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arXiv · 1707.05558

The Finite Satisfiability Problem for Two-Variable, First-Order Logic with one Transitive Relation is Decidable

Ian Pratt-Hartmann
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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.

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Ian Pratt-Hartmann. 2017-07-18. The Finite Satisfiability Problem for Two-Variable, First-Order Logic with one Transitive Relation is Decidable. https://doi.org/10.1002/malq.201700055

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