What is a Relevant Connective?

Relevance through topical unconnectedness

“…Since RM satisfies (QVSP) and neither p nor ∼p are logical theorems, it follows that both p → A and A → p fail to be theorems of RM. It follows then, that RM does not have ubiquitous formulas in the sense of [26] which we looked at in sect. 3-in the Routley-Meyer semantics for the logic there is for every formula A a model in which A holds true at some point, and a model in which A fails to hold true at some point since for every formula A.…”

“…Even though Ackermann's idea hasn't directly been discussed before, the issue of how weakening thwarts relevance has. For instance, in Standefer's recent discussion of what is to count as a properly relevant propositional connective, [26] appeals to so-called ubiquitously true/false formulas. A formula is defined to be ubiquitously true (false) relative to a Routley-Meyer model just in case it is true (false) in every point/world in the model.…”

The Liberation Argument for Inconsistent Mathematics

“…A ∧ ¬A → B and A → (B ∨ ¬B). Stronger conditions can be imposed to avoid other intuitively irrelevant classical laws, although there is little agreement among relevant logicians on which -if any -should be the correct one [Sta22].…”

Routes to relevance: Philosophies of relevant logics

“…"3 There are other connectives commonly considered in the context of relevant logics, such as intensional disjunction, aka fission, þ, omitted for lack of space. For further discussion of options for relevant conenctives, seeStandefer (2022).4 For some discussion of relevant logics in the context of consequence relations, seeAvron (2014),Øgaard (2022), orBadia et al (2022). 5 I use "principle" here as a neutral term for both axioms and rules.6 These both lead to the first implicational paradox, given that (A ∧ B) → A is a logical truth.…”

“…3 3 There are other connectives commonly considered in the context of relevant logics, such as intensional disjunction, aka fission, +, omitted for lack of space. For further discussion of options for relevant conenctives, see Standefer (2022). …”