The Application of Theorem Proving to Question-answering Systems

The Application of Theorem Proving to Question-answering Systems

Author: Claude Cordell Green

Publisher:

Published: 1970

Total Pages: 186

ISBN-13:

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The paper shows how a question-answering system can use first-order logic as its language and an automatic theorem prover, based upon the resolution inference principle, as its deductive mechanism. The resolution proof procedure is extended to a constructive proof procedure. An answer construction algorithm is given whereby the system is able not only to produce yes or no answers but also to find or construct an object satisfying a specified condition. A working computer program, QA3, based on these ideas, is described. Methods are presented for solving state transformation problems. In addition to question-answering, the program can do automatic programming, control and problem solving for a simple robot, pattern recognition, and puzzles. (Author).


Automation of Reasoning

Automation of Reasoning

Author: J. Siekmann

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 641

ISBN-13: 3642819559

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"Kind of crude, but it works, boy, it works!" AZan NeweZZ to Herb Simon, Christmas 1955 In 1954 a computer program produced what appears to be the first computer generated mathematical proof: Written by M. Davis at the Institute of Advanced Studies, USA, it proved a number theoretic theorem in Presburger Arithmetic. Christmas 1955 heralded a computer program which generated the first proofs of some propositions of Principia Mathematica, developed by A. Newell, J. Shaw, and H. Simon at RAND Corporation, USA. In Sweden, H. Prawitz, D. Prawitz, and N. Voghera produced the first general program for the full first order predicate calculus to prove mathematical theorems; their computer proofs were obtained around 1957 and 1958, about the same time that H. Gelernter finished a computer program to prove simple high school geometry theorems. Since the field of computational logic (or automated theorem proving) is emerging from the ivory tower of academic research into real world applications, asserting also a definite place in many university curricula, we feel the time has corne to examine and evaluate its history. The article by Martin Davis in the first of this series of volumes traces the most influential ideas back to the 'prehistory' of early logical thought showing how these ideas influenced the underlying concepts of most early automatic theorem proving programs.


Tests and Proofs

Tests and Proofs

Author: Gordon Fraser

Publisher: Springer Science & Business Media

Published: 2010-06-17

Total Pages: 193

ISBN-13: 3642139760

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This volume contains the proceedings of TAP 2010, the 4th International C- ference on Tests and Proofs held during July 1–2 in M ́ alaga, Spain as part of TOOLS Federated Conferences. TAP 2010wasthe fourth event of an ongoingseriesof conferencesdevoted to the convergence of proofs and tests. In the past, proving and testing were seen as very di?erent and even competing techniques. Proving people would say: If correctness is proved, what do we need tests for? Testers, on the other hand, would claim that proving is too limited in applicability and testing is the only truepathtocorrectness. Ofcourse,bothhaveapoint,buttoquoteEdBrinksma from his 2009 keynote at the Dutch Testing Day and Testcom/FATES: “Who would want to ?y in an airplane with software proved correct, but not tested?” Indeed, the true power lies in the combination of both approaches. Today, m- ern test systems rely on techniques deeply rooted in formal proof techniques, and testing techniques make it possible to apply proof techniques where there was no possibility previously. At a time when even mainstream software engineering conferences start f- turing papers with both “testing” and “proving”in their titles, we are clearly on the verge of a new age where testing and proving are not competing but ?nally accepted as complementary techniques. Albeit, we are not quite there yet, and so the TAP conferences aim to provide a forum for researchers working on the converging topics and to raise general awareness of this convergence.


Symbolic Logic and Mechanical Theorem Proving

Symbolic Logic and Mechanical Theorem Proving

Author: Chin-Liang Chang

Publisher: Academic Press

Published: 2014-06-28

Total Pages: 349

ISBN-13: 0080917283

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This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4-9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.


Logic for Programming, Artificial Intelligence, and Reasoning

Logic for Programming, Artificial Intelligence, and Reasoning

Author: Nachum Dershowitz

Publisher: Springer

Published: 2007-10-07

Total Pages: 573

ISBN-13: 3540755608

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This book constitutes the refereed proceedings of the 14th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2007, held in Yerevan, Armenia. It contains 36 revised full papers, 15 short papers and three invited talks that were carefully selected from 78 submissions. The papers address all current issues in logic programming, logic-based program manipulation, formal method, automated reasoning, and various kinds of AI logics.


Knowledge Representation, Reasoning, and the Design of Intelligent Agents

Knowledge Representation, Reasoning, and the Design of Intelligent Agents

Author: Michael Gelfond

Publisher: Cambridge University Press

Published: 2014-03-10

Total Pages: 363

ISBN-13: 1107782872

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Knowledge representation and reasoning is the foundation of artificial intelligence, declarative programming, and the design of knowledge-intensive software systems capable of performing intelligent tasks. Using logical and probabilistic formalisms based on answer set programming (ASP) and action languages, this book shows how knowledge-intensive systems can be given knowledge about the world and how it can be used to solve non-trivial computational problems. The authors maintain a balance between mathematical analysis and practical design of intelligent agents. All the concepts, such as answering queries, planning, diagnostics, and probabilistic reasoning, are illustrated by programs of ASP. The text can be used for AI-related undergraduate and graduate classes and by researchers who would like to learn more about ASP and knowledge representation.