Comonadic semantics for hybrid logic and bounded fragments

TL;DR

This paper extends comonadic semantics to hybrid logic and bounded fragments, providing new characterizations of logical equivalences and structural decompositions in finite and infinite models.

Contribution

It introduces comonadic models for hybrid logic and bounded fragments, offering novel invariance and decomposition results in finite model theory.

Findings

Characterization of resource-indexed equivalences in hybrid logic

Combinatorial decompositions of structures based on comonadic semantics

Model-theoretic invariance results for bounded formulas

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.