Derivational modal logics with the difference modality

Andrey Kudinov; Valentin Shehtman

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arXiv · 1405.6700

Derivational modal logics with the difference modality

Andrey Kudinov·Valentin Shehtman

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Abstract

In this chapter we study modal logics of topological spaces in the combined language with the derivational modality and the difference modality. We give axiomatizations and prove completeness for the following classes: all spaces, $T_1$-spaces, dense-in-themselves spaces, a zero-dimensional dense-in-itself separable metric space, $R^n$ $(n\ge 2)$. We also discuss the correlation between languages with different combinations of the topological, the derivational, the universal and the difference modality in terms of definability.

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BibTeX RIS

Andrey Kudinov, Valentin Shehtman. 2014-05-26. Derivational modal logics with the difference modality. https://arxiv.org/abs/1405.6700

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