Type Construction and the Logic of Concepts (original) (raw)
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An outline of type-theoretical approaches to lexical semantics
Journal of Language Modelling, 2017
We take the opportunity of the publication of some of the papers of the ESSLLI workshop TYTLES (TYpe Theory and LExical Semantics, ESSLLI 2015, Barcelona) to provide an overview of the possibilities that type theory offers to model lexical semantics, especially the type-theoretical frameworks that properly model compositional semantics. origins of this issue: esslli workshop on type theory and lexical semantics 2015 The program of the ESSLLI 2015 workshop held in Barcelona 1 consisted of twelve selected talks. The corresponding extended abstracts, together with an introduction and a conclusion by the workshop organisers, are available on the web as Cooper and Retoré (2015); it includes: A. Introduction (slides), by Robin Cooper and Christian Retoré.
Towards a Type-Theoretical Account of Lexical Semantics
Journal of Logic, Language and Information, 2010
After a quick overview of the field of study known as "Lexical Semantics", where we advocate the need of accessing additional information besides syntax and Montaguestyle semantics at the lexical level in order to complete the full analysis of an utterance, we summarize the current formulations of a well-known theory of that field. We then propose and justify our own model of the Generative Lexicon Theory, based upon a variation of classical compositional semantics, and outline its formalization. Additionally, we discuss the theoretical place of informational, knowledge-related data supposed to exist within the lexicon as well as within discourse and other linguistic constructs.
Introduction: Modern Perspectives in Type Theoretical Semantics
2017
Type theories, from the early days of Montague Semantics (Montague 1974) to the recent work of using rich or modern type theories, have a long history of being employed as foundational languages of natural language semantics. In this introductory chapter, we will describe and discuss the development of type theories as foundational languages of mathematics, as well as their applications as foundational languages for formal semantics. In the end, a brief description of each chapter in the volume will follow.
Type Theory and Natural Language: Do We Need Two Basic Types? 1
2012
0. A universal, or almost universal distinction, in syntax: Sentence and NP.........................................................1 1. A possibly universal foundation for natural language semantics: types e and t..................................................1 2. Thought experiments: “Monocategoric”? and just one basic semantic type?....................................................3 3. Ingredients for a possible one-basic-type semantics..........................................................................................3 3.1. Neo-Davidsonian semantics of event sentences..........................................................................................3 3.2. Kamp-Heim semantics for indefinite NPs..................................................................................................3 3.3. Open formulas are “almost ” type-neutral....................................................................................................4 3.4. Exploit the similarit...
Logical types and linguistic types
Tertium Non Datur, 1986
One of the primary aims of linguistic semantics is to translate the expressions of natural language into formulas of some logical calculus. These formulas, in turn, can be interpreted in the appropriate models, and semantic notions like truth, entailment, etc. can be formally defined in the usual manner. In addition to the well-known theoretical advantages of such an intermediate logical form, there is a practical advantage as well: given a system of rules for translation from formulas to natural language, it will be possible to translate from one natural language to another (via the interlingua) without actually evaluating the expressions of the source language. Although the calculi used as intermediate language in machine translation range from first-order predicate calculus (e.g. Schubert -Pelletier 1982) to the higher order intensional calculus of Montague Grammar (e.g. Landsbergen 1977), so far no type-free calculus has been employed for this purpose.
We 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 depicted 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's sense to the context, 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,... are finer grained in our framework. We then conclude with the linguistic, logical and computational perspectives opened by the Montagovian generative lexicon.
In this paper we argue that many problems in the semantics of natural language are due to a large gap between semantics (which is an attempt at understanding what we say in language about the world) and the way the world is. This seemingly monumental effort can be grossly simplified if one assumes, as Hobbs (1985) correctly observed some time ago, a theory of the world that reflects the way we talk about it. We demonstrate here that assuming such a strongly-typed ontology of commonsense knowledge reduces certain problems to near triviality.
Towards a Cognitive Semantics of Types
Types are a crucial concept in conceptual modelling, logic, and knowledge representation as they are an ubiquitous device to understand and formalise the classification of objects. We propose a logical treatment of types based on a cognitively inspired modelling that accounts for the amount of information that is actually available to a certain agent in the task of classification. We develop a predicative modal logic whose semantics is based on conceptual spaces that model the actual information that a cognitive agent has about objects, types, and the classification of an object under a certain type. In particular, we account for possible failures in the classification, for the lack of sufficient information, and for some aspects related to vagueness.
Modern Type Theories for Natural Language Semantics ( Introductory Course in Language and Logic )
2016
Modern Type Theories (MTTs) provide us with a new framework for formal semantics with attractive advantages as compared to Montague Grammar. First, MTTs have rich type structures that can be employed effectively to capture various linguistic features that have proved difficult in the Montagovian setting. Second, MTTs are prooftheoretically specified and can hence be usefully implemented in proof assistants such as Coq, where the MTT-semantics has been implemented for computer-assisted reasoning. These two respects may be characterised as saying that the MTT-semantics is both modeltheoretic and proof-theoretic. They offer unique features unavailable in traditional logical systems that have proved very useful in formal semantics. We shall introduce MTTs and how they can be used for formal semantics. The lectures will be informal and explanatory. They will be rigorous but contain a lot of examples, to illustrate the use of MTTs, on the one hand, and to compare the MTT-semantics with Mo...