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Logic, Language, and Meaning, Volume 2: Intensional Logic and Logical Grammar
Although the two volumes of Logic, Language, and Meaning can be used independently of one another, together they provide a comprehensive overview of modern logic as it is used as a tool in the analysis of natural language. Both volumes provide exercises and their solutions.
Volume 2, Intensional logic and Logical Grammar, begins with an introduction to the various principles of intensional semantics, and then provides a treatment of various intensional logics, such as modal propositional logic and modal predicate logic, and tense logic. It also introduces type theory, lambda-abstraction, and categorical syntax. Type theory and intensional logic are combined in the well-known intensional type logic employed by Montague. After the necessary technical logical machinery is thus presented, a detailed introduction to Montague Grammar as a specimen of logical grammar follows. The final chapter is dedicated to an introduction of three new developments in logical grammar: the theory of generalized quantifiers, flexible categorical syntax, and discourse representational theory.
L. T. F. Gamut is a collective pseudonym for J. F. A. K. van Benthem, J. A. G. Groenendijk, D. H. J. de Jongh, M. J. B. Stokhof, all senor staff members in the Institute for Logic, Language & Computation at the University of Amsterdam, and H. J. Verkuyl emeritus professor at the University of Utrecht.
Volume 2, Intensional logic and Logical Grammar, begins with an introduction to the various principles of intensional semantics, and then provides a treatment of various intensional logics, such as modal propositional logic and modal predicate logic, and tense logic. It also introduces type theory, lambda-abstraction, and categorical syntax. Type theory and intensional logic are combined in the well-known intensional type logic employed by Montague. After the necessary technical logical machinery is thus presented, a detailed introduction to Montague Grammar as a specimen of logical grammar follows. The final chapter is dedicated to an introduction of three new developments in logical grammar: the theory of generalized quantifiers, flexible categorical syntax, and discourse representational theory.
L. T. F. Gamut is a collective pseudonym for J. F. A. K. van Benthem, J. A. G. Groenendijk, D. H. J. de Jongh, M. J. B. Stokhof, all senor staff members in the Institute for Logic, Language & Computation at the University of Amsterdam, and H. J. Verkuyl emeritus professor at the University of Utrecht.
349 pages, Paperback
First published January 1, 1982
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About the author
L.T.F. Gamut
5 books3 followersL. T. F. Gamut was a collective pseudonym for the Dutch logicians Johan van Benthem, Jeroen Groenendijk, Dick de Jongh, Martin Stokhof and Henk Verkuyl. Logic, Language and Meaning is one of the most authoritative and widely used graduate textbooks in formal semantics courses. [Source: http://en.wikipedia.org/wiki/L._T._F.... ]
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November 5, 2012
The second volume in a series of two on logic as a tool for formalizing language, meaning and arguments. The first volume dealt with the fundamentals of propositional logic and predicate logic, but it did so in a very thorough way, presenting all the intricate details of the semantics of logics and the ways in which these logics could account for the richness of natural language, making it much more than a mere first introduction to logic. After dealing with the main focus of classical logic, the first volume moved on to some more advanced logics such as second-order logic, and many-valued logic as well as the pragmatics of logical languages, but it is not until the second volume that we really encounter logics with a much higher expressive power and generality.
It starts with so called intensional logics in the form of modal logics and temporal logics and all the complications of having to deal with necessity and temporal aspects of sentences, making for a much more complex semantic framework. After dealing with the basics of different systems of intensional logic and the even more complex matters that come into play as one combines modality and quantification in predicate modal logic, we move on to Russell's theory of types and its stunning ability to generalize many different concepts in more simple logics. The theory of types is subsequently extended into an intensional theory of types and finally a two-sorted theory of types capable of dealing with even intensionality without the special treatment found in the basic intensional theory of types.
Going into the details of all these complicated systems would go much beyond the scope of this short review, suffice it to say that the authors manage to cover an impressive range of subjects of logic focused around the ability to account for the richness of natural language in a formal framework, always guided by some basic principles of representing language as closely as possible to the way in which it is actually used, never letting philosophical principles come before empirical concerns to represent the grammar of natural language as it is; and of maintaining compositionality in translation, meaning the different parts of sentences should be translated separately and then combined into a complex translation of the complete original sentence through general rules of translation, something which is not really possible (if even then) until we reach the full power of the theory of types enriched with the lambda-operator.
After the presentation of all these systems of logic, the book concludes with two chapters: one presenting Montague grammar, a system of formal grammar based on the theory of types and categorial grammar with a thorough discussion of its ability to describe the grammar of natural language; and a final chapter dealing with some recent (as of the writing of this book, in 1982) topics concerning quantifiers and semantics (specifically: the theory of generalized quantifiers, flexible categorial grammar and discourse representation theory).
To give a general overview of this volume as well as the preceding one: the reader is given a thorough presentation of some logics, focused on semantics rather than proof theory and focused on their ability to represent the grammar and semantics of natural language rather than on the meta-logical properties of the logics themselves and/or the philosophical discussions concerning these properties. Consequently, the selection of logics treated is guided toward some logics rather than other and many interesting systems of logic are not detailed. If one is looking for an overview of logics in general and the properties and characteristics of these, these books are not the best books to read. If, on the other hand one is looking for a presentation of logic as being closely tied to linguistics and wants a thorough discussion of the expressive powers of logics in terms of how good they are at representing the structure and meaning of sentenced and arguments in natural language through principled methods, this is an excellent couple of books.
It starts with so called intensional logics in the form of modal logics and temporal logics and all the complications of having to deal with necessity and temporal aspects of sentences, making for a much more complex semantic framework. After dealing with the basics of different systems of intensional logic and the even more complex matters that come into play as one combines modality and quantification in predicate modal logic, we move on to Russell's theory of types and its stunning ability to generalize many different concepts in more simple logics. The theory of types is subsequently extended into an intensional theory of types and finally a two-sorted theory of types capable of dealing with even intensionality without the special treatment found in the basic intensional theory of types.
Going into the details of all these complicated systems would go much beyond the scope of this short review, suffice it to say that the authors manage to cover an impressive range of subjects of logic focused around the ability to account for the richness of natural language in a formal framework, always guided by some basic principles of representing language as closely as possible to the way in which it is actually used, never letting philosophical principles come before empirical concerns to represent the grammar of natural language as it is; and of maintaining compositionality in translation, meaning the different parts of sentences should be translated separately and then combined into a complex translation of the complete original sentence through general rules of translation, something which is not really possible (if even then) until we reach the full power of the theory of types enriched with the lambda-operator.
After the presentation of all these systems of logic, the book concludes with two chapters: one presenting Montague grammar, a system of formal grammar based on the theory of types and categorial grammar with a thorough discussion of its ability to describe the grammar of natural language; and a final chapter dealing with some recent (as of the writing of this book, in 1982) topics concerning quantifiers and semantics (specifically: the theory of generalized quantifiers, flexible categorial grammar and discourse representation theory).
To give a general overview of this volume as well as the preceding one: the reader is given a thorough presentation of some logics, focused on semantics rather than proof theory and focused on their ability to represent the grammar and semantics of natural language rather than on the meta-logical properties of the logics themselves and/or the philosophical discussions concerning these properties. Consequently, the selection of logics treated is guided toward some logics rather than other and many interesting systems of logic are not detailed. If one is looking for an overview of logics in general and the properties and characteristics of these, these books are not the best books to read. If, on the other hand one is looking for a presentation of logic as being closely tied to linguistics and wants a thorough discussion of the expressive powers of logics in terms of how good they are at representing the structure and meaning of sentenced and arguments in natural language through principled methods, this is an excellent couple of books.
August 16, 2021
A great reference for my technical library and my new go to reference for my development goals in NLP. This entire set is brilliant and i could not be more satisfied with the purchase!
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