Switch to: References

Add citations

You must login to add citations.
  1. Deduction Theorems Within RM and Its Extensions.J. Czelakowski & W. Dziobiak - 1999 - Journal of Symbolic Logic 64 (1):279-290.
    In [13], M. Tokarz specified some infinite family of consequence operations among all ones associated with the relevant logic RM or with the extensions of RM and proved that each of them admits a deduction theorem scheme. In this paper, we show that the family is complete in a sense that if C is a consequence operation with $C_{RM} \leq C$ and C admits a deduction theorem scheme, then C is equal to a consequence operation specified in [13]. In algebraic (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • Categorical Abstract Algebraic Logic: More on Protoalgebraicity.George Voutsadakis - 2006 - Notre Dame Journal of Formal Logic 47 (4):487-514.
    Protoalgebraic logics are characterized by the monotonicity of the Leibniz operator on their theory lattices and are at the lower end of the Leibniz hierarchy of abstract algebraic logic. They have been shown to be the most primitive among those logics with a strong enough algebraic character to be amenable to algebraic study techniques. Protoalgebraic π-institutions were introduced recently as an analog of protoalgebraic sentential logics with the goal of extending the Leibniz hierarchy from the sentential framework to the π-institution (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  • Algebraic Study of Two Deductive Systems of Relevance Logic.Josep Maria Font & Gonzalo Rodríguez - 1994 - Notre Dame Journal of Formal Logic 35 (3):369-397.
    In this paper two deductive systems associated with relevance logic are studied from an algebraic point of view. One is defined by the familiar, Hilbert-style, formalization of R; the other one is a weak version of it, called WR, which appears as the semantic entailment of the Meyer-Routley-Fine semantics, and which has already been suggested by Wójcicki for other reasons. This weaker consequence is first defined indirectly, using R, but we prove that the first one turns out to be an (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   16 citations  
  • Nikolaos Galatos.Hiroakira Ono - 2006 - Studia Logica 83 (1-3):1-32.
    No categories
     
    Export citation  
     
    Bookmark  
  • Logics and Operators.Janusz Czelakowski - 1995 - Logic and Logical Philosophy 3:87-100.
    Two connectives are of special interest in metalogical investigations — the connective of implication which is important due to its connections to the notion of inference, and the connective of equivalence. The latter connective expresses, in the material sense, the fact that two sentences have the same logical value while in the strict sense it expresses the fact that two sentences are interderivable on the basis of a given logic. The process of identification of equivalent sentences relative to theories of (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark  
  • Contextual Deduction Theorems.J. G. Raftery - 2011 - Studia Logica 99 (1-3):279-319.
    Logics that do not have a deduction-detachment theorem (briefly, a DDT) may still possess a contextual DDT —a syntactic notion introduced here for arbitrary deductive systems, along with a local variant. Substructural logics without sentential constants are natural witnesses to these phenomena. In the presence of a contextual DDT, we can still upgrade many weak completeness results to strong ones, e.g., the finite model property implies the strong finite model property. It turns out that a finitary system has a contextual (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • Relation Formulas for Protoalgebraic Equality Free Quasivarieties; Pałasińska’s Theorem Revisited.Anvar M. Nurakunov & Michał M. Stronkowski - 2013 - Studia Logica 101 (4):827-847.
    We provide a new proof of the following Pałasińska's theorem: Every finitely generated protoalgebraic relation distributive equality free quasivariety is finitely axiomatizable. The main tool we use are ${\mathcal{Q}}$ Q -relation formulas for a protoalgebraic equality free quasivariety ${\mathcal{Q}}$ Q . They are the counterparts of the congruence formulas used for describing the generation of congruences in algebras. Having this tool in hand, we prove a finite axiomatization theorem for ${\mathcal{Q}}$ Q when it has definable principal ${\mathcal{Q}}$ Q -subrelations. This (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • On the Closure Properties of the Class of Full G-Models of a Deductive System.Josep Maria Font, Ramon Jansana & Don Pigozzi - 2006 - Studia Logica 83 (1-3):215-278.
    In this paper we consider the structure of the class FGModS of full generalized models of a deductive system S from a universal-algebraic point of view, and the structure of the set of all the full generalized models of S on a fixed algebra A from the lattice-theoretical point of view; this set is represented by the lattice FACSs A of all algebraic closed-set systems C on A such that (A, C) ε FGModS. We relate some properties of these structures (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  • Algebraization, Parametrized Local Deduction Theorem and Interpolation for Substructural Logics Over FL.Nikolaos Galatos & Hiroakira Ono - 2006 - Studia Logica 83 (1-3):279-308.
    Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   25 citations  
  • Categorical Abstract Algebraic Logic: Prealgebraicity and Protoalgebraicity.George Voutsadakis - 2007 - Studia Logica 85 (2):215-249.
    Two classes of π are studied whose properties are similar to those of the protoalgebraic deductive systems of Blok and Pigozzi. The first is the class of N-protoalgebraic π-institutions and the second is the wider class of N-prealgebraic π-institutions. Several characterizations are provided. For instance, N-prealgebraic π-institutions are exactly those π-institutions that satisfy monotonicity of the N-Leibniz operator on theory systems and N-protoalgebraic π-institutions those that satisfy monotonicity of the N-Leibniz operator on theory families. Analogs of the correspondence property of (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   6 citations