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.Research partially funded by the Spanish MICINN projects ARINF (TIN2009-14704-C03-01/03) and TASSAT (TIN2010-20967-C04-01/03), MINECO project EdeTRI (TIN2012-39348-C02-01), Agreement Techologies (CONSOLIDER CSD 2007- 0022), Catalan Government (2009SGR-1433/34) and ESF project POST - UP II No. CZ.1.07/2.3.00/30.0041 that is co-financed by the European Social Fund and the state budget of the Czech Republic.Peer Reviewe