Order:
  1.  30
    A Deterministic Weakening of Belnap–Dunn Logic.Minghui Ma & Yuanlei Lin - 2019 - Studia Logica 107 (2):283-312.
    A deterministic weakening \ of the Belnap–Dunn four-valued logic \ is introduced to formalize the acceptance and rejection of a proposition at a state in a linearly ordered informational frame with persistent valuations. The logic \ is formalized as a sequent calculus. The completeness and decidability of \ with respect to relational semantics are shown in terms of normal forms. From an algebraic perspective, the class of all algebras for \ is described, and found to be a subvariety of Berman’s (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  2.  29
    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 (...)
    Direct download (2 more)  
    Translate
     
     
    Export citation  
     
    Bookmark   4 citations  
  3.  20
    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.
    Direct download (2 more)  
    Translate
     
     
    Export citation  
     
    Bookmark   2 citations  
  4.  6
    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 (...)
    Direct download (2 more)  
    Translate
     
     
    Export citation  
     
    Bookmark  
  5.  22
    A Three-Valued Fregean Quantification Logic.Minghui Ma & Yuanlei Lin - 2019 - Journal of Philosophical Logic 48 (2):409-423.
    Kripke’s Fregean quantification logic FQ fails to formalize the usual first-order logic with identity due to the interpretation of the conditional operator. Motivated by Kripke’s syntax and semantics, the three-valued Fregean quantification logic FQ3 is proposed. This three valued logic differs from Kleene and Łukasiewicz’s three-valued logics. The logic FQ3 is decidable. A sound and complete Hilbert-style axiomatic system for the logic FQ3 is presented.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark