English

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

Logic in Computer Science 2024-04-24 v1

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.

Keywords

Cite

@article{arxiv.1707.05558,
  title  = {The Finite Satisfiability Problem for Two-Variable, First-Order Logic with one Transitive Relation is Decidable},
  author = {Ian Pratt-Hartmann},
  journal= {arXiv preprint arXiv:1707.05558},
  year   = {2024}
}
R2 v1 2026-06-22T20:50:09.036Z