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Non-Boolean classical relevant logics II: Classicality through truth-constants

Tore Fjetland Øgaard

Synthese (3-4):1-33 (2021)

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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
The Weak Variable Sharing Property.Tore Fjetland Øgaard - 2023 - Bulletin of the Section of Logic (1):85-99.details An algebraic type of structure is shown forth which is such that if it is a characteristic matrix for a logic, then that logic satisfies Meyer's weak variable sharing property. As a corollary, it is shown that RM and all its odd-valued extensions \(\mathbf{RM}_{2n\mathord{-}1}\) satisfy the weak variable sharing property. It is also shown that a proof to the effect that the "fuzzy" version of the relevant logic R satisfies the property is incorrect. Download Export citation Bookmark
Confused Entailment.Tore Fjetland Øgaard - 2021 - Topoi 41 (1):207-219.details Priest argued in Fusion and Confusion (Priest in Topoi 34(1):55–61, 2015a) for a new concept of logical consequence over the relevant logic B, one where premises my be “confused” together. This paper develops Priest’s idea. Whereas Priest uses a substructural proof calculus, this paper provides a Hilbert proof calculus for it. Using this it is shown that Priest’s consequence relation is weaker than the standard Hilbert consequence relation for B, but strictly stronger than Anderson and Belnap’s original relevant notion of (...) Download 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 Download Export citation Bookmark 1 citation

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