Copredication in homotopy type theory

This paper applies homotopy type theory to formal semantics of natural languages and proposes a new model for the linguistic phenomenon of copredication. Copredication refers to sentences where two predicates which assume different requirements for their arguments are asserted for one single entity, e.g., "the lunch was delicious but took forever". This paper is particularly concerned with copredication sentences with quantification, i.e., cases where the two predicates impose distinct criteria of quantification and individuation, e.g., "Fred picked up and mastered three books." In our solution developed in homotopy type theory and using the rule of existential closure following Heim analysis of indefinites, common nouns are modeled as identifications of their aspects using HoTT identity types, e.g., the common noun book is modeled as identifications of its physical and informational aspects. The previous treatments of copredication in systems of semantics which are based on simple type theory and dependent type theories make the correct predictions but at the expense of ad hoc extensions (e.g., partial functions, dot types and coercive subtyping). The model proposed here, also predicts the correct results but using a conceptually simpler foundation and no ad hoc extensions

Semantic Types, Lexical Sorts and Classifiers

We propose a cognitively and linguistically motivated set of sorts for lexical semantics in a compositional setting: the classifiers in languages that do have such pronouns. These sorts are needed to include lexical considerations in a semantical analyser such as Boxer or Grail. Indeed, all proposed lexical extensions of usual Montague semantics to model restriction of selection, felicitous and infelicitous copredication require a rich and refined type system whose base types are the lexical sorts, the basis of the many-sorted logic in which semantical representations of sentences are stated. However, none of those approaches define precisely the actual base types or sorts to be used in the lexicon. In this article, we shall discuss some of the options commonly adopted by researchers in formal lexical semantics, and defend the view that classifiers in the languages which have such pronouns are an appealing solution, both linguistically and cognitively motivated

The Montagovian Generative Lexicon ΛT yn: a Type Theoretical Framework for Natural Language Semantics

International audienceWe present a framework, named the Montagovian generative lexicon, for computing the semantics of natural language sentences, expressed in many-sorted higher order logic. Word meaning is described by several lambda terms of second order lambda calculus (Girard’s system F): the principal lambda term encodes the argument structure, while the other lambda terms implement meaning transfers. The base types include a type for propositions and many types for sorts of a many-sorted logic for expressing restriction of selection. This framework is able to integrate a proper treatment of lexical phenomena into a Montagovian compositional semantics, like the (im)possible arguments of a predicate, and the adaptation of a word meaning to some contexts. Among these adaptations of a word meaning to contexts, ontological inclusions are handled by coercive subtyping, an extension of system F introduced in the present paper. The benefits of this framework for lexical semantics and pragmatics are illustrated on meaning transfers and coercions, on possible and impossible copredication over different senses, on deverbal ambiguities, and on “fictive motion”. Next we show that the compositional treatment of determiners, quantifiers, plurals, and other semantic phenomena is richer in our framework. We then conclude with the linguistic, logical and computational perspectives opened by the Montagovian generative lexicon

Plurals: individuals and sets in a richly typed semantics

We developed a type-theoretical framework for natural lan- guage semantics that, in addition to the usual Montagovian treatment of compositional semantics, includes a treatment of some phenomena of lex- ical semantic: coercions, meaning, transfers, (in)felicitous co-predication. In this setting we see how the various readings of plurals (collective, dis- tributive, coverings,...) can be modelled

Type-theoretical semantics with coercive subtyping

In the formal semantics based on modern type theories, common nouns are interpreted as types, rather than as functional subsets of entities as in Montague grammar. This brings about important advantages in linguistic interpretations but also leads to a limitation of expressive power because there are fewer operations on types as compared with those on functional subsets. The theory of coercive subtyping adequately extends the modern type theories with a notion of subtyping and, as shown in this paper, plays a very useful role in making type theories more expressive for formal semantics. In particular, it gives a satisfactory treatment of the type-theoretic interpretation of modified common nouns and allows straightforward interpretations of interesting linguistic phenomena such as copredication, whose interpretations have been found difficult in a Montagovian setting. We shall also study some type-theoretic constructs that provide useful representational tools for formal lexical semantics, including how the so-called dot-types for representing logical polysemy may be expressed in a type theory with coercive subtyping

Predication and cognitive context: Between minimalism and contextualism

In this paper, we suggest a strategy for modelling cognitive context within a truth\u2010conditional semantics, using Asher's model of predication. This allows us to introduce the notion of type presupposition intended as a lexical constraint to the composition of the truth\u2010conditional content. More specifi\u2010cally, we suggest that this model of predication produces a notion of truth\u2010conditional meaning where the cognitive context fixes a set of lexical restrictions and forced modifi\u2010cations. We conclude that this model might offer an inter\u2010mediate position between Minimalism and Contextualism: an account that provides intuitive truth conditions within a formal semantic theory

Type Theories and Lexical Networks: using Serious Games as the basis for Multi-Sorted Typed Systems

In this paper, we show how a rich lexico-semantic network which has been built using serious games, JeuxDeMots, can help us in grounding our semantic ontologies as well as different sorts of information in doing formal semantics using rich or modern type theories (type theories within the tradition of Martin Löf). We discuss the domain of base types, adjectival and verbal types, hyperonymy/hyponymy relations as well as more advanced issues like homophony and polysemy. We show how one can take advantage of this wealth in a formal compositional semantics framework. This is a way to sidestep the problem of deciding how your type ontology should look like once you have made a move to a many sorted type system. Furthermore, we show how this kind of information can be extracted  from JeuxdeMots and inserted into a proof-assistant like Coq in order to perform reasoning tasks using modern type theoretic semantics

Aspectual Coercion and Logical Polysemy

Recent work in computational semantics and lexical semantics has made an interesting shift. Motivated by a concern for lexical organization and global coherence in the structure of the lexicon, some researchers have moved towards more expressive semantic descriptions, as well as more powerful methods of composition. There has been some concern expressed, however, as to the general applicability of type-changing operations such as coercion, as well as concerning the power of generative mechanisms operating in the lexicon and semantics. In this paper, we address these concerns directly, and show that, upon closer examination, these critiques are not substantiated by the linguistic data. Without a proper notion of constraints on coercion, however, there can indeed be overgeneration of interpretations in the semantics, and in fact the notion of conditions on coercion has always been integral to the basic spirit of generative lexicons. In particular, we examine the constraints on type coercion in complement constructions of aspectual predicates in English and French. What we discover is a natural explanation for the behavior of coercion that makes reference to different types of event selection while also addressing the polysemous nature of aspectual verb

Formal semantics in modern type theories with coercive subtyping

Abstract. In the formal semantics based on modern type theories, common nouns are interpreted as types, rather than as predicates of entities as in Montague's semantics. This brings about important advantages in linguistic interpretations but also leads to a limitation of expressive power because there are fewer operations on types as compared with those on predicates. The theory of coercive subtyping adequately extends the modern type theories and, as shown in this paper, plays a very useful role in making type theories more expressive for formal semantics. It not only gives a satisfactory solution to the basic problem of 'multiple categorisation' caused by interpreting common nouns as types, but provides a powerful formal framework to model interesting linguistic phenomena such as copredication, whose formal treatment has been found difficult in a Montagovian setting. In particular, we show how to formally introduce dot-types in a type theory with coercive subtyping and study some type-theoretic constructs that provide useful representational tools for reference transfers and multiple word meanings in formal lexical semantics

Cross-sortal Predication and Polysemy

Department of Chinese and Bilingual Studie