Automated deduction : a basis for applications

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Bibliographic Information

Automated deduction : a basis for applications

edited by Wolfgang Bibel and Peter H. Schmitt

（Applied logic series, v.8-10）

Kluwer Academic, c1998

  • set
  • v.1
  • v.2
  • v.3

Available at  / 21 libraries

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Includes bibliographies and indexes

Contents of Works

  • v.1. Foundations. calculi and methods
  • v.2. Systems and implementation techniques
  • v.3. Applications

Description and Table of Contents

Volume

v.1 ISBN 9780792351290

Description

The nationwide research project `Deduktion', funded by the `Deutsche Forschungsgemeinschaft (DFG)' for a period of six years, brought together almost all research groups within Germany engaged in the field of automated reasoning. Intensive cooperation and exchange of ideas led to considerable progress both in the theoretical foundations and in the application of deductive knowledge. This three-volume book covers these original contributions moulded into the state of the art of automated deduction. The three volumes are intended to document and advance a development in the field of automated deduction that can now be observed all over the world. Rather than restricting the interest to purely academic research, the focus now is on the investigation of problems derived from realistic applications. In fact industrial applications are already pursued on a trial basis. In consequence the emphasis of the volumes is not on the presentation of the theoretical foundations of logical deduction as such, as in a handbook; rather the books present the concepts and methods now available in automated deduction in a form which can be easily accessed by scientists working in applications outside of the field of deduction. This reflects the strong conviction that automated deduction is on the verge of being fully included in the evolution of technology. Volume I focuses on basic research in deduction and on the knowledge on which modern deductive systems are based. Volume II presents techniques of implementation and details about system building. Volume III deals with applications of deductive techniques mainly, but not exclusively, to mathematics and the verification of software. Each chapter was read by two referees, one an international expert from abroad and the other a knowledgeable participant in the national project. It has been accepted for inclusion on the basis of these review reports. Audience: Researchers and developers in software engineering, formal methods, certification, verification, validation, specification of complex systems and software, expert systems, natural language processing.

Table of Contents

  • Volume I: Foundations. Calculi and Methods. Preface
  • W. Bibel, P.H. Schmitt. Part One: Tableau and Connection Calculi. Introduction
  • U. Furbach. 1. Analytic Tableaux
  • B. Beckert, R. Hahnle. 2. Clausal Tableaux
  • R. Letz. 3. Variants of Clausal Tableaux
  • P. Baumgartner, U. Furbach. 4. Cuts in Tableaux
  • U. Egly. 5. Compressions and Extensions
  • W. Bibel, et al. Part Two: Special Calculi and Refinements. Introduction
  • U. Petermann. 6. Theory Reasoning
  • P. Baumgartner, U. Petermann. 7. Unification Theory
  • F. Baader, K.U. Schulz. 8. Rigid E-Unification
  • B. Beckert. 9. Sorted Unification and Tree Automata
  • C. Weidenbach. 10. Dimensions of Types in Logic Programming
  • G. Meyer, C. Beierle. 11. Equational Reasoning in Saturation-Based Theorem Proving
  • L. Bachmair, H. Ganzinger. 12. Higher-Order Rewriting and Equational Reasoning
  • T. Nipkow, C. Prehofer. 13. Higher-Order Automated Theorem Proving
  • M. Kohlhase. Index. Volume II: Systems and Implementation Techniques. Introduction
  • T. Nipkow, W. Reif. 1. Structured Specifications and Interactive Proofs with KIV
  • W. Reif, et al. 2. Proof Theory at Work: Program Development in the Minlog System
  • H. Benl, et al. 3. Interactive and Automated Proof Construction in Type Theory
  • M. Strecker, et al. 4. Integrating Automated and Interactive Theorem Proving
  • W. Ahrendt, et al. Part Two: Representation and Optimization Techniques. Introduction
  • J. Siekmann, D. Fehrer. 5. Term Indexing
  • P. Graf, D. Fehrer. 6. Developing Deduction Systems: The Toolbox Style
  • D. Fehrer. 7. Specifications of Inference Rules: Extensions of the PTTP Technique
  • G. Neugebauer, U. Petermann. 8. Proof Analysis, Generalization and Reuse
  • T. Kolbe, C. Walther. Part Three: Parallel Inference Systems. Introduction
  • W. Kuchlin. 9. Parallel Term Rewriting with PaReDuX
  • R. Bundgen, et al. 10. Parallel Theorem Provers Based on SETHEO
  • J. Schumann, et al. 11. Massively Parallel Reasoning
  • S.-E. Bornscheuer, et al. Part Four: Comparison and Cooperation of Theorem Provers. Introduction
  • J. Avenhaus. 12. Extension Methods in Automated Deduction
  • M. Baaz, et al. 13. A Comparison of Equality Reasoning Heuristics
  • J. Denzinger, M. Fuchs. 14. Cooperating Theorem Provers
  • J. Denzinger, I. Dahn. Index. Volume III: Applications. Part One: Automated Theorem Proving in Mathematics. Introduction
  • M. Kohlhase. 1. Lattice-Ordered Groups in Deduction
  • I. Dahn. 2. Superposition Theorem Proving for Commutative Rings
  • J. Stuber. 3. How to Augment a Formal System with a Boolean Algebra Component
  • H.J. Ohlbach, J. Kuhler. 4. Proof Planning: A practical Approach to Mechanized Reasoning in Mathematics
  • M. Kerber. Part Two: Automated Deduction in Software Engineering and hardware Design. Introduction
  • J. Schumann. 5. Program Synthesis
  • C. Kreitz. 6. Termination Analysis for Functional Programs
  • J. Giesl, et al. 7. The WAM Case Study: Verifying Compiler Correctness for Prolog with KIV
  • G. Schellhorn, W. Ahrendt. 8. Using Automated Theorem Provers in Verification of Protocols
  • I. Dahn, J. Schumann. 9. Theorem Proving in Large Theories
  • W. Reif, G. Schellhorn. 10. Analyzing Rule Sets for the Calculation of Banking Fees by a Theorem Prover with Constraints
  • F. Stolzenburg, B. Thomas. 11. Deduction-Based Software Component Retrieval
  • B. Fischer, et al. 12. Rewrite Based hardware Verification with ReDuX
  • R. Bundgen. Index.
Volume

v.2 ISBN 9780792351306

Description

1. BASIC CONCEPTS OF INTERACTIVE THEOREM PROVING Interactive Theorem Proving ultimately aims at the construction of powerful reasoning tools that let us (computer scientists) prove things we cannot prove without the tools, and the tools cannot prove without us. Interaction typi cally is needed, for example, to direct and control the reasoning, to speculate or generalize strategic lemmas, and sometimes simply because the conjec ture to be proved does not hold. In software verification, for example, correct versions of specifications and programs typically are obtained only after a number of failed proof attempts and subsequent error corrections. Different interactive theorem provers may actually look quite different: They may support different logics (first-or higher-order, logics of programs, type theory etc.), may be generic or special-purpose tools, or may be tar geted to different applications. Nevertheless, they share common concepts and paradigms (e.g. architectural design, tactics, tactical reasoning etc.). The aim of this chapter is to describe the common concepts, design principles, and basic requirements of interactive theorem provers, and to explore the band width of variations. Having a 'person in the loop', strongly influences the design of the proof tool: proofs must remain comprehensible, - proof rules must be high-level and human-oriented, - persistent proof presentation and visualization becomes very important.

Table of Contents

  • Volume I: Foundations. Calculi and Methods. Preface
  • W. Bibel, P.H. Schmitt. Part One: Tableau and Connection Calculi. Introduction
  • U. Furbach. 1. Analytic Tableaux
  • B. Beckert, R. Hahnle. 2. Clausal Tableaux
  • R. Letz. 3. Variants of Clausal Tableaux
  • P. Baumgartner, U. Furbach. 4. Cuts in Tableaux
  • U. Egly. 5. Compressions and Extensions
  • W. Bibel, et al. Part Two: Special Calculi and Refinements. Introduction
  • U. Petermann. 6. Theory Reasoning
  • P. Baumgartner, U. Petermann. 7. Unification Theory
  • F. Baader, K.U. Schulz. 8. Rigid E-Unification
  • B. Beckert. 9. Sorted Unification and Tree Automata
  • C. Weidenbach. 10. Dimensions of Types in Logic Programming
  • G. Meyer, C. Beierle. 11. Equational Reasoning in Saturation-Based Theorem Proving
  • L. Bachmair, H. Ganzinger. 12. Higher-Order Rewriting and Equational Reasoning
  • T. Nipkow, C. Prehofer. 13. Higher-Order Automated Theorem Proving
  • M. Kohlhase. Index. Volume II: Systems and Implementation Techniques. Introduction
  • T. Nipkow, W. Reif. 1. Structured Specifications and Interactive Proofs with KIV
  • W. Reif, et al. 2. Proof Theory at Work: Program Development in the Minlog System
  • H. Benl, et al. 3. Interactive and Automated Proof Construction in Type Theory
  • M. Strecker, et al. 4. Integrating Automated and Interactive Theorem Proving
  • W. Ahrendt, et al. PartTwo: Representation and Optimization Techniques. Introduction
  • J. Siekmann, D. Fehrer. 5. Term Indexing
  • P. Graf, D. Fehrer. 6. Developing Deduction Systems: The Toolbox Style
  • D. Fehrer. 7. Specifications of Inference Rules: Extensions of the PTTP Technique
  • G. Neugebauer, U. Petermann. 8. Proof Analysis, Generalization and Reuse
  • T. Kolbe, C. Walther. Part Three: Parallel Inference Systems. Introduction
  • W. Kuchlin. 9. Parallel Term Rewriting with PaReDuX
  • R. Bundgen, et al. 10. Parallel Theorem Provers Based on SETHEO
  • J. Schumann, et al. 11. Massively Parallel Reasoning
  • S.-E. Bornscheuer, et al. Part Four: Comparison and Cooperation of Theorem Provers. Introduction
  • J. Avenhaus. 12. Extension Methods in Automated Deduction
  • M. Baaz, et al. 13. A Comparison of Equality Reasoning Heuristics
  • J. Denzinger, M. Fuchs. 14. Cooperating Theorem Provers
  • J. Denzinger, I. Dahn. Index. Volume III: Applications. Part One: Automated Theorem Proving in Mathematics. Introduction
  • M. Kohlhase. 1. Lattice-Ordered Groups in Deduction
  • I. Dahn. 2. Superposition Theorem Proving for Commutative Rings
  • J. Stuber. 3. How to Augment a Formal System with a Boolean Algebra Component
  • H.J. Ohlbach, J. Kuhler. 4. Proof Planning: A practical Approach to Mechanized Reasoning in Mathematics
  • M. Kerber. Part Two: Automated Deduction in Software Engineering and hardware Design. Introduction
  • J. Schum
Volume

v.3 ISBN 9780792351313

Description

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.

Table of Contents

  • Volume I: Foundations. Calculi and Methods. Preface
  • W. Bibel, P.H. Schmitt. Part One: Tableau and Connection Calculi. Introduction
  • U. Furbach. 1. Analytic Tableaux
  • B. Beckert, R. Hahnle. 2. Clausal Tableaux
  • R. Letz. 3. Variants of Clausal Tableaux
  • P. Baumgartner, U. Furbach. 4. Cuts in Tableaux
  • U. Egly. 5. Compressions and Extensions
  • W. Bibel, et al. Part Two: Special Calculi and Refinements. Introduction
  • U. Petermann. 6. Theory Reasoning
  • P. Baumgartner, U. Petermann. 7. Unification Theory
  • F. Baader, K.U. Schulz. 8. Rigid E-Unification
  • B. Beckert. 9. Sorted Unification and Tree Automata
  • C. Weidenbach. 10. Dimensions of Types in Logic Programming
  • G. Meyer, C. Beierle. 11. Equational Reasoning in Saturation-Based Theorem Proving
  • L. Bachmair, H. Ganzinger. 12. Higher-Order Rewriting and Equational Reasoning
  • T. Nipkow, C. Prehofer. 13. Higher-Order Automated Theorem Proving
  • M. Kohlhase. Index. Volume II: Systems and Implementation Techniques. Introduction
  • T. Nipkow, W. Reif. 1. Structured Specifications and Interactive Proofs with KIV
  • W. Reif, et al. 2. Proof Theory at Work: Program Development in the Minlog System
  • H. Benl, et al. 3. Interactive and Automated Proof Construction in Type Theory
  • M. Strecker, et al. 4. Integrating Automated and Interactive Theorem Proving
  • W. Ahrendt, et al. PartTwo: Representation and Optimization Techniques. Introduction
  • J. Siekmann, D. Fehrer. 5. Term Indexing
  • P. Graf, D. Fehrer. 6. Developing Deduction Systems: The Toolbox Style
  • D. Fehrer. 7. Specifications of Inference Rules: Extensions of the PTTP Technique
  • G. Neugebauer, U. Petermann. 8. Proof Analysis, Generalization and Reuse
  • T. Kolbe, C. Walther. Part Three: Parallel Inference Systems. Introduction
  • W. Kuchlin. 9. Parallel Term Rewriting with PaReDuX
  • R. Bundgen, et al. 10. Parallel Theorem Provers Based on SETHEO
  • J. Schumann, et al. 11. Massively Parallel Reasoning
  • S.-E. Bornscheuer, et al. Part Four: Comparison and Cooperation of Theorem Provers. Introduction
  • J. Avenhaus. 12. Extension Methods in Automated Deduction
  • M. Baaz, et al. 13. A Comparison of Equality Reasoning Heuristics
  • J. Denzinger, M. Fuchs. 14. Cooperating Theorem Provers
  • J. Denzinger, I. Dahn. Index. Volume III: Applications. Part One: Automated Theorem Proving in Mathematics. Introduction
  • M. Kohlhase. 1. Lattice-Ordered Groups in Deduction
  • I. Dahn. 2. Superposition Theorem Proving for Commutative Rings
  • J. Stuber. 3. How to Augment a Formal System with a Boolean Algebra Component
  • H.J. Ohlbach, J. Kuhler. 4. Proof Planning: A practical Approach to Mechanized Reasoning in Mathematics
  • M. Kerber. Part Two: Automated Deduction in Software Engineering and hardware Design. Introduction
  • J. Schum
Volume

set ISBN 9780792351320

Description

The nationwide research project `Deduktion', funded by the `Deutsche Forschungsgemeinschaft (DFG)' for a period of six years, brought together almost all research groups within Germany engaged in the field of automated reasoning. Intensive cooperation and exchange of ideas led to considerable progress both in the theoretical foundations and in the application of deductive knowledge. This three-volume book covers these original contributions moulded into the state of the art of automated deduction. The three volumes are intended to document and advance a development in the field of automated deduction that can now be observed all over the world. Rather than restricting the interest to purely academic research, the focus now is on the investigation of problems derived from realistic applications. In fact industrial applications are already pursued on a trial basis. In consequence the emphasis of the volumes is not on the presentation of the theoretical foundations of logical deduction as such, as in a handbook; rather the books present the concepts and methods now available in automated deduction in a form which can be easily accessed by scientists working in applications outside of the field of deduction. This reflects the strong conviction that automated deduction is on the verge of being fully included in the evolution of technology. Volume I focuses on basic research in deduction and on the knowledge on which modern deductive systems are based. Volume II presents techniques of implementation and details about system building. Volume III deals with applications of deductive techniques mainly, but not exclusively, to mathematics and the verification of software. Each chapter was read by two referees, one an international expert from abroad and the other a knowledgeable participant in the national project. It has been accepted for inclusion on the basis of these review reports. Audience: Researchers and developers in software engineering, formal methods, certification, verification, validation, specification of complex systems and software, expert systems, natural language processing.

Table of Contents

  • Volume I: Foundations. Calculi and Methods. Preface
  • W. Bibel, P.H. Schmitt. Part One: Tableau and Connection Calculi. Introduction
  • U. Furbach. 1. Analytic Tableaux
  • B. Beckert, R. Hahnle. 2. Clausal Tableaux
  • R. Letz. 3. Variants of Clausal Tableaux
  • P. Baumgartner, U. Furbach. 4. Cuts in Tableaux
  • U. Egly. 5. Compressions and Extensions
  • W. Bibel, et al. Part Two: Special Calculi and Refinements. Introduction
  • U. Petermann. 6. Theory Reasoning
  • P. Baumgartner, U. Petermann. 7. Unification Theory
  • F. Baader, K.U. Schulz. 8. Rigid E-Unification
  • B. Beckert. 9. Sorted Unification and Tree Automata
  • C. Weidenbach. 10. Dimensions of Types in Logic Programming
  • G. Meyer, C. Beierle. 11. Equational Reasoning in Saturation-Based Theorem Proving
  • L. Bachmair, H. Ganzinger. 12. Higher-Order Rewriting and Equational Reasoning
  • T. Nipkow, C. Prehofer. 13. Higher-Order Automated Theorem Proving
  • M. Kohlhase. Index. Volume II: Systems and Implementation Techniques. Introduction
  • T. Nipkow, W. Reif. 1. Structured Specifications and Interactive Proofs with KIV
  • W. Reif, et al. 2. Proof Theory at Work: Program Development in the Minlog System
  • H. Benl, et al. 3. Interactive and Automated Proof Construction in Type Theory
  • M. Strecker, et al. 4. Integrating Automated and Interactive Theorem Proving
  • W. Ahrendt, et al. Part Two: Representation and Optimization Techniques. Introduction
  • J. Siekmann, D. Fehrer. 5. Term Indexing
  • P. Graf, D. Fehrer. 6. Developing Deduction Systems: The Toolbox Style
  • D. Fehrer. 7. Specifications of Inference Rules: Extensions of the PTTP Technique
  • G. Neugebauer, U. Petermann. 8. Proof Analysis, Generalization and Reuse
  • T. Kolbe, C. Walther. Part Three: Parallel Inference Systems. Introduction
  • W. Kuchlin. 9. Parallel Term Rewriting with PaReDuX
  • R. Bundgen, et al. 10. Parallel Theorem Provers Based on SETHEO
  • J. Schumann, et al. 11. Massively Parallel Reasoning
  • S.-E. Bornscheuer, et al. Part Four: Comparison and Cooperation of Theorem Provers. Introduction
  • J. Avenhaus. 12. Extension Methods in Automated Deduction
  • M. Baaz, et al. 13. A Comparison of Equality Reasoning Heuristics
  • J. Denzinger, M. Fuchs. 14. Cooperating Theorem Provers
  • J. Denzinger, I. Dahn. Index. Volume III: Applications. Part One: Automated Theorem Proving in Mathematics. Introduction
  • M. Kohlhase. 1. Lattice-Ordered Groups in Deduction
  • I. Dahn. 2. Superposition Theorem Proving for Commutative Rings
  • J. Stuber. 3. How to Augment a Formal System with a Boolean Algebra Component
  • H.J. Ohlbach, J. Kuhler. 4. Proof Planning: A practical Approach to Mechanized Reasoning in Mathematics
  • M. Kerber. Part Two: Automated Deduction in Software Engineering and hardware Design. Introduction
  • J. Schumann. 5. Program Synthesis
  • C. Kreitz. 6. Termination Analysis for Functional Programs
  • J. Giesl, et al. 7. The WAM Case Study: Verifying Compiler Correctness for Prolog with KIV
  • G. Schellhorn, W. Ahrendt. 8. Using Automated Theorem Provers in Verification of Protocols
  • I. Dahn, J. Schumann. 9. Theorem Proving in Large Theories
  • W. Reif, G. Schellhorn. 10. Analyzing Rule Sets for the Calculation of Banking Fees by a Theorem Prover with Constraints
  • F. Stolzenburg, B. Thomas. 11. Deduction-Based Software Component Retrieval
  • B. Fischer, et al. 12. Rewrite Based hardware Verification with ReDuX
  • R. Bundgen. Index.

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