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arXiv · 2110.09844

Comonadic semantics for hybrid logic and bounded fragments

Samson Abramsky·Dan Marsden
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Abstract

In recent work, comonads and associated structures have been used to analyse a range of important notions in finite model theory, descriptive complexity and combinatorics. We extend this analysis to Hybrid logic, a widely-studied extension of basic modal logic, which corresponds to the bounded fragment of first-order logic. In addition to characterising the various resource-indexed equivalences induced by Hybrid logic and the bounded fragment, and the associated combinatorial decompositions of structures, we also give model-theoretic characterisations of bounded formulas in terms of invariance under generated substructures, in both the finite and infinite cases.

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Samson Abramsky, Dan Marsden. 2021-10-19. Comonadic semantics for hybrid logic and bounded fragments. https://arxiv.org/abs/2110.09844

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