Remarks about the unification types of some locally tabular normal modal logics

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

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

It is already known that unifiable formulas in normal modal logic K + Box Box ⊥ are either finitary, or unitary and unifiable formulas in normal modal logic Alt1 + Box Box ⊥ are unitary. In this paper, we prove that for all d≥3, unifiable formulas in normal modal logic K + Box^{d} ⊥ are either finitary, or unitary and unifiable formulas in normal modal logic Alt1 + Box^{d} ⊥ are unitary.

Domaines: Logique en informatique [cs.LO]

Philippe Balbiani, Cigdem Gencer, Maryam Rostamigiv, Tinko Tinchev. Remarks about the unification types of some locally tabular normal modal logics. Logic Journal of the IGPL, 2022, ⟨10.1093/jigpal/jzab033⟩. ⟨hal-03762700⟩