3-SAT = SAT for a class of normal modal logics

Stéphane Demri (1)

1 Leibniz - IMAG - Laboratoire Leibniz

For the classical propositional logic SAT polynomially reduces to 3-SAT. In this note we show that for some propositional normal modal logics a similar result holds when modal clauses are considered. The proof given herein is a modal extension of Cook's proof for classical propositional logic. The difficulty of the proof rests on the use of a modal context for each reduction step. Improvements of the reduction algorithm for logics extending S4 are also given. Possible extensions of this work are also briefly discussed.

Mots clés: modal logic; 3SAT; reduction; modal logic S4

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

Stéphane Demri. 3-SAT = SAT for a class of normal modal logics. Information Processing Letters, 1995, 54 (5), pp.281-287. ⟨10.1016/0020-0190(95)00060-P⟩. ⟨hal-03194860⟩