Unary negation

Abstract

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 Projective Beth Property.

2 figures

References in corpus (1)

• Logical Queries over Views: Decidability and Expressiveness

Cited by in corpus (6)

• Ontology-based Data Access: A Study through Disjunctive Datalog, CSP, and MMSNP
• Satisfiability and Containment of Recursive SHACL
• Queries with Guarded Negation (full version)
• A Uniform One-Dimensional Fragment with Alternation of Quantifiers
• Finite Model Reasoning in Expressive Fragments of First-Order Logic
• One-Dimensional Fragment over Words and Trees