This is a book about the meanings of words and how they can combine to form larger meaningful units, as well as how they can fail to combine when the ...

The paper shows how ideas that explain the sense of an expression as a method or algorithm for finding its reference, preshadowed in Frege’s dictum that sense is the way in which a referent is given, can be formalized on the basis of the ideas in Thomason (1980). To this end, the function that sends propositions to truth values or sets of possible worlds in Thomason (1980) must be replaced by a relation and the meaning postulates governing the behaviour of (...) this relation must be given in the form of a logic program. The resulting system does not only throw light on the properties of sense and their relation to computation, but also shows circular behaviour if some ingredients of the Liar Paradox are added. The connection is natural, as algorithms can be inherently circular and the Liar is explained as expressing one of those. Many ideas in the present paper are closely related to those in Moschovakis (1994), but receive a considerably lighter formalization. (shrink)

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. (shrink)

The Generative Lexicon presents a novel and exciting theory of lexical semantics that addresses the problem of the "multiplicity of word meaning" - that is, how ...

It is the aim of INDICES to document recent explorations in the various fields of philosophical logic and formal linguistics and their applications in other disciplines. The main emphasis of this series is on self-contained monographs covering particular areas of recent research and surveys of methods, problems, and results in all fields of inquiry where recourse to logical analysis and logical methods has been fruitful. INDICES will contain monographs dealing with the central areas of philosophical logic (extensional and intensional systems, (...) indexical logics, non-classical logics, philosophy of logic, etc.) as well as studies in which these systems are applied to specific issues in philosophy, in the formal semantics of natural languages, the foundations of linguistic theory, in computational linguistics, and in theoretical computer science. Constructive type theory was first presented in 1970, by the Swedish logician Per Martin-Lof. It has become one of the main approaches used in the foundations of mathematics and computer science. But it has remained relatively unknown among linguists and philosophers, although it provides a considerable extension of the concepts and techniques of logic. The book first gives an introduction to type theory from the point of view of linguistics and the philosophy of language. Type theory is then applied in the areas of quantification, anaphora, temporal reference, and the structure of text and discourse. By virtue of the type-theoretical concepts of proof object and context, various phenomena of dependence and progression in language can be discussed in precise terms, and several well-known problems can be solved. A categorial grammar is presented togenerate formally a fragment of English, together with an example of a computer implementation. (shrink)

Here, the author, develops a type theory, studies its properties, and explains its uses in applications to computer science. In particular, type theory is shown to offer a powerful and uniform language for programming, program specification and development, and logical reasoning.

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 Montague-style 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. The formalization of the structure of natural language utterances around a surface form (phenogrammatics), a deep structure (tectogrammatics) and the meaning thereof as a logical form (semantics) has developed from the original theories of Curry and Montague to form coherent, type-driven models. Most of these new theories rely upon variations of the compositional analysis of the sentence: from pheno to tectogrammatics, and then to semantics. Our contribution to this work aims at giving such a model a means to overcome the problems posed by polysemous lexical units during the semantical analysis of the tectogrammatical form. Building upon an assumed “deep structure”, we formalize parts of Pustejovsky’s Generative Lexicon Theory, linguistically motivated in Pustejovsky (The generative lexicon, MIT Press, Cambridge, MA, 1995), in a pre-processing of the semantics of the sentence. The mechanisms of Lexical Semantics we propose are an additional layer of classical Montague compositional semantics, and, as such, integrate smoothly within such an analysis; we proceed by converting the lexical data to modifiers of the logical form. This treatment of Lexical Semantics furthermore induces us to think that some sort of non-evident background knowledge of the common use of words is necessary to perform a correct semantic analysis of an utterance. This “commonsense metaphysics” would therefore not be strictly confined to pragmatics, as is often assumed. (shrink)

How can computers distinguish the coherent from the unintelligible, recognize new information in a sentence, or draw inferences from a natural language passage? Computational semantics is an exciting new field that seeks answers to these questions, and this volume is the first textbook wholly devoted to this growing subdiscipline. The book explains the underlying theoretical issues and fundamental techniques for computing semantic representations for fragments of natural language. This volume will be an essential text for computer scientists, linguists, and anyone (...) interested in the development of computational semantics. (shrink)

This book provides a systematic study of three foundational issues in the semantics of natural language that have been relatively neglected in the past few decades. focuses on the formal characterization of intensions, the nature of an adequate type system for natural language semantics, and the formal power of the semantic representation language proposes a theory that offers a promising framework for developing a computational semantic system sufficiently expressive to capture the properties of natural language meaning while remaining computationally tractable (...) written by two leading researchers and of interest to students and researchers in formal semantics, computational linguistics, logic, artificial intelligence, and the philosophy of language. (shrink)