7 found
Order:
  1.  41
    Structural Completeness in Substructural Logics.J. S. Olson, J. G. Raftery & C. J. Van Alten - 2008 - Logic Journal of the IGPL 16 (5):453-495.
    Hereditary structural completeness is established for a range of substructural logics, mainly without the weakening rule, including fragments of various relevant or many-valued logics. Also, structural completeness is disproved for a range of systems, settling some previously open questions.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   27 citations  
  2.  81
    Correspondences between Gentzen and Hilbert Systems.J. G. Raftery - 2006 - Journal of Symbolic Logic 71 (3):903 - 957.
    Most Gentzen systems arising in logic contain few axiom schemata and many rule schemata. Hilbert systems, on the other hand, usually contain few proper inference rules and possibly many axioms. Because of this, the two notions tend to serve different purposes. It is common for a logic to be specified in the first instance by means of a Gentzen calculus, whereupon a Hilbert-style presentation ‘for’ the logic may be sought—or vice versa. Where this has occurred, the word ‘for’ has taken (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   24 citations  
  3.  23
    Varieties of de Morgan monoids: Covers of atoms.T. Moraschini, J. G. Raftery & J. J. Wannenburg - 2020 - Review of Symbolic Logic 13 (2):338-374.
    The variety DMM of De Morgan monoids has just four minimal subvarieties. The join-irreducible covers of these atoms in the subvariety lattice of DMM are investigated. One of the two atoms consisting of idempotent algebras has no such cover; the other has just one. The remaining two atoms lack nontrivial idempotent members. They are generated, respectively, by 4-element De Morgan monoids C4 and D4, where C4 is the only nontrivial 0-generated algebra onto which finitely subdirectly irreducible De Morgan monoids may (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  4.  50
    Structural Completeness in Relevance Logics.J. G. Raftery & K. Świrydowicz - 2016 - Studia Logica 104 (3):381-387.
    It is proved that the relevance logic \ has no structurally complete consistent axiomatic extension, except for classical propositional logic. In fact, no other such extension is even passively structurally complete.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  5.  19
    Epimorphisms, Definability and Cardinalities.T. Moraschini, J. G. Raftery & J. J. Wannenburg - 2020 - Studia Logica 108 (2):255-275.
    We characterize, in syntactic terms, the ranges of epimorphisms in an arbitrary class of similar first-order structures. This allows us to strengthen a result of Bacsich, as follows: in any prevariety having at most \ non-logical symbols and an axiomatization requiring at most \ variables, if the epimorphisms into structures with at most \ elements are surjective, then so are all of the epimorphisms. Using these facts, we formulate and prove manageable ‘bridge theorems’, matching the surjectivity of all epimorphisms in (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  6.  48
    Fragments of R-Mingle.W. J. Blok & J. G. Raftery - 2004 - Studia Logica 78 (1-2):59-106.
    The logic RM and its basic fragments (always with implication) are considered here as entire consequence relations, rather than as sets of theorems. A new observation made here is that the disjunction of RM is definable in terms of its other positive propositional connectives, unlike that of R. The basic fragments of RM therefore fall naturally into two classes, according to whether disjunction is or is not definable. In the equivalent quasivariety semantics of these fragments, which consist of subreducts of (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  7.  43
    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   3 citations