FO^2 with one transitive relation is decidable
نویسندگان
چکیده
We show that the satisfiability problem for the two-variable first-order logic, FO2, over transitive structures when only one relation is required to be transitive, is decidable. The result is optimal, as FO2 over structures with two transitive relations, or with one transitive and one equivalence relation, are known to be undecidable, so in fact, our result completes the classification of FO2logics over transitive structures with respect to decidability. We show that the satisfiability problem is in 2-NExpTime. Decidability of the finite satisfiability problem remains open. 1998 ACM Subject Classification F.1.1 Models of Computation, F.4.1 Mathematical Logic, F.4.3 Formal Languages
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