Evaluating Automated Theorem Provers for First-Order Modal Logics

First-order modal logics have many applications, e.g., in planning, natural language processing, program verification, querying knowledge bases, and modeling communication. This paper gives an overview of several new implementations of theorem provers for first-order modal logics based on different proof calculi. Among these calculi are the standard sequent calculus, a prefixed tableau calculus, an embedding into simple type theory, and an instance-based method. All these theorem provers are tested and evaluated on the QMLTP problem library for first-order modal logic. The results of these test runs are compared and analyzed.

[1]  James W. Garson,et al.  Quantification in Modal Logic , 1984 .

[2]  Robert C. Moore.  A Formal Theory of Knowledge and Action , 1984 .

[3]  Raymond Reiter,et al.  What should a database know? , 1988, PODS '88.

[4]  Hector J. Levesque,et al.  Intention is Choice with Commitment , 1990, Artif. Intell..

[5]  Modern Logic: A Text in Elementary Symbolic Logic , 1994 .

[6]  Jens Otten.  ileanTAP: An Intuitionistic Theorem Prover , 1997, TABLEAUX.

[7]  Philippe Bretier,et al.  ARTIMIS: Natural Dialogue Meets Rational Agency , 1997, IJCAI.

[8]  Bernhard Beckert,et al.  Free Variable Tableaux for Propositional Modal Logics , 1997, TABLEAUX.

[9]  Wiebe van der Hoek,et al.  First steps in modal logic , 1997 .

[10]  Kurt Stenzel,et al.  Proving System Correctness with KIV 3.0 , 1997, CADE.

[11]  Dominique Longin,et al.  Belief Reconstruction in Cooperative Dialogues , 1998, AIMSA.

[12]  Matthew Stone,et al.  Abductive Planning with Sensing , 1998, AAAI/IAAI.

[13]  Christoph Kreitz,et al.  Connection-based Theorem Proving in Classical and Non-classical Logics , 1999, J. Univers. Comput. Sci..

[14]  Dieter Hutter,et al.  VSE: formal methods meet industrial needs , 2000, International Journal on Software Tools for Technology Transfer.

[15]  Francesco M. Donini,et al.  Design and Results of TANCS-2000 Non-classical (Modal) Systems Comparison , 2000, TABLEAUX.

[16]  Matthew Stone,et al.  Towards a Computational Account of Knowledge, Action and Inference in Instructions , 2000 .

[17]  Roderic A. Girle,et al.  Modal Logics and Philosophy , 2000 .

[18]  Ullrich Hustadt,et al.  MSPASS: Modal Reasoning by Translation and First-Order Resolution , 2000, TABLEAUX.

[19]  Roel Wieringa,et al.  Regular database update logics , 2001, Theor. Comput. Sci..

[20]  Fahiem Bacchus,et al.  A Knowledge-Based Approach to Planning with Incomplete Information and Sensing , 2002, AIPS.

[21]  Stephan Schulz,et al.  E - a brainiac theorem prover , 2002, AI Commun..

[22]  M. Fitting.  Types, Tableaus, and Gödel's God , 2002 .

[23]  Virginie Thion,et al.  A General Theorem Prover for Quantified Modal Logics , 2002, TABLEAUX.

[24]  Peter F. Patel-Schneider,et al.  A New General Method to Generate Random Modal Formulae for Testing Decision Procedures , 2003, J. Artif. Intell. Res..

[25]  Matthew Stone,et al.  Microplanning with Communicative Intentions: The SPUD System , 2001, Comput. Intell..

[26]  Bernhard Beckert,et al.  leanTAP: Lean tableau-based deduction , 1995, Journal of Automated Reasoning.

[27]  Love Ekenberg,et al.  A transition logic for schemata conflicts , 2004, Data Knowl. Eng..

[28]  Peter Balsiger,et al.  A Benchmark Method for the Propositional Modal Logics K, KT, S4 , 2004, Journal of Automated Reasoning.

[29]  J.F.A.K. van Benthem,et al.  Logic in Philosophy , 2005 .

[30]  Christoph Kreitz,et al.  The ILTP Problem Library for Intuitionistic Logic , 2007, Journal of Automated Reasoning.

[31]  Frank Wolter,et al.  Handbook of Modal Logic , 2007, Studies in logic and practical reasoning.

[32]  Torben Braüner,et al.  First-order modal logic , 2007, Handbook of Modal Logic.

[33]  Diego Calvanese,et al.  EQL-Lite: Effective First-Order Query Processing in Description Logics , 2007, IJCAI.

[34]  Ronald P. A. Petrick,et al.  Planning Dialog Actions , 2007, SIGDIAL.

[35]  Geoff Sutcliffe.  The CADE-22 automated theorem proving system competition - CASC-22 , 2010, AI Commun..

[36]  Chad E. Brown,et al.  Analytic Tableaux for Higher-Order Logic with Choice , 2010, Journal of Automated Reasoning.

[37]  Thomas Raths,et al.  The QMLTP Library: Benchmarking Theorem Provers for Modal Logics , 2011 .

[38]  Geoff Sutcliffe.  The 5th IJCAR automated theorem proving system competition - CASC-J5 , 2011, AI Commun..

[39]  Lawrence C. Paulson,et al.  Quantified Multimodal Logics in Simple Type Theory , 2009, Logica Universalis.