Unary negation

Luc Segoufin, Balder Cate, Erich Grädel
2013 Logical Methods in Computer Science  
We study fragments of first-order logic and of least fixed point logic that allow only unary negation: negation of formulas with at most one free variable. These logics generalize many interesting known formalisms, including modal logic and the μ-calculus, as well as conjunctive queries and monadic Datalog. We show that satisfiability and finite satisfiability are decidable for both fragments, and we pinpoint the complexity of satisfiability, finite satisfiability, and model checking. We also
more » ... ow that the unary negation fragment of first-order logic is model-theoretically very well behaved. In particular, it enjoys Craig Interpolation and the Projective Beth Property.
doi:10.2168/lmcs-9(3:25)2013 fatcat:r6qnfeehqncspnigfcarq2zocy