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

Ian Pratt-Hartmann
2017 arXiv   pre-print
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.
arXiv:1707.05558v1 fatcat:dcll44gbyrfqtdrfyogovdyame