Unary negation

Balder ten Cate (1) , Luc Segoufin (2)

1 UC Santa Cruz - University of California [Santa Cruz]
2 LSV - Laboratoire Spécification et Vérification [Cachan]

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 $\mu$-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 show that the unary negation fragment of first-order logic is model-theoretically very well behaved. In particular, it enjoys Craig interpolation and the Beth property.

Mots clés: Decidability; Logic; Unary negation

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]

Balder ten Cate, Luc Segoufin. Unary negation. Symposium on Theoretical Aspects of Computer Science (STACS2011), Mar 2011, Dortmund, Germany. pp.344-355. ⟨hal-00573634⟩