A Completeness Proof for a Logic with an Alternative Necessity Operator

Stéphane Demri (1, 2)

1 Leibniz - IMAG - Laboratoire Leibniz
2 CNRS - Centre National de la Recherche Scientifique

We show the completeness of a Hilbert-style system LK defined by M. Valiev involving the knowledge operator K dedicated to the reasoning with incomplete information. The completeness proof uses a variant of Makinson's canonical model construction. Furthermore we prove that the theoremhood problem for LK is co-NP-complete, using techniques similar to those used to prove that the satisfiability problem for propositional S5 is NP-complete.

Mots clés: knowledge logic; contingency; completeness; complexity; NP

Domaines: Informatique [cs]; Logique en informatique [cs.LO]

Stéphane Demri. A Completeness Proof for a Logic with an Alternative Necessity Operator. Studia Logica, 1997, 58 (1), pp.99-112. ⟨10.1023/A:1004944015811⟩. ⟨hal-03193865⟩