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

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.

Cited by in corpus (2)

• Register Automata with Extrema Constraints, and an Application to Two-Variable Logic
• The Fluted Fragment with Transitive Relations