PreprintCC BY 4.0arXiv
On Three-Valued Dependence-Like Logics
Abstract
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.
Versions
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BibTeX
@misc{petrukhin2026threevalued,
title = {{On Three-Valued Dependence-Like Logics}},
author = {Yaroslav Petrukhin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08293},
eprint = {2610.08293},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08293},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On Three-Valued Dependence-Like Logics
AU - Yaroslav Petrukhin
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08293
UR - https://arxiv.org/abs/2610.08293
AB - 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.
ER -