On Three-Valued Dependence-Like Logics
DOI:
https://doi.org/10.12775/LLP.2026.016Keywords
dependence logic, relating logic, three-valued logic, proof theory, bisequent calculi, cut admissibilityAbstract
In this paper, we investigate connections between dependence logics, viewed as a subclass of relating logics, and three-valued logics. More specifically, we identify common features of Epstein’s subject-matter semantics and the variable-inclusion conditions characteristic of some infectious many-valued logics. Inspired by Del Cerro and Lugardon’s sequent calculi for dependence logics, in which classical connectives are combined with connectives satisfying Epstein-style conditions, we introduce two three-valued dependence-like logics that combine classical conjunction and disjunction with infectious negation and implication. We also provide sound, complete, and cut-free bisequent calculi for these logics.
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