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  1. Shortest Axiomatizations of Implicational S4 and S.Zachary Ernst, Branden Fitelson, Kenneth Harris & Larry Wos - 2002 - Notre Dame Journal of Formal Logic 43 (3):169-179.
    Shortest possible axiomatizations for the implicational fragments of the modal logics S4 and S5 are reported. Among these axiomatizations is included a shortest single axiom for implicational S4—which to our knowledge is the first reported single axiom for that system—and several new shortest single axioms for implicational S5. A variety of automated reasoning strategies were essential to our discoveries.
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  • A Second Pretabular Classical Relevance Logic.Asadollah Fallahi - 2018 - Studia Logica 106 (1):191-214.
    Pretabular logics are those that lack finite characteristic matrices, although all of their normal proper extensions do have some finite characteristic matrix. Although for Anderson and Belnap’s relevance logic R, there exists an uncountable set of pretabular extensions :1249–1270, 2008), for the classical relevance logic \\rightarrow B\}\) there has been known so far a pretabular extension: \. In Section 1 of this paper, we introduce some history of pretabularity and some relevance logics and their algebras. In Section 2, we introduce (...)
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  • Jaśkowski's Criterion and Three-Valued Paraconsistent Logics.Alexander S. Karpenko - 1999 - Logic and Logical Philosophy 7:81.
    A survey is given of three-valued paraconsistent propositionallogics connected with Jaśkowski’s criterion for constructing paraconsistentlogics. Several problems are raised and four new matrix three-valued paraconsistent logics are suggested.
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  • 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 (...)
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  • A Constructive Analysis of RM.Arnon Avron - 1987 - Journal of Symbolic Logic 52 (4):939 - 951.
  • What is Relevance Logic?Arnon Avron - 2014 - Annals of Pure and Applied Logic 165 (1):26-48.
    We suggest two precise abstract definitions of the notion of ‘relevance logic’ which are both independent of any proof system or semantics. We show that according to the simpler one, R → source is the minimal relevance logic, but R itself is not. In contrast, R and many other logics are relevance logics according to the second definition, while all fragments of linear logic are not.
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  • Maximal and Premaximal Paraconsistency in the Framework of Three-Valued Semantics.Ofer Arieli, Arnon Avron & Anna Zamansky - 2011 - Studia Logica 97 (1):31 - 60.
    Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain from classical logic as much as possible. In this paper we introduce the strongest possible notion of maximal paraconsistency, and investigate it in the context of logics that are based on deterministic or non-deterministic three-valued matrices. We show that all reasonable paraconsistent logics based on three-valued deterministic matrices are maximal in our strong sense. This applies to practically all three-valued (...)
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  • Relevant Entailment--Semantics and Formal Systems.Arnon Avron - 1984 - Journal of Symbolic Logic 49 (2):334-342.