Proof Theory and Automated Deduction

Proof Theory and Automated Deduction PDF

Author: Jean Goubault-Larrecq

Publisher: Springer Science & Business Media

Published: 2001-11-30

Total Pages: 448

ISBN-13: 9781402003684

DOWNLOAD EBOOK →

Interest in computer applications has led to a new attitude to applied logic in which researchers tailor a logic in the same way they define a computer language. In response to this attitude, this text for undergraduate and graduate students discusses major algorithmic methodologies, and tableaux and resolution methods. The authors focus on first-order logic, the use of proof theory, and the computer application of automated searches for proofs of mathematical propositions. Annotation copyrighted by Book News, Inc., Portland, OR

Automated Deduction - CADE-17

Automated Deduction - CADE-17 PDF

Author: David McAllester

Publisher: Springer

Published: 2000-06-05

Total Pages: 544

ISBN-13: 9783540676645

DOWNLOAD EBOOK →

For the past 25 years the CADE conference has been the major forum for the presentation of new results in automated deduction. This volume contains the papers and system descriptions selected for the 17th International Conference on Automated Deduction, CADE-17, held June 17-20, 2000,at Carnegie Mellon University, Pittsburgh, Pennsylvania (USA). Fifty-three research papers and twenty system descriptions were submitted by researchers from ?fteen countries. Each submission was reviewed by at least three reviewers. Twenty-four research papers and ?fteen system descriptions were accepted. The accepted papers cover a variety of topics related to t- orem proving and its applications such as proof carrying code, cryptographic protocol veri?cation, model checking, cooperating decision procedures, program veri?cation, and resolution theorem proving. The program also included three invited lectures: “High-level veri?cation using theorem proving and formalized mathematics” by John Harrison, “Sc- able Knowledge Representation and Reasoning Systems” by Henry Kautz, and “Connecting Bits with Floating-Point Numbers: Model Checking and Theorem Proving in Practice” by Carl Seger. Abstracts or full papers of these talks are included in this volume.In addition to the accepted papers, system descriptions, andinvited talks, this volumecontains one page summaries of four tutorials and ?ve workshops held in conjunction with CADE-17.

An Introduction to Proof Theory

An Introduction to Proof Theory PDF

Author: Paolo Mancosu

Publisher: Oxford University Press

Published: 2021-08-12

Total Pages: 336

ISBN-13: 0192649299

DOWNLOAD EBOOK →

An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.

Goal-Directed Proof Theory

Goal-Directed Proof Theory PDF

Author: Dov M. Gabbay

Publisher: Springer Science & Business Media

Published: 2000-08-31

Total Pages: 282

ISBN-13: 9780792364733

DOWNLOAD EBOOK →

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.

Proof Theory and Automated Deduction

Proof Theory and Automated Deduction PDF

Author: Jean Goubault-Larrecq

Publisher: Springer

Published: 2001-12-14

Total Pages: 0

ISBN-13: 9789401139816

DOWNLOAD EBOOK →

The last twenty years have witnessed an accelerated development of pure and ap plied logic, particularly in response to the urgent needs of computer science. Many traditional logicians have developed interest in applications and in parallel a new generation of researchers in logic has arisen from the computer science community. A new attitude to applied logic has evolved, where researchers tailor a logic for their own use in the same way they define a computer language, and where auto mated deduction for the logic and its fragments is as important as the logic itself. In such a climate there is a need to emphasise algorithmic logic methodologies alongside any individual logics. Thus the tableaux method or the resolution method are as central to todays discipline of logic as classical logic or intuitionistic logic are. From this point of view, J. Goubault and I. Mackie's book on Proof Theory and Automated Deduction is most welcome. It covers major algorithmic methodolo gies as well as a variety of logical systems. It gives a wide overview for the ap plied consumer of logic while at the same time remains relatively elementary for the beginning student. A decade ago I put forward my view that a logical system should be presented as a point in a grid. One coordinate is its philosphy, motivation, its accepted theorems and its required non-theorems. The other coordinate is the algorithmic methodol ogy and execution chosen for its effective presentation. Together these two aspects constitute a 'logic'.

Automated Deduction - A Basis for Applications Volume I Foundations - Calculi and Methods Volume II Systems and Implementation Techniques Volume III Applications

Automated Deduction - A Basis for Applications Volume I Foundations - Calculi and Methods Volume II Systems and Implementation Techniques Volume III Applications PDF

Author: Wolfgang Bibel

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 340

ISBN-13: 9401704376

DOWNLOAD EBOOK →

We are invited to deal with mathematical activity in a sys tematic way [ ... ] one does expect and look for pleasant surprises in this requirement of a novel combination of psy chology, logic, mathematics and technology. Hao Wang, 1970, quoted from(Wang, 1970). The field of mathematics has been a key application area for automated theorem proving from the start, in fact the very first automatically found the orem was that the sum of two even numbers is even (Davis, 1983). The field of automated deduction has witnessed considerable progress and in the last decade, automated deduction methods have made their way into many areas of research and product development in computer science. For instance, deduction systems are increasingly used in software and hardware verification to ensure the correctness of computer hardware and computer programs with respect to a given specification. Logic programming, while still falling somewhat short of its expectations, is now widely used, deduc tive databases are well-developed and logic-based description and analysis of hard-and software is commonplace today.

Basic Proof Theory

Basic Proof Theory PDF

Author: Anne Sjerp Troelstra

Publisher:

Published: 1996

Total Pages: 343

ISBN-13: 9780521572231

DOWNLOAD EBOOK →

Introduction to proof theory and its applications in mathematical logic, theoretical computer science and artificial intelligence.

Automated Deduction - CADE-16

Automated Deduction - CADE-16 PDF

Author: Harald Ganzinger

Publisher: Springer Science & Business Media

Published: 1999-06-23

Total Pages: 442

ISBN-13: 3540662227

DOWNLOAD EBOOK →

This book constitutes the refereed proceedings of the 16th International Conference on Automated Deduction, CADE-16, held in Trento, Italy in July 1999 as part of FLoC'99. The 21 revised full papers presented were carefully reviewed and selected from a total of 83 submissions. Also included are 15 system descriptions and two invited full papers. The book addresses all current issues in automated deduction and theorem proving, ranging from logical foundations to deduction systems design and evaluation

Proof Theory of Modal Logic

Proof Theory of Modal Logic PDF

Author: Heinrich Wansing

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 317

ISBN-13: 9401727988

DOWNLOAD EBOOK →

Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.

Automated Deduction - CADE-21

Automated Deduction - CADE-21 PDF

Author: Frank Pfenning

Publisher: Springer Science & Business Media

Published: 2007-07-05

Total Pages: 532

ISBN-13: 3540735941

DOWNLOAD EBOOK →

A veritable one-stop-shop for anyone looking to get up to speed on what is going down in the field of automated deduction right now. This book contains the refereed proceedings of the 21st International Conference on Automated Deduction, CADE-21, held in Bremen, Germany, in July 2007. The 28 revised full papers and 6 system descriptions presented were selected from 64 submissions. All current aspects of automated deduction are addressed, ranging from theoretical and methodological issues to presentation and evaluation of theorem provers and logical reasoning systems.