About the unification type of $\mathbf {K}+\square \square \bot $

Abstract

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 $\mathbf {K}+\square \square \bot $ , unifiable formulas are either finitary, or unitary.