On finite satisfiability of the guarded fragment with equivalence or transitive guards

Authors:
Emanuel Kieroński;Lidia Tendera
Affiliations:
Institute of Computer Science, University of Wrocław;Institute of Mathematics and Informatics, Opole University
Venue:
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Year:
2007

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Abstract

The guarded fragment of first-order logic, GF, enjoys the finite model property, so the satisfiability and the finite satisfiability problems coincide. We are concerned with two extensions of the two-variable guarded fragment that do not possess the finite model property, namely, GF2 with equivalence and GF2 with transitive guards. We prove that in both cases every finitely satisfiable formula has a model of at most double exponential size w.r.t. its length. To obtain the result we invent a strategy of building finite models that are formed from a number of multidimensional grids placed over a cylindrical surface. The construction yields a 2NEXPTIME-upper bound on the complexity of the finite satisfiability problem for these fragments. For the case with equivalence guards we improve the bound to 2EXPTIME.