About the unification type of K + Box Box false

Philippe Balbiani (1, 2) , Cigdem Gencer (1, 3) , Maryam Rostamigiv (1, 4) , Tinko Tinchev (4)

1 IRIT-LILaC - Logique, Interaction, Langue et Calcul
2 CNRS - Centre National de la Recherche Scientifique
3 Istanbul University
4 Sofia University "St. Kliment Ohridski"

The unification problem in a propositional logic is to determine, given a formula ϕ, whether there exists a substitution σ such that σ(ϕ) is in that logic. In that case, σ is a unifier of ϕ. When a unifiable formula has minimal complete sets of unifiers, it is either infinitary, finitary, or unitary, depending on the cardinality of its minimal complete sets of unifiers. Otherwise, it is nullary. In this paper, we prove that in modal logic K + ⊥, unifiable formulas are either finitary, or unitary.

Mots clés: Propositional modal logics; Locally tabular modal logics; Unification problem; Unification types

Domaines: Logique en informatique [cs.LO]

Philippe Balbiani, Cigdem Gencer, Maryam Rostamigiv, Tinko Tinchev. About the unification type of K + Box Box false. Annals of Mathematics and Artificial Intelligence, 2021, 90, pp.481-497. ⟨hal-03762105⟩