Best Unifiers in Transitive Modal Logics

Authors:
Vladimir V. Rybakov
Affiliations:
School of Computing, Mathematics and IT, Manchester Metropolitan University, Manchester, UK M 1 5GD and Mathematical Institute, Siberian Federal University, Krasnoyarsk, Russia
Venue:
Studia Logica
Year:
2011

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Abstract

This paper offers a brief analysis of the unification problem in modal transitive logics related to the logic S4: S4 itself, K4, Grz and Gödel-Löb provability logic GL. As a result, new, but not the first, algorithms for the construction of `best' unifiers in these logics are being proposed. The proposed algorithms are based on our earlier approach to solve in an algorithmic way the admissibility problem of inference rules for S4 and Grz. The first algorithms for the construction of `best' unifiers in the above mentioned logics have been given by S. Ghilardi in [16]. Both the algorithms in [16] and ours are not much computationally efficient. They have, however, an obvious significant theoretical value a portion of which seems to be the fact that they stem from two different methodological approaches.