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  1. Neighbourhood Semantics for FDE-Based Modal Logics.S. Drobyshevich & D. Skurt - 2021 - Studia Logica 109 (6):1273-1309.
    We investigate some non-normal variants of well-studied paraconsistent and paracomplete modal logics that are based on N. Belnap’s and M. Dunn’s four-valued logic. Our basic non-normal modal logics are characterized by a weak extensionality rule, which reflects the four-valued nature of underlying logics. Aside from introducing our basic framework of bi-neighbourhood semantics, we develop a correspondence theory in order to prove completeness results with respect to our neighbourhood semantics for non-normal variants of \, \ and \.
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  • Belnap–Dunn Modal Logic with Value Operators.Yuanlei Lin & Minghui Ma - 2020 - Studia Logica 109 (4):759-789.
    The language of Belnap–Dunn modal logic \ expands the language of Belnap–Dunn four-valued logic with the modal operator \. We introduce the polarity semantics for \ and its two expansions \ and \ with value operators. The local finitary consequence relation \ in the language \ with respect to the class of all frames is axiomatized by a sequent system \ where \. We prove by using translations between sequents and formulas that these languages under the polarity semantics have the (...)
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  • Polarity Semantics for Negation as a Modal Operator.Yuanlei Lin & Minghui Ma - 2020 - Studia Logica 108 (5):877-902.
    The minimal weakening \ of Belnap-Dunn logic under the polarity semantics for negation as a modal operator is formulated as a sequent system which is characterized by the class of all birelational frames. Some extensions of \ with additional sequents as axioms are introduced. In particular, all three modal negation logics characterized by a frame with a single state are formalized as extensions of \. These logics have the finite model property and they are decidable.
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  • A Paraconsistent Conditional Logic.Minghui Ma & Chun-Ting Wong - 2020 - Journal of Philosophical Logic 49 (5):883-903.
    We develop a paraconsistent logic by introducing new models for conditionals with acceptive and rejective selection functions which are variants of Chellas’ conditional models. The acceptance and rejection conditions are substituted for truth conditions of conditionals. The paraconsistent conditional logic is axiomatized by a sequent system \ which is an extension of the Belnap-Dunn four-valued logic with a conditional operator. Some acceptive extensions of \ are shown to be sound and complete. We also show the finite acceptive model property and (...)
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  • Countably Many Weakenings of Belnap–Dunn Logic.Minghui Ma & Yuanlei Lin - 2020 - Studia Logica 108 (2):163-198.
    Every Berman’s variety \ which is the subvariety of Ockham algebras defined by the equation \ and \) determines a finitary substitution invariant consequence relation \. A sequent system \ is introduced as an axiomatization of the consequence relation \. The system \ is characterized by a single finite frame \ under the frame semantics given for the formal language. By the duality between frames and algebras, \ can be viewed as a \-valued logic as it is characterized by a (...)
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