Nominal Scope in Situation Semantics

This paper s introduces a semantical storage approach for representing nominal quantifi-cation in situation semantics. Quantificational determiners are treated as denoting binary relations, and their domains and ranges are defined. The linguistic meaning of an expression is given as a pair of its quantificational storage and basis. The storage contains the mean-ings of quantified NPs occurring in (/), while the basis represents the semantical structure of the result of the substitution of those NPs with parameters. Scope ambiguity is avail-able when more than one quantifier is in the storage. A generalized quantificational rule moves some of the quantifiers out of the storage into the basis. There is a restriction that prohibites relevant free parameters from being left out of the binding scope. The storage is empty when there are no quantified NPs occurring in 0, or when there is enough linguistic or extra-linguistic information for resolving scope ambiguities. 1 Some Situation Theoretical Notations A complete guide on the existing literature on situation theory and related topics is given by [Seligman and Moss 1997]. Quantification and anaphora in situation semantics are considered in great detail in [Gawron and Peters 1990]. The present approach differs from the later one in using the semantical storage and the lambda abstraction tools of situation theory to cope with the quantification in a computational mode. For another approach to compositional situation semantics that copes with quantification scope problems as well as with embedded beliefs, se

Quantificational variability effects with plural definites : quantification over individuals or situations?

In this paper we compare the behaviour of adverbs of frequency (de Swart 1993) like usually with the behaviour of adverbs of quantity like for the most part in sentences that contain plural definites. We show that sentences containing the former type of Q-adverb evidence that Quantificational Variability Effects (Berman 1991) come about as an indirect effect of quantification over situations: in order for quantificational variability readings to arise, these sentences have to obey two newly observed constraints that clearly set them apart from sentences containing corresponding quantificational DPs, and that can plausibly be explained under the assumption that quantification over (the atomic parts of) complex situations is involved. Concerning sentences with the latter type of Q-adverb, on the other hand, such evidence is lacking: with respect to the constraints just mentioned, they behave like sentences that contain corresponding quantificational DPs. We take this as evidence that Q-adverbs like for the most part do not quantify over the atomic parts of sum eventualities in the cases under discussion (as claimed by Nakanishi and Romero (2004)), but rather over the atomic parts of the respective sum individuals

Anaphora and the Logic of Change

This paper shows how the dynamic interpretation of natural language introduced in work by Hans Kamp and Irene Heim can be modeled in classical type logic. This provides a synthesis between Richard Montague's theory of natural language semantics and the work by Kamp and Heim

Variable types for meaning assembly: a logical syntax for generic noun phrases introduced by most

This paper proposes a way to compute the meanings associated with sentences with generic noun phrases corresponding to the generalized quantifier most. We call these generics specimens and they resemble stereotypes or prototypes in lexical semantics. The meanings are viewed as logical formulae that can thereafter be interpreted in your favourite models. To do so, we depart significantly from the dominant Fregean view with a single untyped universe. Indeed, our proposal adopts type theory with some hints from Hilbert \epsilon-calculus (Hilbert, 1922; Avigad and Zach, 2008) and from medieval philosophy, see e.g. de Libera (1993, 1996). Our type theoretic analysis bears some resemblance with ongoing work in lexical semantics (Asher 2011; Bassac et al. 2010; Moot, Pr\'evot and Retor\'e 2011). Our model also applies to classical examples involving a class, or a generic element of this class, which is not uttered but provided by the context. An outcome of this study is that, in the minimalism-contextualism debate, see Conrad (2011), if one adopts a type theoretical view, terms encode the purely semantic meaning component while their typing is pragmatically determined

Semantic Ambiguity and Perceived Ambiguity

I explore some of the issues that arise when trying to establish a connection between the underspecification hypothesis pursued in the NLP literature and work on ambiguity in semantics and in the psychological literature. A theory of underspecification is developed `from the first principles', i.e., starting from a definition of what it means for a sentence to be semantically ambiguous and from what we know about the way humans deal with ambiguity. An underspecified language is specified as the translation language of a grammar covering sentences that display three classes of semantic ambiguity: lexical ambiguity, scopal ambiguity, and referential ambiguity. The expressions of this language denote sets of senses. A formalization of defeasible reasoning with underspecified representations is presented, based on Default Logic. Some issues to be confronted by such a formalization are discussed.Comment: Latex, 47 pages. Uses tree-dvips.sty, lingmacros.sty, fullname.st

Genitive quantifiers in Japanese as reverse partitives

Quantificational determiners in Japanese can be marked with genitive case. Current analyses (for example by Watanabe, Natural Language and Linguistic Theory, to appear) treat the genetive case marker in these cases as semantically vacuous, but we show that it has semantic effects. We propose a new analysis as reverse partitives. Following Jackendoff (MIT-Press, 1977), we assume that partitives always contain two NPs one of which is phonologically deleted. We claim that, while in normal partitives the higher noun is deleted, in reverse partitives the lower noun is deleted

A Denotational Semantics for First-Order Logic

In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic. Additionally, by allowing an assignment of a non-ground term to a variable we introduce in this framework logical variables. The semantics combines a number of well-known ideas from the areas of semantics of imperative programming languages and logic programming. In the resulting computational view conjunction corresponds to sequential composition, disjunction to ``don't know'' nondeterminism, existential quantification to declaration of a local variable, and negation to the ``negation as finite failure'' rule. The soundness result shows correctness of the semantics with respect to the notion of truth. The proof resembles in some aspects the proof of the soundness of the SLDNF-resolution.Comment: 17 pages. Invited talk at the Computational Logic Conference (CL 2000). To appear in Springer-Verlag Lecture Notes in Computer Scienc

Foundations for structured programming with GADTs

GADTs are at the cutting edge of functional programming and become more widely used every day. Nevertheless, the semantic foundations underlying GADTs are not well understood. In this paper we solve this problem by showing that the standard theory of data types as carriers of initial algebras of functors can be extended from algebraic and nested data types to GADTs. We then use this observation to derive an initial algebra semantics for GADTs, thus ensuring that all of the accumulated knowledge about initial algebras can be brought to bear on them. Next, we use our initial algebra semantics for GADTs to derive expressive and principled tools — analogous to the well-known and widely-used ones for algebraic and nested data types — for reasoning about, programming with, and improving the performance of programs involving, GADTs; we christen such a collection of tools for a GADT an initial algebra package. Along the way, we give a constructive demonstration that every GADT can be reduced to one which uses only the equality GADT and existential quantification. Although other such reductions exist in the literature, ours is entirely local, is independent of any particular syntactic presentation of GADTs, and can be implemented in the host language, rather than existing solely as a metatheoretical artifact. The main technical ideas underlying our approach are (i) to modify the notion of a higher-order functor so that GADTs can be seen as carriers of initial algebras of higher-order functors, and (ii) to use left Kan extensions to trade arbitrary GADTs for simpler-but-equivalent ones for which initial algebra semantics can be derive