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The Finite Satisfiability Problem for Two-Variable, First-Order Logic with one Transitive Relation is Decidable (1707.05558v1)
Published 18 Jul 2017 in cs.LO
Abstract: We consider the two-variable fragment of first-order logic with one distinguished binary predicate constrained to be interpreted as a transitive relation. The finite satisfiability problem for this logic is shown to be decidable, in triply exponential non-deterministic time. The complexity falls to doubly exponential non-deterministic time if the distinguished binary predicate is constrained to be interpreted as a partial order.