Unification in pretabular extensions of S4
Stepan Igorevich Bashmakov
TL;DR
This paper investigates the unification properties of five specific pretabular extensions of the modal logic S4, providing a systematic analysis and classification of their unification types and unifiers.
Contribution
It systematically classifies the unification types of all five pretabular extensions of S4 and describes complete sets of unifiers for each logic.
Findings
PM2 and PM3 have finitary unification
PM1, PM4, and PM5 have unitary unification
Complete sets of unifiers are described for all logics
Abstract
L.L. Maksimova and L. Esakia, V. Meskhi showed that the modal logic S4 has exactly 5 pretabular extensions: PM1-PM5. In this paper, we study and systematize the problem of unification for all given pretabular logics. We showed that PM2,PM3 have finitary, and PM1,PM4,PM5 have unitary types of unification. Complete sets of unifiers in logics are described.
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