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Proof Methods for Modal and Intuitionistic Logics

2013-04-18 Philosophy
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Release : 2013-04-18
Genre : Philosophy
Kind : eBook
Book Rating : 945/5 ( reviews)

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Book Synopsis Proof Methods for Modal and Intuitionistic Logics by : M. Fitting

Download or read book Proof Methods for Modal and Intuitionistic Logics written by M. Fitting. This book was released on 2013-04-18. Available in PDF, EPUB and Kindle. Book excerpt: "Necessity is the mother of invention. " Part I: What is in this book - details. There are several different types of formal proof procedures that logicians have invented. The ones we consider are: 1) tableau systems, 2) Gentzen sequent calculi, 3) natural deduction systems, and 4) axiom systems. We present proof procedures of each of these types for the most common normal modal logics: S5, S4, B, T, D, K, K4, D4, KB, DB, and also G, the logic that has become important in applications of modal logic to the proof theory of Peano arithmetic. Further, we present a similar variety of proof procedures for an even larger number of regular, non-normal modal logics (many introduced by Lemmon). We also consider some quasi-regular logics, including S2 and S3. Virtually all of these proof procedures are studied in both propositional and first-order versions (generally with and without the Barcan formula). Finally, we present the full variety of proof methods for Intuitionistic logic (and of course Classical logic too). We actually give two quite different kinds of tableau systems for the logics we consider, two kinds of Gentzen sequent calculi, and two kinds of natural deduction systems. Each of the two tableau systems has its own uses; each provides us with different information about the logics involved. They complement each other more than they overlap. Of the two Gentzen systems, one is of the conventional sort, common in the literature.

Interpolation and Definability

2005-05-12 Computers
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Release : 2005-05-12
Genre : Computers
Kind : eBook
Book Rating : 744/5 ( reviews)

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Book Synopsis Interpolation and Definability by : Dov M. Gabbay

Download or read book Interpolation and Definability written by Dov M. Gabbay. This book was released on 2005-05-12. Available in PDF, EPUB and Kindle. Book excerpt: This book is a specialized monograph on interpolation and definability, a notion central in pure logic and with significant meaning and applicability in all areas where logic is applied, especially computer science, artificial intelligence, logic programming, philosophy of science and natural language.Suitable for researchers and graduate students in mathematics, computer science and philosophy, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (second edition), J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and NonmonotonicReasoning, P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2, and David J. Pym and Eike Ritter's Reductive Logic and Proof Search: Proof theory, semantics and control.

Automated Proof Search in Non-classical Logics

1990 Computers
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Release : 1990
Genre : Computers
Kind : eBook
Book Rating : 442/5 ( reviews)

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Book Synopsis Automated Proof Search in Non-classical Logics by : Lincoln A. Wallen

Download or read book Automated Proof Search in Non-classical Logics written by Lincoln A. Wallen. This book was released on 1990. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Proof Theory of Modal Logic

1996-10-31 Computers
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Release : 1996-10-31
Genre : Computers
Kind : eBook
Book Rating : 208/5 ( reviews)

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Book Synopsis Proof Theory of Modal Logic by : Heinrich Wansing

Download or read book Proof Theory of Modal Logic written by Heinrich Wansing. This book was released on 1996-10-31. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with formal, mechanizable reasoning in modal logics, that is, logics of necessity, possibility, belief, time computations etc. It is therefore of immense interest for various interrelated disciplines such as philosophy, AI, computer science, logic, cognitive science and linguistics. The book consists of 15 original research papers, divided into three parts. The first part contains papers which give a profound description of powerful proof-theoretic methods as applied to the normal modal logic S4. Part II is concerned with a number of generalizations of the standard proof-theoretic formats, while the third part presents new and important results on semantics-based proof systems for modal logic.

Automated Proof Search in Non-classical Logics

1987 Automatic theorem proving
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Release : 1987
Genre : Automatic theorem proving
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Automated Proof Search in Non-classical Logics by : Lincoln Anthony Wallen

Download or read book Automated Proof Search in Non-classical Logics written by Lincoln Anthony Wallen. This book was released on 1987. Available in PDF, EPUB and Kindle. Book excerpt:

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