Best Unifiers in Transitive Modal Logics

Studia Logica 99 (1-3):321-336 (2011)
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
Keywords Modal logics  unification  best unifiers  admissible rules
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DOI 10.1007/s11225-011-9354-y
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References found in this work BETA
Proof Theory for Admissible Rules.Rosalie Iemhoff & George Metcalfe - 2009 - Annals of Pure and Applied Logic 159 (1):171-186.
Unification in Modal and Description Logics.Franz Baader & Silvio Ghilardi - 2011 - Logic Journal of the IGPL 19 (6):705-730.
Unification in Intuitionistic Logic.Silvio Ghilardi - 1999 - Journal of Symbolic Logic 64 (2):859-880.
Best Solving Modal Equations.Silvio Ghilardi - 2000 - Annals of Pure and Applied Logic 102 (3):183-198.
Independent Bases of Admissible Rules.Emil Jerábek - 2008 - Logic Journal of the IGPL 16 (3):249-267.

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