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A Class of Simpler Logical Matrices for the Variable-Sharing Property

G. Robles & J. M. Méndez

Logic and Logical Philosophy 20 (3):241-249 (2011)

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Routes to relevance: Philosophies of relevant logics.Shawn Standefer - 2024 - Philosophy Compass 19 (2):e12965.details Relevant logics are a family of non-classical logics characterized by the behavior of their implication connectives. Unlike some other non-classical logics, such as intuitionistic logic, there are multiple philosophical views motivating relevant logics. Further, different views seem to motivate different logics. In this article, we survey five major views motivating the adoption of relevant logics: Use Criterion, sufficiency, meaning containment, theory construction, and truthmaking. We highlight the philosophical differences as well as the different logics they support. We end with some (...) No categories Direct download (3 more) Export citation Bookmark
The (Greatest) Fragment of Classical Logic that Respects the Variable-Sharing Principle (in the FMLA-FMLA Framework).Damian E. Szmuc - 2021 - Bulletin of the Section of Logic 50 (4):421-453.details We examine the set of formula-to-formula valid inferences of Classical Logic, where the premise and the conclusion share at least a propositional variable in common. We review the fact, already proved in the literature, that such a system is identical to the first-degree entailment fragment of R. Epstein's Relatedness Logic, and that it is a non-transitive logic of the sort investigated by S. Frankowski and others. Furthermore, we provide a semantics and a calculus for this logic. The semantics is defined (...) Classical Logic in Logic and Philosophy of Logic Logical Consequence and Entailment in Logic and Philosophy of Logic Many-Valued Logic in Logic and Philosophy of Logic Proof Theory in Logic and Philosophy of Logic Substructural Logic in Logic and Philosophy of Logic Direct download (4 more) Export citation Bookmark 2 citations
What is a Relevant Connective?Shawn Standefer - 2022 - Journal of Philosophical Logic 51 (4):919-950.details There appears to be few, if any, limits on what sorts of logical connectives can be added to a given logic. One source of potential limitations is the motivating ideology associated with a logic. While extraneous to the logic, the motivating ideology is often important for the development of formal and philosophical work on that logic, as is the case with intuitionistic logic. One family of logics for which the philosophical ideology is important is the family of relevant logics. In (...) Logical Connectives in Logic and Philosophy of Logic Direct download (4 more) Export citation Bookmark 5 citations
Admissibility of Ackermann's rule δ in relevant logics.Gemma Robles - 2013 - Logic and Logical Philosophy 22 (4):411-427.details It is proved that Ackermann’s rule δ is admissible in a wide spectrum of relevant logics satisfying certain syntactical properties. Logic and Philosophy of Logic Nonclassical Logics in Logic and Philosophy of Logic Relevance Logic in Logic and Philosophy of Logic Direct download (8 more) Export citation Bookmark 3 citations
Strong Depth Relevance.Shay Allen Logan - 2021 - Australasian Journal of Logic 18 (6):645-656.details Relevant logics infamously have the property that they only validate a conditional when some propositional variable is shared between its antecedent and consequent. This property has been strengthened in a variety of ways over the last half-century. Two of the more famous of these strengthenings are the strong variable sharing property and the depth relevance property. In this paper I demonstrate that an appropriate class of relevant logics has a property that might naturally be characterized as the supremum of these (...) Intuitionistic Logic in Logic and Philosophy of Logic Paraconsistent Logic in Logic and Philosophy of Logic Relevance Logic in Logic and Philosophy of Logic Substructural Logic in Logic and Philosophy of Logic Direct download (3 more) Export citation Bookmark 10 citations
Variable-Sharing as Relevance.Shawn Standefer - forthcoming - In Igor Sedlár, Shawn Standefer & Andrew Tedder (eds.), New Directions in Relevant Logic.details Logic and Philosophy of Logic, General Works in Logic and Philosophy of Logic Paraconsistent Logic in Logic and Philosophy of Logic Relevance Logic in Logic and Philosophy of Logic Substructural Logic in Logic and Philosophy of Logic Direct download Export citation Bookmark 1 citation
Logic in the Deep End.Graham Leach-Krouse, Shay Logan & Blane Worley - forthcoming - Analysis.details Weak enough relevant logics are often closed under depth substitutions. To determine the breadth of logics with this feature, we show there is a largest sublogic of R closed under depth substitutions and that this logic can be recursively axiomatized. Relevance Logic in Logic and Philosophy of Logic Direct download (2 more) Export citation Bookmark

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