Projective unification in modal logic

Logic Journal of the IGPL 20 (1):121-153 (2012)
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Abstract

A projective unifier for a modal formula A, over a modal logic L, is a unifier σ for A such that the equivalence of σ with the identity map is the consequence of A. Each projective unifier is a most general unifier for A. Let L be a normal modal logic containing S4. We show that every unifiable formula has a projective unifier in L iff L contains S4.3. The syntactic proof is effective. As a corollary, we conclude that all normal modal logics L containing S4.3 are almost structurally complete, i.e. all admissible rules having unifiable premises are derivable in L. Moreover, L is structurally complete iff L contains McKinsey axiom M

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References found in this work

Unifiability in extensions of K4.Çiğdem Gencer & Dick de Jongh - 2009 - Logic Journal of the IGPL 17 (2):159-172.

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