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Blocking the Routes to Triviality with Depth Relevance

Gemma Robles & José M. Méndez

Journal of Logic, Language and Information 23 (4):493-526 (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 (...) Download Export citation Bookmark
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 (...) Download Export citation Bookmark 5 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 (...) Download Export citation Bookmark 10 citations
Relevant first-order logic LP# and Curry’s paradox resolution.Jaykov Foukzon - 2015 - Pure and Applied Mathematics Journal Volume 4, Issue 1-1, January 2015 DOI: 10.11648/J.Pamj.S.2015040101.12.details In 1942 Haskell B. Curry presented what is now called Curry's paradox which can be found in a logic independently of its stand on negation. In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this article the non-classical resolution of Curry’s Paradox and Shaw-Kwei' sparadox without rejection any contraction postulate is proposed. In additional relevant paraconsistent logic C ̌_n^#,1≤n<ω, in fact,provide an effective way of circumventing triviality of da Costa’s paraconsistent Set Theories〖NF〗n^C. Download Export citation Bookmark

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