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Logic, Language, and Meaning Introduction to Logic

ISBN-10: 0226280853
ISBN-13: 9780226280851
Edition: 1991
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Description: 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  More...

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Book details

Copyright year: 1991
Publisher: University of Chicago Press
Publication date: 12/15/1990
Binding: Paperback
Pages: 296
Size: 6.25" wide x 9.25" long x 0.75" tall
Weight: 1.056
Language: English

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 1, Introduction to Logic, begins with a historical overview and then offers a thorough introduction to standard propositional and first-order predicate logic. It provides both a syntactic and a semantic approach to inference and validity, and discusses their relationship. Although language and meaning receive special attention, this introduction is also accessible to those with a more general interest in logic. In addition, the volume contains a survey of such topics as definite descriptions, restricted quantification, second-order logic, and many-valued logic. The pragmatic approach to non-truthconditional and conventional implicatures are also discussed. Finally, the relation between logic and formal syntax is treated, and the notions of rewrite rule, automation, grammatical complexity, and language hierarchy are explained.

Foreword
Preface
Introduction
Arguments, Valid Arguments, and Argument Schemata
Logic and Meaning
Logical Constants and Logical Systems
Logic and Linguistics before the Twentieth Century
The Twentieth Century
Logical Form versus Grammatical Form
Ordinary Language Philosophy
Linguistics and Philosophy
Formal Languages
Propositional Logic
Truth-Functional Connectives
Connectives and Truth Tables
Formulas
Functions
The Semantics of Propositional Logic
Truth Functions
Coordinating and Subordinating Connectives
Predicate Logic
Atomic Setences
Quantifying Expressions: Quantifiers
Formulas
Some More Quantifying Expressions and Their Translations
Sets
The Semantics of Predicate Logic
Interpretation Functions
Interpretation by Substitution
Interpretation by Means of Assignments
Universal Validity
Rules
Identity
Some Properties of Relations
Function Symbols
Arguments and Inferences
Arguments and Argument Schemata
Semantic Inference Relations
Semantic Validity
The Principle of Extensionality
Natural Deduction: A Syntactic Approach to Inference
Introduction and Elimination Rules
Conjunction
Implication
Disjunction
Negation
Quantifiers
Rules
Soundness and Completeness
Beyond Standard Logic
Introduction
Definite Descriptions
Restricted Quantification: Many-Sorted Predicate Logic
Second-Order Logic
Many-Valued Logic
Introduction
Three-Valued Logical Systems
Three-Valued Logics and the Semantic Notion of Presupposition
Logical Systems with More than Three Values
Four-Valued Logics and the Semantic Notion of Presupposition
The Limits of Many-Valued Logics in the Analysis of Presupposition
Elimination of Variables
Pragmatics: Meaning and Usage
Non-Truth-Conditional Aspects of Meaning
Logical Conjunction and Word Order
Usage and the Cooperation Principle
Inclusive and Exclusive Disjunction
Disjunctions and Informativeness
Conversational Maxims and Conversational Implicatures
The Controversial Implicatures of Disjunctions
Implication and Informativeness
Presuppositions and Conversational Implicatures
Conventional Implicatures, Presuppositions, and Implications
Formal Syntax
The Hierarchy of Rewrite Rules
Grammars and Automata
The Theory of Formal Languages
Grammatical Complexity of Natural Languages
Grammars, Automata, and Logic Solutions to Exercises
Bibliographical
Notes
References
Index

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