Unification in modal logic Alt1

Philippe Balbiani (1, 2) , Tinko Tinchev (3)

1 IRIT-LILaC - Logique, Interaction, Langue et Calcul
2 CNRS - Centre National de la Recherche Scientifique
3 Софийски университет = Sofia University

ALT1 is the least modal logic containing the formula characterizing deterministic frames. The unification problem in ALT1 is to determine, given a formula A(x1,...,xn), whether there exists formulas B1, ..., Bn such that A(B1,...,Bn) is in ALT1. In this paper, we show that the unification problem in ALT1 is in PSPACE. We also show that there exists an ALT1-unifiable formula that has no minimal complete set of unifiers. Finally, we study sub-Boolean variants of the unification problem in ALT1.

Mots clés: Modal logic Alt1; Computability of unifiability; Unificationtype; Sub-Boolean variants

Domaines: Intelligence artificielle [cs.AI]; Apprentissage [cs.LG]; Logique en informatique [cs.LO]; Informatique et langage [cs.CL]

Philippe Balbiani, Tinko Tinchev. Unification in modal logic Alt1. 11th conference on Advances in Modal logic (AiML 2016), Aug 2016, Budapest, Hungary. pp.117-134. ⟨hal-01650177⟩