Labelled calculi for lattice-based modal logics

Ineke van der Berg; Andrea De Domenico; Giuseppe Greco; Krishna Manoorkar; Alessandra Palmigiano; Mattia Panettiere

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arXiv · 2401.09887

Labelled calculi for lattice-based modal logics

Ineke van der Berg·Andrea De Domenico·Giuseppe Greco·Krishna Manoorkar·Alessandra Palmigiano·Mattia Panettiere

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Abstract

We introduce labelled sequent calculi for the basic normal non-distributive modal logic L and 31 of its axiomatic extensions, where the labels are atomic formulas of a first order language which is interpreted on the canonical extensions of the algebras in the variety corresponding to the logic L. Modular proofs are presented that these calculi are all sound, complete and conservative w.r.t. L, and enjoy cut elimination and the subformula property. The introduction of these calculi showcases a general methodology for introducing labelled calculi for the class of LE-logics and their analytic axiomatic extensions in a principled and uniform way.

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Ineke van der Berg, Andrea De Domenico, Giuseppe Greco, Krishna Manoorkar, Alessandra Palmigiano, Mattia Panettiere. 2024-01-18. Labelled calculi for lattice-based modal logics. https://arxiv.org/abs/2401.09887

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