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G. Reger, M. Suda, A. Voronkov:
"Finding Finite Models in Multi-sorted First-Order Logic";
Talk: 19th International Conference on Theory and Applications of Satisfiability Testing, SAT 2016, Bordeaux, France; 2016-07-05 - 2016-07-08; in: "Theory and Applications of Satisfiability Testing - SAT 2016 - 19th International Conference, Bordeaux, France, July 5-8, 2016, Proceedings", Springer, LNCS 9710 (2016), 323 - 341.

This work extends the existing MACE-style finite model finding approach to multi-sorted first order logic. This existing approach iteratively assumes increasing domain sizes and encodes the related ground problem as a SAT problem. When moving to the multi-sorted setting each sort may have a different domain size, leading to an explosion in the search space. This paper focusses on methods to tame that search space. The key approach adds additional information to the SAT encoding to suggest which domains should be grown. Evaluation of an implementation of techniques in the Vampire theorem prover shows that they dramatically reduce the search space and that this is an effective approach to find finite models in multi-sorted first order logic.

finite model finding, multi-sorted first-order logic, vampire

http://dx.doi.org/10.1007/978-3-319-40970-2_20

http://publik.tuwien.ac.at/files/publik_255026.pdf