The QMLTP Problem Library for First-Order Modal Logics

The Quantified Modal Logic Theorem Proving (QMLTP) library provides a platform for testing and evaluating automated theorem proving (ATP) systems for first-order modal logics. The main purpose of the library is to stimulate the development of new modal ATP systems and to put their comparison onto a firm basis. Version 1.1 of the QMLTP library includes 600 problems represented in a standardized extended TPTP syntax. Status and difficulty rating for all problems were determined by running comprehensive tests with existing modal ATP systems. In the presented version 1.1 of the library the modal logics K, D, T, S4 and S5 with constant, cumulative and varying domains are considered. Furthermore, a small number of problems for multi-modal logic are included as well.

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

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

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

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

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

[6]  John Domingue,et al.  Artificial Intelligence: Methodology, Systems, and Applications, 12th International Conference, AIMSA 2006, Varna, Bulgaria, September 12-15, 2006, Proceedings , 2006, AIMSA.

[7]  Nikolaj Bjørner,et al.  Automated Deduction - CADE-23 - 23rd International Conference on Automated Deduction, Wroclaw, Poland, July 31 - August 5, 2011. Proceedings , 2011, CADE.

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

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

[10]  S. Korner,et al.  The philosophy of mathematics , 1960 .

[11]  Geoff Sutcliffe.  The 4th IJCAR Automated Theorem Proving System Competition - CASC-J4 , 2009, AI Commun..

[12]  Jens Otten.  Implementing Connection Calculi for First-order Modal Logics , 2012, IWIL@LPAR.

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

[14]  Sally Popkorn.  First Steps in Modal Logic , 1995 .

[15]  Geoff Sutcliffe.  The TPTP Problem Library and Associated Infrastructure , 2009, Journal of Automated Reasoning.

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

[17]  T. Sider.  Logic for Philosophy , 2010 .

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

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

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

[21]  Richard L. Mendelsohn,et al.  First-Order Modal Logic , 1998 .

[22]  Roy Dyckhoff.  Automated Reasoning with Analytic Tableaux and Related Methods , 2000, Lecture Notes in Computer Science.

[23]  Sally Popkorn.  First steps in Modal Logic: Löb logic , 1994 .

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

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

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

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

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

[29]  Lawrence C. Paulson,et al.  LEO-II - A Cooperative Automatic Theorem Prover for Classical Higher-Order Logic (System Description) , 2008, IJCAR.

[30]  Chad E. Brown.  Reducing Higher-Order Theorem Proving to a Sequence of SAT Problems , 2013, Journal of Automated Reasoning.

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