On the Implementation of a Fuzzy DL Solver over Infinite-Valued Product Logic with SMT Solvers

In this paper we explain the design and preliminary implementation of a solver for the positive satisfiability problem of concepts in a fuzzy description logic over the infinite-valued product logic. This very solver also answers 1-satisfiability in quasi-witnessed models. The solver works by first performing a direct reduction of the problem to a satisfiability problem of a quantifier free boolean formula with non-linear real arithmetic properties, and secondly solves the resulting formula with an SMT solver. We show that the satisfiability problem for such formulas is still a very challenging problem for even the most advanced SMT solvers, and so it represents an interesting problem for the community working on the theory and practice of SMT solvers.

[1]  Umberto Straccia,et al.  On the (un)decidability of fuzzy description logics under Łukasiewicz t-norm , 2013, Inf. Sci..

[2]  Umberto Straccia,et al.  A Fuzzy Description Logic with Product T-norm , 2007, 2007 IEEE International Fuzzy Systems Conference.

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

[4]  Volker Haarslev,et al.  Automated Reasoning in ALCQ\mathcal{ALCQ} via SMT , 2011, CADE.

[5]  Jeff Z. Pan,et al.  An Argument-Based Approach to Using Multiple Ontologies , 2009, SUM.

[6]  Lluis Godo,et al.  An SMT-Based Solver for Continuous t-norm Based Logics , 2012, SUM.

[7]  Umberto Straccia,et al.  Mixed Integer Programming, General Concept Inclusions and Fuzzy Description Logics , 2007, EUSFLAT Conf..

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

[9]  Nikolaj Bjørner,et al.  Z3: An Efficient SMT Solver , 2008, TACAS.

[10]  Marco Cerami,et al.  Decidability of a Description Logic over Infinite-Valued Product Logic , 2010, KR.

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

[12]  Rajeev Alur,et al.  A Temporal Logic of Nested Calls and Returns , 2004, TACAS.

[13]  Franz Baader,et al.  Tableau Algorithms for Description Logics , 2000, TABLEAUX.

[14]  Boris Motik,et al.  Reducing SHIQ-Description Logic to Disjunctive Datalog Programs , 2004, KR.

[15]  Petr Hájek,et al.  Making fuzzy description logic more general , 2005, Fuzzy Sets Syst..