What is modal logic

In this provocative book, Barwise and Perry tackle the slippery subject of \"meaning, \" a subject that has long vexed linguists, language philosophers, and logicians.

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Situations and Attitudes.

13 EADERS of Mr. Bertrand Russell's philosophical £v works know that one of his pupils before the outbreak of the war, an Austrian, Mr. Ludwig Wittgenstein, caused him to change his views in some important particulars. Curiosity can now be satisfied. The “Tractatus Logico-Philosophicus “which Mr. Ogden has included in his new library of philosophy is a remarkable and strikingly original work. It is published in German and English in parallel pages. It is difficult to appreciate the reason for this, seeing that the author is evidently familiar with our language and has himself carefully revised the proofs of the translation. Also we should have liked to have the Tractatus without Mr. Russell's Introduction, not, we hasten to add, on account of any fault or shortcoming in that introduction, which is highly appreciative and in part a defence of himself, in part explanatory of the author, but for the reason that good wine needs no bush and that Mr. Russell's bush has the unfortunate effect of dulling the palate instead of whetting the appetite. In his penultimate sentence Mr. Russell says; “To have constructed a theory of logic which is not at any point obviously wrong is to have achieved a work of extraordinary difficulty and importance.” We agree, but how uninspiring when compared with Mr. Wittgenstein's own statement of aim: “What can be said at all can be said clearly, and whereof one cannot speak, thereof one must be silent.” Tractatus Logico-Philosophicus. By Ludwig Wittgenstein. (International Library of Psychology, Philosophy and Scientific Method.) Pp. 189. (London: Kegan Paul and Co., Ltd.; New York: Harcourt, Brace and Co., Inc., 1922.) 10s. 6d. net.

Tractatus Logico-Philosophicus

Compositional question answering begins by mapping questions to logical forms, but training a semantic parser to perform this mapping typically requires the costly annotation of the target logical forms. In this paper, we learn to map questions to answers via latent logical forms, which are induced automatically from question-answer pairs. In tackling this challenging learning problem, we introduce a new semantic representation which highlights a parallel between dependency syntax and efficient evaluation of logical forms. On two standard semantic parsing benchmarks (Geo and Jobs), our system obtains the highest published accuracies, despite requiring no annotated logical forms.

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Learning Dependency-Based Compositional Semantics

From Discourse to Logic

This paper embeds the core part of Discourse Representation Theory in the classical theory of types plus a few simple axioms that allow the theory to express key facts about variables and assignments on the object level of the logic. It is shown how the embedding can be used to combine core analyses of natural language phenomena in Discourse Representation Theory with analyses that can be obtained in Montague Semantics.

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Combining Montague semantics and discourse representation

Preface 1. Introduction 2. Two type logics 3. The logic IL 4. PTQ revisited 5. Going Partial I: propositional logic and predicate logic 6. Going Partial II: type theory 7. Situations, persistence and weak consequence 8. Propositional attitudes 9. Names Appendix Bibliography Index.

Meaning and Partiality

Type-logical semantics studies linguistic meaning with the help of the theory of types. The latter originated with Russell as an answer to the paradoxes, but has the additional virtue that it is very close to ordinary language. In fact, type theory is so much more similar to language than predicate logic is, that adopting it as a vehicle of representation can overcome the mismatches between grammatical form and predicate logical form that were observed by Frege and Russell. The grammatical forms of ordinary language sentences consequently may be taken to be much less misleading than logicians in the first half of the 20th century often thought them to be. This was realized by Richard Montague, who used the theory of types to translate fragments of ordinary language into a logical language. Semantics is commonly divided into lexical semantics, which studies the meaning of words, and compositional semantics, which studies the way in which complex phrases obtain a meaning from their constituents. The strength of type-logical semantics lies with the latter, but type-logical theories can be combined with many competing hypotheses about lexical meaning, provided these hypotheses are expressed using the language of type theory.

Type-logical semantics

In Van Benthem, 1986 it was observed that the Curry-Howard correspondence between proofs and λ-terms can be exploited to obtain a very elegant and principled match between Lambek Categorial Grammar and Montague Semantics. The correspondence associates each proof of the calculus with a λ-term and Van Benthem shows how such terms can be used as a recipe for obtaining the meaning of a complex expression in terms of the meanings of its parts. The method is easily extended to various other forms of Lambek calculi, including multimodal calculi (see Moortgat, 1997 and references therein).

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Language, Lambdas, and Logic

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.

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Reinhard Muskens

Papers

Combining Montague semantics and discourse representation

Meaning and Partiality

Type-logical semantics

Language, Lambdas, and Logic

Sense and the Computation of Reference