1.  48
    Protoalgebraic Gentzen Systems and the Cut Rule.Àngel J. Gil & Jordi Rebagliato - 2000 - Studia Logica 65 (1):53-89.
    In this paper we show that, in Gentzen systems, there is a close relation between two of the main characters in algebraic logic and proof theory respectively: protoalgebraicity and the cut rule. We give certain conditions under which a Gentzen system is protoalgebraic if and only if it possesses the cut rule. To obtain this equivalence, we limit our discussion to what we call regular sequent calculi, which are those comprising some of the structural rules and some logical rules, in (...)
    Direct download (5 more)  
    Export citation  
    Bookmark   6 citations  
  2.  15
    A Finite Hilbert‐Style Axiomatization of the Implication‐Less Fragment of the Intuitionistic Propositional Calculus.Jordi Rebagliato & Ventura Verdú - 1994 - Mathematical Logic Quarterly 40 (1):61-68.
    In this paper we obtain a finite Hilbert-style axiomatization of the implicationless fragment of the intuitionistic propositional calculus. As a consequence we obtain finite axiomatizations of all structural closure operators on the algebra of {–}-formulas containing this fragment.
    Direct download  
    Export citation  
    Bookmark   4 citations  
  3.  23
    A Strong Completeness Theorem for the Gentzen Systems Associated with Finite Algebras.Àngel J. Gil, Jordi Rebagliato & Ventura Verdú - 1999 - Journal of Applied Non-Classical Logics 9 (1):9-36.
    ABSTRACT In this paper we study consequence relations on the set of many sided sequents over a propositional language. We deal with the consequence relations axiomatized by the sequent calculi defined in [2] and associated with arbitrary finite algebras. These consequence relations are examples of what we call Gentzen systems. We define a semantics for these systems and prove a Strong Completeness Theorem, which is an extension of the Completeness Theorem for provable sequents stated in [2]. For the special case (...)
    Direct download (3 more)  
    Export citation  
    Bookmark   3 citations