Year:

  1.  9
    On GE-Algebras.Ravikumar Bandaru, Arsham Borumand Saeid & Young Bae Jun - 2021 - Bulletin of the Section of Logic 50 (1):81-96.
    Hilbert algebras are important tools for certain investigations in intuitionistic logic and other non-classical logic and as a generalization of Hilbert algebra a new algebraic structure, called a GE-algebra, is introduced and studied its properties. We consider filters, upper sets and congruence kernels in a GE-algebra. We also characterize congruence kernels of transitive GE-algebras.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  2.  4
    Soju Filters in Hoop Algebras.Rajab Ali Borzooei, Gholam Reza Rezaei, Mona Aaly Kologhani & Young Bae Jun - 2021 - Bulletin of the Section of Logic 50 (1):97-123.
    The notions of soju filters in a hoop algebra are introduced, and related properties are investigated. Relations between a soju sub-hoop, a soju filter and an implicative soju filter are discussed. Conditions for a soju filter to be implicative are displayed, and characterizations of an implicative soju filters are considered. The extension property of an implicative soju filter is established.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  3.  13
    Super-Strict Implications.Guido Gherardi & Eugenio Orlandelli - 2021 - Bulletin of the Section of Logic 50 (1):1-34.
    This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis' strict implication that avoids not only the paradoxes of material implication but also those of strict implication. The semantics of super-strict implications is obtained by strengthening the relational semantics for strict implication. We consider all logics of super-strict implications that are based on relational frames for modal logics in the modal cube. it is shown that all logics of super-strict implications are connexive (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  4.  8
    One-Sided Sequent Systems for Nonassociative Bilinear Logic: Cut Elimination and Complexity.Paweł Płaczek - 2021 - Bulletin of the Section of Logic 50 (1):55-80.
    Bilinear Logic of Lambek amounts to Noncommutative MALL of Abrusci. Lambek proves the cut–elimination theorem for a one-sided sequent system for this logic. Here we prove an analogous result for the nonassociative version of this logic. Like Lambek, we consider a left-sided system, but the result also holds for its right-sided version, by a natural symmetry. The treatment of nonassociative sequent systems involves some subtleties, not appearing in associative logics. We also prove the PTime complexity of the multiplicative fragment of (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  5.  7
    A Semi-Lattice of Four-Valued Literal-Paraconsistent-Paracomplete Logics.Natalya Tomova - 2021 - Bulletin of the Section of Logic 50 (1):35-53.
    In this paper, we consider the class of four-valued literal-paraconsistent-paracomplete logics constructed by combination of isomorphs of classical logic CPC. These logics form a 10-element upper semi-lattice with respect to the functional embeddinig one logic into another. The mechanism of variation of paraconsistency and paracompleteness properties in logics is demonstrated on the example of two four-element lattices included in the upper semi-lattice. Functional properties and sets of tautologies of corresponding literal-paraconsistent-paracomplete matrices are investigated. Among the considered matrices there are the (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
 Previous issues
  
Next issues