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Generalizing the Depth Relevance Condition: Deep Relevant Logics Not Included in R-Mingle

Gemma Robles & José M. Méndez

Notre Dame Journal of Formal Logic 55 (1):107-127 (2014)

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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
Proof Invariance.Blane Worley - forthcoming - Australasian Journal of Logic.details We explore depth substitution invariance, or hyperformalism, and extend known results in this realm to justification logics extending weak relevant logics. We then examine the surprising invariance of justifications over formulas and restrict our attention to the substitution of proofs in the original relevant logic. The results of this paper indicate that depth invariance is a recalcitrant feature of the logic and that proof structures in hyperformal logics are quite inflexible. Nonclassical Logic, Misc in Logic and Philosophy of Logic Relevance Logic in Logic and Philosophy of Logic Direct download Export citation Bookmark
Blocking the Routes to Triviality with Depth Relevance.Gemma Robles & José M. Méndez - 2014 - Journal of Logic, Language and Information 23 (4):493-526.details In Rogerson and Restall’s, the “class of implication formulas known to trivialize ” is recorded. The aim of this paper is to show how to invalidate any member in this class by using “weak relevant model structures”. Weak relevant model structures verify deep relevant logics only. Science, Logic, and Mathematics Direct download (2 more) Export citation Bookmark 4 citations
Topic Transparency and Variable Sharing in Weak Relevant Logics.Thomas Macaulay Ferguson & Shay Allen Logan - forthcoming - Erkenntnis:1-28.details In this paper, we examine a number of relevant logics’ variable sharing properties from the perspective of theories of topic or subject-matter. We take cues from Franz Berto’s recent work on topic to show an alignment between families of variable sharing properties and responses to the topic transparency of relevant implication and negation. We then introduce and defend novel variable sharing properties stronger than strong depth relevance—which we call cn-relevance and lossless cn-relevance—showing that the properties are satisfied by the weak (...) Relevance Logic in Logic and Philosophy of Logic Direct download (3 more) Export citation Bookmark 1 citation
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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