm of fibred semantics (or layered logics, see Gabbay (1990)) in order to combine the two components of a feature-based grammar logic. We demonstrate the method for the augmentation of Lambek categorial grammar with Kasper/Rounds-style feature logic. These are combined by replacing (or annotating) atomic formulas of the first logic, i.e. the basic syntactic types, by (...) formulas of the second. Modelling such a combined logic is less trivial than one might expect. The direct application of the fibred semantics method where a combined atomic formula like np (num: sg & pers: 3rd) denotes those strings which have the indicated property and the categorial operators denote the usual left- and right-residuals of these string sets, does not match the intuitive, unification-based proof theory. Unification implements a global bookkeeping with respect to a proof whereas the direct fibring method restricts its view to the atoms of the grammar logic. The solution is to interpret the (embedded) feature terms as global feature constraints while maintaining the same kind of fibred structures. For this adjusted semantics, the anticipated proof system is sound and complete. (shrink)

The present study investigates whether quantifier scope is computed incrementally during online sentence processing. We exploited the free word order in German to manipulate whether the verbal predicate preceded or followed the second quantifier in doubly quantified sentences that required the computation of inverse scope. A possessive pronoun in the first quantifier that had to be bound by the second quantifier was used to enforce scope inversion. We tested whether scope inversion causes difficulty and whether this difficulty emerges even at (...) a point before comprehenders have encountered the main verb. We report three pretests and two reading time experiments. The first two pretests were offline tests that established (1) that the sentences exhibited the assumed scope preferences and (2) that variable binding forced scope inversion. The third pretest employed self-paced reading to show that interpreting a bound variable is not difficult per se and that difficulty in the critical construction must thus be due to inverting scope. Incremental processing of quantifier scope was investigated in a self-paced reading experiment. We observed difficulty right after the second quantifier, but only if it appeared after the main verb, that is, after the predication was complete. Further evidence for late scope inversion comes from an eyetracking experiment. Again, a scope inversion effect could only be observed at the end of the sentence. Taken together, our study demonstrates that in German inverse scope is only computed at the sentence boundary. (shrink)

We characterize pairs of monotone generalized quantifiers Q1 and Q2 over finite domains that give rise to an entailment relation between their two relative scope construals. This relation between quantifiers, which is referred to as scope dominance, is used for identifying entailment relations between the two scopal interpretations of simple sentences of the form NP1–V–NP2. Simple numerical or set-theoretical considerations that follow from our main result are used for characterizing such relations. The variety of examples in which they hold are (...) shown to go far beyond the familiar existential-universal type. (shrink)

Free choice permission, a crucial test case concerning the semantics/ pragmatics boundary, usually receives a pragmatic treatment. But its pragmatic features follow from its semantics. We observe that free choice inferences are defeasible, and defend a semantics of free choice permission as strong permission expressed in terms of a modal conditional in a nonmonotonic logic.

In previous work we have developed Property Theory with Curry Typing (PTCT), an intensional first-order logic for natural language semantics. PTCT permits fine-grained specifications of meaning. It also supports polymorphic types and separation types. We develop an intensional number theory within PTCT in order to represent proportional generalized quantifiers like "most", and we suggest a dynamic type-theoretic approach to anaphora and ellipsis resolution. Here we extend the type system to include product types, and use these to define a permutation function (...) that generates underspecified scope representations within PTCT. We indicate how filters can be added to encode constraints on possible scope readings. Our account offers several important advantages over other current theories of underspecification. (shrink)

It is commonly claimed that, when a constituent is the focus of an occurrence of a sentence, certain alternatives to that constituent are relevant to our understanding of the sentence. Normally these are alternatives to the denotation of the focused constituent. However, Krifka (2007) briefly discusses the notion of expression focus, where the alternatives are linguistic items. Yet an adequate account of expression focus has not been given within the literature. This is despite the fact that it holds the potential (...) to provide analyses of several important metalinguistic phenomena, including metalinguistic negotiation, metalinguistic negation and embedded pejorative expressions. This paper provides an account of expression focus and shows the explanatory power it holds with respect to metalinguistic phenomena. (shrink)

We present a formal analysis of iconic coverbal gesture. Our model describes the incomplete meaning of gesture that’s derivable from its form, and the pragmatic reasoning that yields a more specific interpretation. Our formalism builds reported.

This paper uses classical logic for a simultaneous description of the syntax and semantics of a fragment of English and it is argued that such an approach to natural language allows procedural aspects of linguistic theory to get a purely declarative formulation. In particular, it will be shown how certain construction rules in Discourse Representation Theory, such as the rule that indefinites create new discourse referents and definites pick up an existing referent, can be formulated declaratively if logic is used (...) as a metalanguage for English. In this case the declarative aspects of a rule are highlighted when we focus on the model theory of the description language while a procedural perspective is obtained when its proof theory is concentrated on. Themes of interest are Discourse Representation Theory, resolution of anaphora, resolution of presuppositions, and underspecification. (shrink)

Paulina Sliwa (2015) argues that knowing why p is necessary and sufficient for understanding why p. She tries to rebut recent attacks against the necessity and sufficiency claims, and explains the gradability of understanding why in terms of knowledge. I argue that her attempts do not succeed, but I indicate more promising ways to defend reductionism about understanding why throughout the discussion.

Discourse Representation Theory is a specific name for the work of Hans Kamp in the area of dynamic interpretation of natural language. Also, it has gradually become a generic term for proposals for dynamic interpretation of natural language in the same spirit. These proposals have in common that each new sentence is interpreted in terms of the contribution it makes to an existing piece of interpreted discourse. The interpretation conditions for sentences are given as instructions for updating the representation of (...) the discourse. (shrink)

Ambiguities in natural language can multiply so fast that no person or machine can be expected to process a text of even moderate length by enumerating all possible disambiguations. A sentence containing $n$ scope bearing elements which are freely permutable will have $n!$ readings, if there are no other, say lexical or syntactic, sources of ambiguity. A series of $m$ such sentences would lead to $(n!)^m$ possibilities. All in all the growth of possibilities will be so fast that generating readings (...) first and testing their acceptability afterwards will not be feasible. -/- This insight has led a series of researchers to adopt a level of representation at which ambiguities remain unresolved. The idea here is not to generate and test many possible interpretations but to first generate one `underspecified' representation which in a sense represents all its complete specifications and then use whatever information is available to further specify the result. -/- One central hypothesis in the paper will be that the relation between an underspecified representation and its full representations is not so much the relation between one structure and a set of other structures but is in fact the relation between a description (a set of logical sentences) and its models. (shrink)