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arXiv · 2605.24717

Refutation calculi for lattice-based logics: from display to tableaux

Andrea De Domenico·Giuseppe Greco·Alessandra Palmigiano·Mario Piazza·Andrea Sabatini
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Abstract

Refutation calculi are formal systems developed to derive the invalid formulas of a given logic. While the notion of refutation calculi has played a key role in the development of tableaux calculi, a refutation approach to display calculi has not yet been attempted. In this paper, we introduce refutation display calculi for basic LE-logics, i.e., those logics canonically associated with basic normal lattice expansions of any signature. In particular, we prove soundness and completeness via proof-analysis results on derivable sequents. Finally, we obtain terminating tableaux calculi from these refutation display calculi.

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BibTeXRIS

Andrea De Domenico, Giuseppe Greco, Alessandra Palmigiano, Mario Piazza, Andrea Sabatini. 2026-05-23. Refutation calculi for lattice-based logics: from display to tableaux. https://arxiv.org/abs/2605.24717

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