# Goal Directed Proof Theory

The book is suitable for self study, its only prerequisite being some elementary knowledge of logic and proof theory.

Author: Dov M. Gabbay

Publisher: Springer Science & Business Media

ISBN: 9789401717137

Category: Philosophy

Page: 268

View: 637

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.
Categories: Philosophy

# Goal Directed Proof Theory

Author: Dov M. Gabbay

Publisher:

ISBN: 9401717141

Category:

Page: 284

View: 704

Categories:

# Handbook of Tableau Methods

An annual tableaux conference is being held and proceedings are published. The present volume is a Handbook a/Tableaux pre senting to the community a wide coverage of tableaux systems for a variety of logics.

Author: M. D'Agostino

Publisher: Springer Science & Business Media

ISBN: 9789401717540

Category: Philosophy

Page: 670

View: 746

Recent years have been blessed with an abundance of logical systems, arising from a multitude of applications. A logic can be characterised in many different ways. Traditionally, a logic is presented via the following three components: 1. an intuitive non-formal motivation, perhaps tie it in to some application area 2. a semantical interpretation 3. a proof theoretical formulation. There are several types of proof theoretical methodologies, Hilbert style, Gentzen style, goal directed style, labelled deductive system style, and so on. The tableau methodology, invented in the 1950s by Beth and Hintikka and later per fected by Smullyan and Fitting, is today one of the most popular, since it appears to bring together the proof-theoretical and the semantical approaches to the pre of a logical system and is also very intuitive. In many universities it is sentation the style first taught to students. Recently interest in tableaux has become more widespread and a community crystallised around the subject. An annual tableaux conference is being held and proceedings are published. The present volume is a Handbook a/Tableaux pre senting to the community a wide coverage of tableaux systems for a variety of logics. It is written by active members of the community and brings the reader up to frontline research. It will be of interest to any formal logician from any area.
Categories: Philosophy

# Handbook of Philosophical Logic

We are confident that the second edition will prove to be just as good! The first edition was the second handbook published for the logic com- nity.

Author: Dov M. Gabbay

Publisher: Springer Science & Business Media

ISBN: 9789401704649

Category: Philosophy

Page: 368

View: 376

It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as well as to consumers of logic in many applied areas. The main logic article in the Encyclopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good! The first edition was the second handbook published for the logic com- nity. It followed the North Holland one volume Handbook of Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook of Philosophical Logic, published 1983-1989 came at a fortunate temporal junction at the evolution of logic. This was the time when logic was gaining ground in computer science and artificial intelligence circles. These areas were under increasing commercial pressure to provide devices which help and/or replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organi- tion on the one hand and to provide the theoretical basis for the computer program constructs on the other.
Categories: Philosophy

Reiter [ 14 ] presented a goal - directed proof theory for normal default theories . But Reiter and Criscuolo [ 15 ] showed that semi - normal defaults were needed in DL to give priorities between defaults to eliminate anomalous ...

Author: Jacques Wainer

Publisher: Springer Science & Business Media

ISBN: 3540604367

Category: Computers

Page: 342

View: 197

Invited papers; knowledge representation and automated reasoning; tutoring systems; machine learning; neural networks; distributed AI; knowledge acquisition and knowledge bases; posters.
Categories: Computers

# Proof Theory for Fuzzy Logics

Atomic goals q might then be matched (if possible) with the “head” of a formula B → q in the database, and its “body” B asked in turn. Goal-directed proof search can also be refined, e.g. by: 1. putting constraints on databases, ...

Author: George Metcalfe

Publisher: Springer Science & Business Media

ISBN: 9781402094095

Category: Mathematics

Page: 276

View: 542

Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than ten years of intensive work by researchers in the area, including the authors. In addition to providing alternative elegant presentations of fuzzy logics, proof-theoretic methods are useful for addressing theoretical problems (including key standard completeness results) and developing efficient deduction and decision algorithms. Proof-theoretic presentations also place fuzzy logics in the broader landscape of non-classical logics, revealing deep relations with other logics studied in Computer Science, Mathematics, and Philosophy. The book builds methodically from the semantic origins of fuzzy logics to proof-theoretic presentations such as Hilbert and Gentzen systems, introducing both theoretical and practical applications of these presentations.
Categories: Mathematics

# The Semantics and Proof Theory of the Logic of Bunched Implications

In BI, a similar class of hereditary Harrop formulae supports goaldirected proof (we simplify, for brevity): Program clauses P := I | A PAP G – A P + P G – A Goals G ::= T | I | A G A G | G V G | P → G | G + G | P → G. In ...

Author: David J. Pym

Publisher: Springer Science & Business Media

ISBN: 9789401700917

Category: Mathematics

Page: 290

View: 649

This is a monograph about logic. Specifically, it presents the mathe matical theory of the logic of bunched implications, BI: I consider Bl's proof theory, model theory and computation theory. However, the mono graph is also about informatics in a sense which I explain. Specifically, it is about mathematical models of resources and logics for reasoning about resources. I begin with an introduction which presents my (background) view of logic from the point of view of informatics, paying particular attention to three logical topics which have arisen from the development of logic within informatics: • Resources as a basis for semantics; • Proof-search as a basis for reasoning; and • The theory of representation of object-logics in a meta-logic. The ensuing development represents a logical theory which draws upon the mathematical, philosophical and computational aspects of logic. Part I presents the logical theory of propositional BI, together with a computational interpretation. Part II presents a corresponding devel opment for predicate BI. In both parts, I develop proof-, model- and type-theoretic analyses. I also provide semantically-motivated compu tational perspectives, so beginning a mathematical theory of resources. I have not included any analysis, beyond conjecture, of properties such as decidability, finite models, games or complexity. I prefer to leave these matters to other occasions, perhaps in broader contexts.
Categories: Mathematics

# Security and Trust Management

Besides describing and justifying the use of goal-directed proof search for BLsf, we make two minor technical contributions ... In Section4, we present our theoretical results, showing that goal-directed search is sound and complete and ...

Author: Audun Jøsang

Publisher: Springer

ISBN: 9783642380044

Category: Computers

Page: 321

View: 678

This book constitutes the thoroughly refereed post-conference proceedings of the 8th International Workshop on Security and Trust Management, STM 2012, held in Pisa, Italy, in September 2012 - in conjunction with the 17th European Symposium Research in Computer Security (ESORICS 2012). The 20 revised full papers were carefully reviewed and selected from 57 submissions. The papers are organized into topical sections on policy enforcement and monitoring; access control; trust, reputation, and privacy; distributed systems and physical security; authentication and security policies.
Categories: Computers

# Foundations of Software Science and Computation Structures

24th International Conference, FOSSACS 2021, Held as Part of the European Joint Conferences on Theory and Practice of Software, ... The focusing principle is a restriction of the proofsearch space that can capture various goal-directed ...

Author: Stefan Kiefer

Publisher: Springer Nature

ISBN: 9783030719951

Category: Computer software

Page:

View: 793

This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems.
Categories: Computer software

# Proof Theory

This two-way procedure enables a more goal-directed proving process than is possible in axiomatic calculi. Sequent calculi, the other sort of calculi introduced by Gentzen, are a step beyond the natural deduction systems.

Author: Katalin Bimbo

Publisher: CRC Press

ISBN: 9781466564688

Category: Mathematics

Page: 386

View: 220

Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems. Addressing this deficiency, Proof Theory: Sequent Calculi and Related Formalisms presents a comprehensive treatment of sequent calculi, including a wide range of variations. It focuses on sequent calculi
Categories: Mathematics

Reiter ( 14 ) presented a goal - directed proof theory for normal default theories . But Reiter and Criscuolo ( 15 ) showed that semi - normal defaults were needed in DL to give priorities between defaults to eliminate anomalous ...

Author:

Publisher:

ISBN: UOM:39015038407907

Category: Artificial intelligence

Page:

View: 335

Categories: Artificial intelligence

# Computer Science Logic

Goal-directed Proof Theory. Kluwer, 2000. 5. D. Gabbay and N. Olivetti. Goal oriented deductions. In D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, volume 9, pages 199–285. Kluwer, second edition, 2002. 6.

Author: Jerzy Marcinkowski

Publisher: Springer

ISBN: 9783540301240

Category: Computers

Page: 522

View: 538

This book constitutes the refereed proceedings of the 18th International Workshop on Computer Science Logic, CSL 2004, held as the 13th Annual Conference of the EACSL in Karpacz, Poland, in September 2004. The 33 revised full papers presented together with 5 invited contributions were carefully reviewed and selected from 88 papers submitted. All current aspects of logic in computer science are addressed ranging from mathematical logic and logical foundations to methodological issues and applications of logics in various computing contexts.
Categories: Computers

# Logic Colloquium 01

Proof. We follow the same induction steps as the proof of Theorem 4.5 and further assume the interpolant is in the ... Only small changes are required to accommodate the slightly different goal directed proof theory of K4, T and S4, ...

Author: Matthias Baaz

Publisher: Cambridge University Press

ISBN: 9781108695442

Category: Mathematics

Page:

View: 832

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the twentieth publication in the Lecture Notes in Logic series, contains the proceedings of the 2001 European Summer Meeting of the Association for Symbolic Logic, held at the Vienna University of Technology. Two long articles present accessible expositions on resolution theorem proving and the determinacy of long games. The remaining articles cover separate research topics in many areas of mathematical logic, including applications in computer science, proof theory, set theory, model theory, computability theory, linguistics and aspects of philosophy. This collection will interest not only mathematical logicians but also philosophical logicians, historians of logic, computer scientists, formal linguists and mathematicians working in algebra, abstract analysis and topology.
Categories: Mathematics

# A Modern Perspective on Type Theory

D.M. Gabbay and N. Olivetti : Goal - Directed Proof Theory . 2000 ISBN 0-7923-6473-2 22. M.-A. Williams and H. Rott ( eds . ) : Frontiers in Belief Revision . 2001 ISBN 0-7923-7021 - X 23. E. Morscher and A. Hieke ( eds . ) ...

Author: F.D. Kamareddine

Publisher: Springer Science & Business Media

ISBN: 1402023340

Category: Mathematics

Page: 360

View: 364

This book provides an overview of type theory. The first part of the book is historical, yet at the same time, places historical systems in the modern setting. The second part deals with modern type theory as it developed since the 1940s, and with the role of propositions as types (or proofs as terms. The third part proposes new systems that bring more advantages together.
Categories: Mathematics

# Questions Inferences and Scenarios

Can we prove anything by means of pure questioning? How to model goal-directed problem solving? These are the main issues of Andrzej Wiśniewski's "Questions, Inferences, and Scenarios".

Author: Andrzej Wisniewski

Publisher:

ISBN: 1848901208

Category: Mathematics

Page: 190

View: 661

"The importance of questions is beyond doubt. But the degree of attention paid to them in logic and linguistics is still less than they deserve." (from the Preface) What is a question? How to represent questions in formal languages? How to model reasoning in which questions are involved? Can we prove anything by means of pure questioning? How to model goal-directed problem solving? These are the main issues of Andrzej Wi niewski's "Questions, Inferences, and Scenarios." This book offers a state-of-the-art exposition of Inferential Erotetic Logic, that is, an approach to the logic of questions focused on inferences which lead to questions as conclusions. Wi niewski characterizes semantic relations which determine validity of these inferences within the framework of Minimal Erotetic Semantics, applicable to a wide range of formal languages. He elaborates in detail the concept of erotetic search scenario, a tool for modelling problem solving. Moreover, the author presents some applications of Inferential Erotetic Logic in proof theory. Andrzej Wi niewski is one of the most prominent contemporary researchers in the logic of questions. Currently, he is a full professor at the Department of Logic and Cognitive Science, Institute of Psychology, Adam Mickiewicz University in Pozna, Poland.
Categories: Mathematics

# Logic Programming

Goal-directed, or uniform, proofs are se- quentcalculus proofsin which right-decompositionrules are always used to ... this system forms an important link between the proof theory and the operational semantics in the next section.

Author: Sandro Etalle

Publisher: Springer Science & Business Media

ISBN: 9783540366355

Category: Computers

Page: 474

View: 506

This book constitutes the refereed proceedings of the 22nd International Conference on Logic Programming, ICLP 2006, held in Seattle, WA, USA, in August 2006. This volume presents 20 revised full papers and 6 application papers together with 2 invited talks, 2 tutorials and special interest papers, as well as 17 poster presentations and the abstracts of 7 doctoral consortium articles. Coverage includes all issues of current research in logic programming.
Categories: Computers

# Logic Language Information and Computation

Although it seems likely that Cr is a useful relevant logic, it has an elegant proof theory which has an adequate ... The main objective of those goal directed proofs is to push the heuristics a reasoner uses to construct a proof for a ...

Author: Lev D. Beklemishev

Publisher: Springer Science & Business Media

ISBN: 9783642209192

Category: Mathematics

Page: 311

View: 780

This book constitutes the refereed proceedings of the 18th Workshop on Logic, Language, Information and Communication, WoLLIC 2011, held in Philadelphia, PA, USA, in May 2011. The 21 revised full papers presented were carefully reviewed and selected from 35 submissions. Among the topics covered are various aspects of mathematical logic, computer science logics, philosophical logics, such as complexity theory, model theory, partial order, Hoare logics, hybrid logics, Turing machines, etc.
Categories: Mathematics

# Automated Model Building

2000 ISBN 0-7923-6350-7 D.M. Gabbay and N. Olivetti: Goal-Directed Proof Theory. 2000 ISBN 0-7923-6473-2 M.-A. Williams and H. Rott (eds.): Frontiers in Belief Revision. 2001 ISBN 0-7923-7021-X E. Morscher and A. Hieke (eds.): ...

Author: Ricardo Caferra

Publisher: Springer Science & Business Media

ISBN: 9781402026539

Category: Philosophy

Page: 341

View: 317

On the history of the book: In the early 1990s several new methods and perspectives in au- mated deduction emerged. We just mention the superposition calculus, meta-term inference and schematization, deductive decision procedures, and automated model building. It was this last ?eld which brought the authors of this book together. In 1994 they met at the Conference on Automated Deduction (CADE-12) in Nancy and agreed upon the general point of view, that semantics and, in particular, construction of models should play a central role in the ?eld of automated deduction. In the following years the deduction groups of the laboratory LEIBNIZ at IMAG Grenoble and the University of Technology in Vienna organized several bilateral projects promoting this topic. This book emerged as a main result of this cooperation. The authors are aware of the fact, that the book does not cover all relevant methods of automated model building (also called model construction or model generation); instead the book focuses on deduction-based symbolic methods for the construction of Herbrand models developed in the last 12 years. Other methods of automated model building, in particular also ?nite model building, are mainly treated in the ?nal chapter; this chapter is less formal and detailed but gives a broader view on the topic and a comparison of di?erent approaches. Howtoreadthisbook: In the introduction we give an overview of automated deduction in a historical context, taking into account its relationship with the human views on formal and informal proofs.
Categories: Philosophy

# Inference on the Low Level

2000 ISBN 0-7923–6.350-7 D.M. Gabbay and N. Olivetti: Goal-Directed Proof Theory. 2000 ISBN 0-7923–6473–2 M.-A. Williams and H. Rott (eds.): Frontiers in Belief Revision. 2001 ISBN 0-7923–7021-X E. Morscher and A. Hieke (eds.): ...

Author: Hannes Leitgeb

Publisher: Springer Science & Business Media

ISBN: 9781402028069

Category: Mathematics

Page: 386

View: 172

In contrast to the prevailing tradition in epistemology, the focus in this book is on low-level inferences, i.e., those inferences that we are usually not consciously aware of and that we share with the cat nearby which infers that the bird which she sees picking grains from the dirt, is able to fly. Presumably, such inferences are not generated by explicit logical reasoning, but logical methods can be used to describe and analyze such inferences. Part 1 gives a purely system-theoretic explication of belief and inference. Part 2 adds a reliabilist theory of justification for inference, with a qualitative notion of reliability being employed. Part 3 recalls and extends various systems of deductive and nonmonotonic logic and thereby explains the semantics of absolute and high reliability. In Part 4 it is proven that qualitative neural networks are able to draw justified deductive and nonmonotonic inferences on the basis of distributed representations. This is derived from a soundness/completeness theorem with regard to cognitive semantics of nonmonotonic reasoning. The appendix extends the theory both logically and ontologically, and relates it to A. Goldman's reliability account of justified belief.
Categories: Mathematics

# Formalized Probability Theory and Applications Using Theorem Proving

3.2.3 Theories A HOL4 theory is a collection of valid HOL4 types, constants, axioms and theorems and is usually stored as a file in computers. ... A backward or a goal directed proof method is the reverse of the forward proof method.

Author: Hasan, Osman

Publisher: IGI Global

ISBN: 9781466683167

Category: Mathematics

Page: 298

View: 221

Scientists and engineers often have to deal with systems that exhibit random or unpredictable elements and must effectively evaluate probabilities in each situation. Computer simulations, while the traditional tool used to solve such problems, are limited in the scale and complexity of the problems they can solve. Formalized Probability Theory and Applications Using Theorem Proving discusses some of the limitations inherent in computer systems when applied to problems of probabilistic analysis, and presents a novel solution to these limitations, combining higher-order logic with computer-based theorem proving. Combining practical application with theoretical discussion, this book is an important reference tool for mathematicians, scientists, engineers, and researchers in all STEM fields.
Categories: Mathematics