Building Theorem Provers

This talk discusses some of the challenges of building a usable theorem prover. These include the chasm between theory and code, conflicting requirements, feature interaction, and competitive performance. The talk draws on the speaker's experiences with devising extensions of resolution and building theorem provers that have been used as embedded reasoners in various systems.

[1]  I. V. Ramakrishnan,et al.  Term Indexing , 1995, Lecture Notes in Computer Science.

[2]  Evgeny Dantsin,et al.  A Nondeterministic Polynomial-Time Unification Algorithm for Bags, Sets and Trees , 1999, FoSSaCS.

[3]  Larry Wos,et al.  Experiments in Automated Deduction with Condensed Detachment , 1992, CADE.

[4]  Richard C. T. Lee,et al.  Symbolic logic and mechanical theorem proving , 1973, Computer science classics.

[5]  Cordell Green.  Theorem-Proving by Resolution as a Basis for Question-Answering Systems , 2010 .

[6]  Richard Waldinger,et al.  A Guide to Snark , 2000 .

[7]  Larry Wos.  A Milestone Reached and a Secret Revealed , 2004, Journal of Automated Reasoning.

[8]  Larry Wos,et al.  Subsumption, a Sometimes Undervalued Procedure , 1991, Computational Logic - Essays in Honor of Alan Robinson.

[9]  Andrei Voronkov,et al.  An AC-Compatible Knuth-Bendix Order , 2003, CADE.

[10]  Larry Wos,et al.  Automated reasoning - 33 basic research problems , 1988 .

[11]  Albert Rubio.  A Fully Syntactic AC-RPO , 1999, RTA.

[12]  Toby Walsh,et al.  Automated Deduction—CADE-11 , 1992, Lecture Notes in Computer Science.

[13]  Donald W. Loveland,et al.  A Simplified Format for the Model Elimination Theorem-Proving Procedure , 1969, J. ACM.

[14]  Alan Robinson,et al.  Handbook of automated reasoning , 2001 .

[15]  Robin Milner,et al.  Theories for the Global Ubiquitous Computer , 2004, FoSSaCS.

[16]  Michael R. Lowry,et al.  Deductive Composition of Astronomical Software from Subroutine Libraries , 1994, CADE.

[17]  Zohar Manna,et al.  A Deductive Approach to Program Synthesis , 1979, TOPL.

[18]  Tanel Tammet,et al.  Chain Resolution for the Semantic Web , 2004, IJCAR.

[19]  Bernd Löchner,et al.  Things to Know When Implementing Lpo , 2006, Int. J. Artif. Intell. Tools.

[20]  Anthony Preston,et al.  Book review: Automated Reasoning: 33 Basic Research Problems by Larry Wos (Prentice Hall 1988) , 1988, SGAR.

[21]  François Fages.  Associative-Commutative Unification , 1987, J. Symb. Comput..

[22]  Jacques D. Fleuriot,et al.  IsaPlanner: A Prototype Proof Planner in Isabelle , 2003, CADE.

[23]  E. Feigenbaum,et al.  Computers and Thought , 1963 .

[24]  Mark E. Stickel,et al.  Automated deduction by theory resolution , 1985, Journal of Automated Reasoning.

[25]  Mark E. Stickel,et al.  Complete Sets of Reductions for Some Equational Theories , 1981, JACM.

[26]  Christoph Walther,et al.  A Many-Sorted Calculus Based on Resolution and Paramodulation , 1982, IJCAI.

[27]  Allen Newell,et al.  Empirical explorations with the logic theory machine: a case study in heuristics , 1995 .

[28]  Richard J. Waldinger.  Whatever Happened to Deductive Question Answering? , 2007, LPAR.

[29]  William McCune,et al.  Solution of the Robbins Problem , 1997, Journal of Automated Reasoning.

[30]  Mark T. Maybury.  New Directions in Question Answering , 2004 .

[31]  Andrei Paskevich,et al.  Connection Tableaux with Lazy Paramodulation , 2006, Journal of Automated Reasoning.

[32]  Alan M. Frisch.  The Substitutional Framework for Sorted Deduction: Fundamental Results on Hybrid Reasoning , 1991, Artif. Intell..

[33]  Douglas E. Appelt,et al.  Deductive Question Answering from Multiple Resources , 2004, New Directions in Question Answering.

[34]  Mark E. Stickel,et al.  A prolog technology theorem prover: Implementation by an extended prolog compiler , 1986, Journal of Automated Reasoning.

[35]  Hector J. Levesque,et al.  Knowledge Representation and Reasoning , 2004 .

[36]  Donald W. Loveland,et al.  Automated theorem proving: a logical basis , 1978, Fundamental studies in computer science.

[37]  Tobias Nipkow,et al.  Term rewriting and all that , 1998 .

[38]  John K. Dixon.  Z-Resolution: Theorem-Proving with Compiled Axioms , 1973, JACM.

[39]  Mabry Tyson,et al.  An Analysis of Consecutively Bounded Depth-First Search with Applications in Automated Deduction , 1985, IJCAI.

[40]  Richard E. Korf,et al.  Iterative-Deepening-A*: An Optimal Admissible Tree Search , 1985, IJCAI.

[41]  Mark E. Stickel,et al.  A Prolog Technology Theorem Prover: A New Exposition and Implementation in Prolog , 1990, Theor. Comput. Sci..

[42]  Eyal Amir,et al.  Logic-Based Subsumption Architecture , 1999, IJCAI.

[43]  William McCune,et al.  OTTER 3.3 Reference Manual , 2003, ArXiv.

[44]  Mark E. Stickel,et al.  A Unification Algorithm for Associative-Commutative Functions , 1981, JACM.

[45]  Frank Wolter,et al.  Monodic fragments of first-order temporal logics: 2000-2001 A.D , 2001, LPAR.

[46]  Larry Wos,et al.  What Is Automated Reasoning? , 1987, J. Autom. Reason..

[47]  James R. Slagle,et al.  Experiments with a deductive question-answering program , 1965, CACM.

[48]  Diego Calvanese,et al.  The Description Logic Handbook: Theory, Implementation, and Applications , 2003, Description Logic Handbook.

[49]  Wayne Snyder,et al.  Goal Directed Strategies for Paramodulation , 1991, RTA.

[50]  Peter Graf,et al.  Term Indexing , 1996, Lecture Notes in Computer Science.

[51]  Alan Bundy,et al.  Automated Deduction — CADE-12 , 1994, Lecture Notes in Computer Science.

[52]  I. V. Ramakrishnan,et al.  Term Indexing , 2001, Handbook of Automated Reasoning.