Decidability of modal logics of non-$k$-colorable graphs

Ilya Shapirovsky

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arXiv · 2303.09934

Decidability of modal logics of non-$k$-colorable graphs

Ilya Shapirovsky

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Abstract

We consider the bimodal language, where the first modality is interpreted by a binary relation in the standard way, and the second is interpreted by the relation of inequality. It follows from Hughes (1990), that in this language, non-$k$-colorability of a graph is expressible for every finite $k$. We show that modal logics of classes of non-$k$-colorable graphs (directed or non-directed), and some of their extensions, are decidable.

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Ilya Shapirovsky. 2023-03-17. Decidability of modal logics of non-$k$-colorable graphs. https://arxiv.org/abs/2303.09934

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