Equivalence

Abstract

Abstract We consider the two-variable fragment of first-order logic, but where k distinguished binary predicates are constrained to be interpreted as equivalence relations. We show that, if k=1, the resulting logic has the finite model property, and that the satisfiability problem remains NExpTime-complete. We further show that, if k=2, the resulting logic loses the finite model property, and that the satisfiability and finite satisfiability problems become 2-NExpTime-complete. Finally, we show that, if k=3, the satisfiability and finite satisfiability problems for the resulting logic become undecidable.