4 found
Sort by:
  1. C. J. van Alten (2006). On Varieties of Biresiduation Algebras. Studia Logica 83 (1-3):425-445.
    A biresiduation algebra is a 〈/,\,1〉-subreduct of an integral residuated lattice. These algebras arise as algebraic models of the implicational fragment of the Full Lambek Calculus with weakening. We axiomatize the quasi-variety B of biresiduation algebras using a construction for integral residuated lattices. We define a filter of a biresiduation algebra and show that the lattice of filters is isomorphic to the lattice of B-congruences and that these lattices are distributive. We give a finite basis of terms for generating filters (...)
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  2. C. J. van Alten (2005). The Finite Model Property for Knotted Extensions of Propositional Linear Logic. Journal of Symbolic Logic 70 (1):84-98.
    The logics considered here are the propositional Linear Logic and propositional Intuitionistic Linear Logic extended by a knotted structural rule: γ, xn → y / γ, xm → y. It is proved that the class of algebraic models for such a logic has the finite embeddability property, meaning that every finite partial subalgebra of an algebra in the class can be embedded into a finite full algebra in the class. It follows that each such logic has the finite model property (...)
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  3. C. J. van Alten & J. G. Raftery (2004). Embedding Theorems and Rule Separation in Logics Without Weakening. Studia Logica 76 (2).
    No categories
     
    My bibliography  
     
    Export citation  
  4. C. J. van Alten & J. G. Raftery (1999). The Finite Model Property for the Implicational Fragment of IPC Without Exchange and Contraction. Studia Logica 63 (2):213-222.
    The aim of this paper is to show that the implicational fragment BKof the intuitionistic propositional calculus (IPC) without the rules of exchange and contraction has the finite model property with respect to the quasivariety of left residuation algebras (its equivalent algebraic semantics). It follows that the variety generated by all left residuation algebras is generated by the finite left residuation algebras. We also establish that BKhas the finite model property with respect to a class of structures that constitute a (...)
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation