Equivalence and counting

Abstract

Abstract We consider the two-variable fragment of first-order logic with counting quantifiers, but where k distinguished binary predicates are constrained to be interpreted as equivalence relations. We show that, if k=1, the satisfiability and finite satisfiability problems for the resulting logic remain NExpTime-complete. Our treatment here employs the full power of the results on integer linear programming obtained in Chapter 7. In addition, we show that, if k=2, the satisfiability and finite satisfiability problems for the resulting logic become undecidable.