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This text offers an innovative approach to the teaching of logic, which is rigorous but entirely non-symbolic. By introducing students to deductive inferences in natural language, the book breaks new ground pedagogically. Cannon focuses on such topics as using a tableaux technique to assess inconsistency; using generative grammar; employing logical analyses of sentences; and dealing with quantifier expressions and syllogisms. An appendix covers truth-functional logic.
Book Synopsis Deductive Logic in Natural Language by : Douglas Cannon
Download or read book Deductive Logic in Natural Language written by Douglas Cannon and published by Broadview Press. This book was released on 2002-11-13 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text offers an innovative approach to the teaching of logic, which is rigorous but entirely non-symbolic. By introducing students to deductive inferences in natural language, the book breaks new ground pedagogically. Cannon focuses on such topics as using a tableaux technique to assess inconsistency; using generative grammar; employing logical analyses of sentences; and dealing with quantifier expressions and syllogisms. An appendix covers truth-functional logic.
This text offers an innovative approach to the teaching of logic, which is rigorous but entirely non-symbolic. By introducing students to deductive inferences in natural language, the book breaks new ground pedagogically. Cannon focuses on such topics as using a tableaux technique to assess inconsistency; using generative grammar; employing logical analyses of sentences; and dealing with quantifier expressions and syllogisms. An appendix covers truth-functional logic.
Book Synopsis Deductive Logic in Natural Language by : Douglas Cannon
Download or read book Deductive Logic in Natural Language written by Douglas Cannon and published by Broadview Press. This book was released on 2002-11-13 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text offers an innovative approach to the teaching of logic, which is rigorous but entirely non-symbolic. By introducing students to deductive inferences in natural language, the book breaks new ground pedagogically. Cannon focuses on such topics as using a tableaux technique to assess inconsistency; using generative grammar; employing logical analyses of sentences; and dealing with quantifier expressions and syllogisms. An appendix covers truth-functional logic.
The main purpose of this volume is to demonstrate several significant distinctions between the predicate calculus and natural language, distinctions that make the former inadequate for the study of the semantics and logic of the latter.
Book Synopsis Logic & Natural Language by : Hanoch Ben-Yami
Download or read book Logic & Natural Language written by Hanoch Ben-Yami and published by Routledge. This book was released on 2004 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this volume is to demonstrate several significant distinctions between the predicate calculus and natural language, distinctions that make the former inadequate for the study of the semantics and logic of the latter.
Frege's invention of the predicate calculus has been the most influential event in the history of modern logic. The calculus’ place in logic is so central that many philosophers think, in fact, of it when they think of logic. This book challenges the position in contemporary logic and philosophy of language of the predicate calculus claiming that it is based on mistaken assumptions. Ben-Yami shows that the predicate calculus is different from natural language in its fundamental semantic characteristics, primarily in its treatment of reference and quantification, and that as a result the calculus is inadequate for the analysis of the semantics and logic of natural language. Ben-Yami develops both an alternative analysis of the semantics of natural language and an alternative deductive system comparable in its deductive power to first order predicate calculus but more adequate than it for the representation of the logic of natural language. Ben-Yami's book is a revolutionary challenge to classical first order predicate calculus, casting doubt on many of the central claims of modern logic.
Book Synopsis Logic & Natural Language by : Hanoch Ben-Yami
Download or read book Logic & Natural Language written by Hanoch Ben-Yami and published by Routledge. This book was released on 2019-09-16 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Frege's invention of the predicate calculus has been the most influential event in the history of modern logic. The calculus’ place in logic is so central that many philosophers think, in fact, of it when they think of logic. This book challenges the position in contemporary logic and philosophy of language of the predicate calculus claiming that it is based on mistaken assumptions. Ben-Yami shows that the predicate calculus is different from natural language in its fundamental semantic characteristics, primarily in its treatment of reference and quantification, and that as a result the calculus is inadequate for the analysis of the semantics and logic of natural language. Ben-Yami develops both an alternative analysis of the semantics of natural language and an alternative deductive system comparable in its deductive power to first order predicate calculus but more adequate than it for the representation of the logic of natural language. Ben-Yami's book is a revolutionary challenge to classical first order predicate calculus, casting doubt on many of the central claims of modern logic.
Book Synopsis Deductive Logic and Descriptive Language by : Frank R. Harrison
Download or read book Deductive Logic and Descriptive Language written by Frank R. Harrison and published by Prentice Hall. This book was released on 1969 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:
This book is intended for students in computer science, formal linguistics, mathematical logic and to colleagues interested in categorial grammars and their logical foundations. These lecture notes present categorial grammars as deductive systems, in the approach called parsing-as-deduction, and the book includes detailed proofs of their main properties. The papers are organized in topical sections on AB grammars, Lambek’s syntactic calculus, Lambek calculus and montague grammar, non-associative Lambek calculus, multimodal Lambek calculus, Lambek calculus, linear logic and proof nets and proof nets for the multimodal Lambek calculus.
Book Synopsis The Logic of Categorial Grammars by : Richard Moot
Download or read book The Logic of Categorial Grammars written by Richard Moot and published by Springer. This book was released on 2012-06-30 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for students in computer science, formal linguistics, mathematical logic and to colleagues interested in categorial grammars and their logical foundations. These lecture notes present categorial grammars as deductive systems, in the approach called parsing-as-deduction, and the book includes detailed proofs of their main properties. The papers are organized in topical sections on AB grammars, Lambek’s syntactic calculus, Lambek calculus and montague grammar, non-associative Lambek calculus, multimodal Lambek calculus, Lambek calculus, linear logic and proof nets and proof nets for the multimodal Lambek calculus.
Book Synopsis Practical Reasoning in Natural Language by : Stephen N. Thomas
Download or read book Practical Reasoning in Natural Language written by Stephen N. Thomas and published by . This book was released on 1981 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt:
This book takes an idea first explored by medieval logicians 800 years ago and revisits it armed with the tools of contemporary linguistics, logic, and computer science. The idea - the Holy Grail of the medieval logicians - was the thought that all of logic could be reduced to two very simple rules that are sensitive to logical polarity (for example, the presence and absence of negations). Ludlow and Živanović pursue this idea and show how it has profound consequences for our understanding of the nature of human inferential capacities. They also show its consequences for some of the deepest issues in contemporary linguistics, including the nature of quantification, puzzles about discourse anaphora and pragmatics, and even insights into the source of aboutness in natural language. The key to their enterprise is a formal relation they call "p-scope" - a polarity-sensitive relation that controls the operations that can be carried out in their Dynamic Deductive System. They show that with p-scope in play, deductions can be carried out using sublogical operations like those they call COPY and PRUNE - operations that are simple syntactic operations on sentences. They prove that the resulting deductive system is complete and sound. The result is a beautiful formal tapestry in which p-scope unlocks important properties of natural language, including the property of "restrictedness," which they prove to be equivalent to the semantic notion of conservativity. More than that, they show that restrictedness is also a key to understanding quantification and discourse anaphora, and many other linguistic phenomena.
Book Synopsis Language, Form, and Logic by : Peter Ludlow
Download or read book Language, Form, and Logic written by Peter Ludlow and published by Oxford University Press. This book was released on 2022-02-24 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes an idea first explored by medieval logicians 800 years ago and revisits it armed with the tools of contemporary linguistics, logic, and computer science. The idea - the Holy Grail of the medieval logicians - was the thought that all of logic could be reduced to two very simple rules that are sensitive to logical polarity (for example, the presence and absence of negations). Ludlow and Živanović pursue this idea and show how it has profound consequences for our understanding of the nature of human inferential capacities. They also show its consequences for some of the deepest issues in contemporary linguistics, including the nature of quantification, puzzles about discourse anaphora and pragmatics, and even insights into the source of aboutness in natural language. The key to their enterprise is a formal relation they call "p-scope" - a polarity-sensitive relation that controls the operations that can be carried out in their Dynamic Deductive System. They show that with p-scope in play, deductions can be carried out using sublogical operations like those they call COPY and PRUNE - operations that are simple syntactic operations on sentences. They prove that the resulting deductive system is complete and sound. The result is a beautiful formal tapestry in which p-scope unlocks important properties of natural language, including the property of "restrictedness," which they prove to be equivalent to the semantic notion of conservativity. More than that, they show that restrictedness is also a key to understanding quantification and discourse anaphora, and many other linguistic phenomena.
Clear focus on its application of formal logic to ordinary English is the most distinctive feature of this textbook for the introductory course in deductive logic. Great care is taken with the appropriate translation into logical languages of ordinary English sentences. Evaluation of these translations promotes a more effective use of ordinary language. The Principles of Deductive Logic presents symbolic logic in a fuller and more leisurely fashion than other introductory textbooks. Early chapters cover informal material, including definition and informal fallacies. The remainder of the text is devoted to the treatment of four distinct artificial languages. The Categorical language is the language of syllogistic logic. The Extended Categorical language enriches this first language with the symbolic connectives for conjunction and negation. The Propositional Connective language and the First-Order language (with identity) are the two basic languages of modern logic. Each language is accompanied by a deductive system, and is used as an instrument for exploring ordinary language, including ordinary arguments The book contains a large number of exercises whose answers are supplied in the back of the book, and many more that can be assigned as homework. A solution's manual is available to instructors upon their request. The request must be written on college or university letterhead.
Book Synopsis Principles of Deductive Logic by :
Download or read book Principles of Deductive Logic written by and published by SUNY Press. This book was released on with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clear focus on its application of formal logic to ordinary English is the most distinctive feature of this textbook for the introductory course in deductive logic. Great care is taken with the appropriate translation into logical languages of ordinary English sentences. Evaluation of these translations promotes a more effective use of ordinary language. The Principles of Deductive Logic presents symbolic logic in a fuller and more leisurely fashion than other introductory textbooks. Early chapters cover informal material, including definition and informal fallacies. The remainder of the text is devoted to the treatment of four distinct artificial languages. The Categorical language is the language of syllogistic logic. The Extended Categorical language enriches this first language with the symbolic connectives for conjunction and negation. The Propositional Connective language and the First-Order language (with identity) are the two basic languages of modern logic. Each language is accompanied by a deductive system, and is used as an instrument for exploring ordinary language, including ordinary arguments The book contains a large number of exercises whose answers are supplied in the back of the book, and many more that can be assigned as homework. A solution's manual is available to instructors upon their request. The request must be written on college or university letterhead.
Deductive Logic is designed as an intermediate-level text directed at upper-division students from philosophy and the humanities. Its focus is exclusively on deductive logic, avoiding altogether topics such as informal reasoning and scientific method normally included in introductory logic courses. Its exposition of logical topics is informal, with emphasis on explaining the basic concepts and procedures of modern symbolic logic in the simplest and most intuitive manner possible rather than on developing a rigorous formal system and providing proofs of its properties. The fact that the text presupposes a course offered to philosophy students and serves to introduce them to logic as the "language of philosophy" has strongly influenced the selection of topics. The topics here are controversial, and the problems not easily resolved, but this text strives to relate the formal logical structures introduced to issues of philosophic interest.
Book Synopsis Deductive Logic by : David S. Clarke
Download or read book Deductive Logic written by David S. Clarke and published by University Press of America. This book was released on 1998 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deductive Logic is designed as an intermediate-level text directed at upper-division students from philosophy and the humanities. Its focus is exclusively on deductive logic, avoiding altogether topics such as informal reasoning and scientific method normally included in introductory logic courses. Its exposition of logical topics is informal, with emphasis on explaining the basic concepts and procedures of modern symbolic logic in the simplest and most intuitive manner possible rather than on developing a rigorous formal system and providing proofs of its properties. The fact that the text presupposes a course offered to philosophy students and serves to introduce them to logic as the "language of philosophy" has strongly influenced the selection of topics. The topics here are controversial, and the problems not easily resolved, but this text strives to relate the formal logical structures introduced to issues of philosophic interest.
