Finitary unification in locally tabular modal logics characterized. (English) Zbl 07483254
Summary: We provide necessary and sufficient conditions for finitary unification in locally tabular modal logics, solely in terms of Kripke models. We apply the conditions to establish the unification types of logics determined by simple finite frames. In particular, we show that unification is finitary (or unitary) in the logic determined by the fork (frame \(\mathfrak{F}_4\), see Fig. 6), the rhombus (frame \(\mathfrak{F}_5)\), in \(\textsf{GL.3}_m , \textsf{GrzBd}_2, \textsf{S4Bd}_2\) and other logics; whereas it is nullary in the logic of \(\mathfrak{F}_6\), and of the pentagon \(\mathfrak{F}_{N 5} \). In Appendix analogous results are given for superintuitionistic logics.
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