Modal Logics with Weak Forms of Recursion: PSPACE Specimens

Stéphane Demri (1, 2)

1 LSV - Laboratoire Spécification et Vérification
2 CNRS - Centre National de la Recherche Scientifique

We analyze the computational complexity of extensions of the multimodal version of the standard modal logic K by finite addition of axiom schemes that can be read as the production rules of a formal grammar. By using proof-theoretical means, we show that every right linear grammar logic has a satisfiability problem in deterministic exponential time and we exhibit countably infinite classes of right linear grammar logics that contain weak forms of recursion for which the satisfiability problem can be solved in polynomial space.

Mots clés: multimodal logic; PSPACE; proof system; right linear grammar logics; grammar logic; complexity; strategy; decision procedure; EXPTIME

Domaines: Informatique [cs]; Logique en informatique [cs.LO]; Théorie et langage formel [cs.FL]; Intelligence artificielle [cs.AI]

Stéphane Demri. Modal Logics with Weak Forms of Recursion: PSPACE Specimens. Advances in Modal Logic (AIML'00), WORLD SCIENTIFIC, pp.113-138, 2002, 979-981-238-179-8. ⟨10.1142/9789812776471_0007⟩. ⟨hal-03194865⟩