Satisfiability solving and model generation for quantified first-order logic formulas

  • Authors:
  • Christoph D. Gladisch

  • Affiliations:
  • Karlsruhe Institute of Technology, Institute for Theoretical Informatics, Germany

  • Venue:
  • FoVeOOS'10 Proceedings of the 2010 international conference on Formal verification of object-oriented software
  • Year:
  • 2010

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Abstract

The generation of models, i.e. interpretations, that satisfy first-order logic (FOL) formulas is an important problem in different application domains, such as, e.g., formal software verification, testing, and artificial intelligence. Satisfiability modulo theory (SMT) solvers are the state-of-the-art techniques for handling this problem. A major bottleneck is, however, the handling of quantified formulas. Our contribution is a model generation technique for quantified formulas that is powered by a verification technique. The model generation technique can be used either stand-alone for model generation, or as a precomputation step for SMT solvers to eliminate quantifiers. Quantifier elimination in this sense is sound for showing satisfiability but not for refutational or validity proofs. A prototype of this technique is implemented.