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  1. Kripke-Completeness and Sequent Calculus for Quasi-Boolean Modal Logic.Minghui Ma & Juntong Guo - forthcoming - Studia Logica:1-30.
    Quasi-Boolean modal algebras are quasi-Boolean algebras with a modal operator satisfying the interaction axiom. Sequential quasi-Boolean modal logics and the relational semantics are introduced. Kripke-completeness for some quasi-Boolean modal logics is shown by the canonical model method. We show that every descriptive persistent quasi-Boolean modal logic is canonical. The finite model property of some quasi-Boolean modal logics is proved. A cut-free Gentzen sequent calculus for the minimal quasi-Boolean logic is developed and we show that it has the Craig interpolation property.
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  • Paradox, truth and logic part I: Paradox and truth.Peter W. Woodruff - 1984 - Journal of Philosophical Logic 13 (2):213 - 232.
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  • Four valued semantics and the liar.Albert Visser - 1984 - Journal of Philosophical Logic 13 (2):181 - 212.
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  • Basic Quasi-Boolean Expansions of Relevance Logics.Gemma Robles & José M. Méndez - 2021 - Journal of Philosophical Logic 50 (4):727-754.
    The basic quasi-Boolean negation expansions of relevance logics included in Anderson and Belnap’s relevance logic R are defined. We consider two types of QB-negation: H-negation and D-negation. The former one is of paraintuitionistic or superintuitionistic character, the latter one, of dual intuitionistic nature in some sense. Logics endowed with H-negation are paracomplete; logics with D-negation are paraconsistent. All logics defined in the paper are given a Routley-Meyer ternary relational semantics.
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  • Sequent Calculi for Semi-De Morgan and De Morgan Algebras.Minghui Ma & Fei Liang - 2018 - Studia Logica 106 (3):565-593.
    A contraction-free and cut-free sequent calculus \ for semi-De Morgan algebras, and a structural-rule-free and single-succedent sequent calculus \ for De Morgan algebras are developed. The cut rule is admissible in both sequent calculi. Both calculi enjoy the decidability and Craig interpolation. The sequent calculi are applied to prove some embedding theorems: \ is embedded into \ via Gödel–Gentzen translation. \ is embedded into a sequent calculus for classical propositional logic. \ is embedded into the sequent calculus \ for intuitionistic (...)
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  • Positive fragments of relevance logic and algebras of binary relations.Robin Hirsch & Szabolcs Mikulás - 2011 - Review of Symbolic Logic 4 (1):81-105.
    We prove that algebras of binary relations whose similarity type includes intersection, union, and one of the residuals of relation composition form a nonfinitely axiomatizable quasivariety and that the equational theory is not finitely based. We apply this result to the problem of the completeness of the positive fragment of relevance logic with respect to binary relations.
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  • Relevance logics and relation algebras.Katalin Bimbó, J. Michael Dunn & Roger D. Maddux - 2009 - Review of Symbolic Logic 2 (1):102-131.
    Relevance logics are known to be sound and complete for relational semantics with a ternary accessibility relation. This paper investigates the problem of adequacy with respect to special kinds of dynamic semantics (i.e., proper relation algebras and relevant families of relations). We prove several soundness results here. We also prove the completeness of a certain positive fragment of R as well as of the first-degree fragment of relevance logics. These results show that some core ideas are shared between relevance logics (...)
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  • Restricted Rules of Inference and Paraconsistency.Sankha S. Basu & Mihir K. Chakraborty - 2022 - Logic Journal of the IGPL 30 (3):534-560.
    In this paper, we study two companions of a logic, viz., the left variable inclusion companion and the restricted rules companion, their nature and interrelations, especially in connection with paraconsistency. A sufficient condition for the two companions to coincide has also been proved. Two new logical systems—intuitionistic paraconsistent weak Kleene logic (IPWK) and paraconsistent pre-rough logic (PPRL)—are presented here as examples of logics of left variable inclusion. IPWK is the left variable inclusion companion of intuitionistic propositional logic and is also (...)
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