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Best Unifiers in Transitive Modal Logics

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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.

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Authors and Affiliations

  1. School of Computing, Mathematics and IT, Manchester Metropolitan University, Chester Street, Manchester, M 1 5GD, UK

    Vladimir V. Rybakov

  2. Mathematical Institute, Siberian Federal University, Krasnoyarsk, Russia

    Vladimir V. Rybakov

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  1. Vladimir V. Rybakov
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Correspondence to Vladimir V. Rybakov.

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Dedicated to the outstanding logician Ryszard Wójcicki on the occasion of his 80th birthday

Special issue in honor of Ryszard Wójcicki on the occasion of his 80th birthday

Edited by J. Czelakowski, W. Dziobiak, and J. Malinowski

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Rybakov, V.V. Best Unifiers in Transitive Modal Logics. Stud Logica 99, 321 (2011). https://doi.org/10.1007/s11225-011-9354-y

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