Automated Proof Search in Non-classical Logics
Automated Proof Search in Non-classical Logics

Author: Lincoln A. Wallen

Publisher: MIT Press (MA)

Published: 1990

Total Pages: 239

ISBN-13: 9780262231442

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This book develops and demonstrates efficient matrix proof methods for automated deduction within an important and comprehensive class of first order and intuitionistic logics. Traditional techniques for the design of efficient proof systems are abstracted from their original setting which allows their application to a wider class of mathematical logic. The logics discussed are used throughout computer science and artificial intelligence. Contents: Introduction I. Automated Deduction in Classical Logic. Proof search in classical sequent calculi. A matrix characterization of classical validity. II. Automated Proof Deduction in Modal Logics. The semantics and proof theory of modal logics. Proof search in modal sequent calculi. Matrix characterizations of modal validity. Alternative proof methods for modal logics. Matrix based proof search. III. Automated Deduction in Intuitionistic Logic. A Matrix proof method. Conclusions. Lincoln A. Wallen is a B.P. Venture Research Fellow at the University of Texas at Austin Automated Deduction in Nonclassical Logics is included in the Artificial Intelligence series, edited by Patrick Winston Michael Brady, and Daniel Bobrow.

Arnon Avron on Semantics and Proof Theory of Non-Classical Logics
Arnon Avron on Semantics and Proof Theory of Non-Classical Logics

Author: Ofer Arieli

Publisher: Springer Nature

Published: 2021-07-30

Total Pages: 369

ISBN-13: 3030712583

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This book is a collection of contributions honouring Arnon Avron’s seminal work on the semantics and proof theory of non-classical logics. It includes presentations of advanced work by some of the most esteemed scholars working on semantic and proof-theoretical aspects of computer science logic. Topics in this book include frameworks for paraconsistent reasoning, foundations of relevance logics, analysis and characterizations of modal logics and fuzzy logics, hypersequent calculi and their properties, non-deterministic semantics, algebraic structures for many-valued logics, and representations of the mechanization of mathematics. Avron’s foundational and pioneering contributions have been widely acknowledged and adopted by the scientific community. His research interests are very broad, spanning over proof theory, automated reasoning, non-classical logics, foundations of mathematics, and applications of logic in computer science and artificial intelligence. This is clearly reflected by the diversity of topics discussed in the chapters included in this book, all of which directly relate to Avron’s past and present works. This book is of interest to computer scientists and scholars of formal logic.

First-Order Logic and Automated Theorem Proving
First-Order Logic and Automated Theorem Proving

Author: Melvin Fitting

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 258

ISBN-13: 1468403575

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There are many kinds of books on formal logic. Some have philosophers as their intended audience, some mathematicians, some computer scientists. Although there is a common core to all such books they will be very dif ferent in emphasis, methods, and even appearance. This book is intended for computer scientists. But even this is not precise. Within computer sci ence formal logic turns up in a number of areas, from program verification to logic programming to artificial intelligence. This book is intended for computer scientists interested in automated theorem proving in classical logic. To be more precise yet, it is essentially a theoretical treatment, not a how-to book, although how-to issues are not neglected. This does not mean, of course, that the book will be of no interest to philosophers or mathematicians. It does contain a thorough presentation of formal logic and many proof techniques, and as such it contains all the material one would expect to find in a course in formal logic covering completeness but not incompleteness issues. The first item to be addressed is, what are we talking about and why are we interested in it. We are primarily talking about truth as used in mathematical discourse, and our interest in it is, or should be, self-evident. Truth is a semantic concept, so we begin with models and their properties. These are used to define our subject.

Automated Deduction in Classical and Non-Classical Logics
Automated Deduction in Classical and Non-Classical Logics

Author: Ricardo Caferra

Publisher: Springer

Published: 2003-07-31

Total Pages: 306

ISBN-13: 3540465081

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This volume presents a collection of thoroughly reviewed revised full papers on automated deduction in classical, modal, and many-valued logics, with an emphasis on first-order theories. Five invited papers by prominent researchers give a consolidated view of the recent developments in first-order theorem proving. The 14 research papers presented went through a twofold selection process and were first presented at the International Workshop on First-Order Theorem Proving, FTP'98, held in Vienna, Austria, in November 1998. The contributed papers reflect the current status in research in the area; most of the results presented rely on resolution or tableaux methods, with a few exceptions choosing the equational paradigm.

Goal-Directed Proof Theory
Goal-Directed Proof Theory

Author: Dov M. Gabbay

Publisher: Springer Science & Business Media

Published: 2000-08-31

Total Pages: 282

ISBN-13: 9780792364733

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Goal Directed Proof Theory presents a uniform and coherent methodology for automated deduction in non-classical logics, the relevance of which to computer science is now widely acknowledged. The methodology is based on goal-directed provability. It is a generalization of the logic programming style of deduction, and it is particularly favourable for proof search. The methodology is applied for the first time in a uniform way to a wide range of non-classical systems, covering intuitionistic, intermediate, modal and substructural logics. The book can also be used as an introduction to these logical systems form a procedural perspective. Readership: Computer scientists, mathematicians and philosophers, and anyone interested in the automation of reasoning based on non-classical logics. The book is suitable for self study, its only prerequisite being some elementary knowledge of logic and proof theory.