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  1. Variable-Sharing as Relevance.Shawn Standefer - 2024 - In Andrew Tedder, Shawn Standefer & Igor Sedlar (eds.), New Directions in Relevant Logic. Springer.
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  • Confused Entailment.Tore Fjetland Øgaard - 2021 - Topoi 41 (1):207-219.
    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 (...)
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  • Non-Boolean classical relevant logics II: Classicality through truth-constants.Tore Fjetland Øgaard - 2021 - Synthese (3-4):1-33.
    This paper gives an account of Anderson and Belnap’s selection criteria for an adequate theory of entailment. The criteria are grouped into three categories: criteria pertaining to modality, those pertaining to relevance, and those related to expressive strength. The leitmotif of both this paper and its prequel is the relevant legitimacy of disjunctive syllogism. Relevant logics are commonly held to be paraconsistent logics. It is shown in this paper, however, that both E and R can be extended to explosive logics (...)
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  • Boolean negation and non-conservativity III: the Ackermann constant.Tore Fjetland Øgaard - 2021 - Logic Journal of the IGPL 29 (3):370-384.
    It is known that many relevant logics can be conservatively extended by the truth constant known as the Ackermann constant. It is also known that many relevant logics can be conservatively extended by Boolean negation. This essay, however, shows that a range of relevant logics with the Ackermann constant cannot be conservatively extended by a Boolean negation.
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  • Boolean negation and non-conservativity I: Relevant modal logics.Tore Fjetland Øgaard - 2021 - Logic Journal of the IGPL 29 (3):340-362.
    Many relevant logics can be conservatively extended by Boolean negation. Mares showed, however, that E is a notable exception. Mares’ proof is by and large a rather involved model-theoretic one. This paper presents a much easier proof-theoretic proof which not only covers E but also generalizes so as to also cover relevant logics with a primitive modal operator added. It is shown that from even very weak relevant logics augmented by a weak K-ish modal operator, and up to the strong (...)
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  • Farewell to Suppression-Freedom.Tore Fjetland Øgaard - 2020 - Logica Universalis 14 (3):297-330.
    Val Plumwood and Richard Sylvan argued from their joint paper The Semantics of First Degree Entailment and onward that the variable sharing property is but a mere consequence of a good entailment relation, indeed they viewed it as a mere negative test of adequacy of such a relation, the property itself being a rather philosophically barren concept. Such a relation is rather to be analyzed as a sufficiency relation free of any form of premise suppression. Suppression of premises, therefore, gained (...)
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  • Substitution in relevant logics.Tore Fjetland Øgaard - 2019 - Review of Symbolic Logic (3):1-26.
    This essay discusses rules and semantic clauses relating to Substitution—Leibniz’s law in the conjunctive-implicational form s=t ∧ A(s) → A(t)—as these are put forward in Priest’s books "In Contradiction" and "An Introduction to Non-Classical Logic: From If to Is." The stated rules and clauses are shown to be too weak in some cases and too strong in others. New ones are presented and shown to be correct. Justification for the various rules are probed and it is argued that Substitution ought (...)
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