Two variable fragment of Term Modal Logic

Anantha Padmanabha; R. Ramanujam

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arXiv · 1904.10260

Two variable fragment of Term Modal Logic

Anantha Padmanabha·R. Ramanujam

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Abstract

Term modal logics (TML) are modal logics with unboundedly many modalities, with quantification over modal indices, so that we can have formulas of the form $\exists y. \forall x. (\Box_x P(x,y) \supset\Diamond_y P(y,x))$. Like First order modal logic, TML is also "notoriously" undecidable, in the sense that even very simple fragments are undecidable. In this paper, we show the decidability of one interesting fragment, that of two variable TML. This is in contrast to two-variable First order modal logic, which is undecidable.

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Anantha Padmanabha, R. Ramanujam. 2019-04-23. Two variable fragment of Term Modal Logic. https://arxiv.org/abs/1904.10260

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