Actual Issues for Relevant Logics

Abstract

In this paper, I motivate the addition of an actuality operator to relevant logics. Straightforward ways of doing this are in tension with standard motivations for relevant logics, but I show how to add the operator in a way that permits one to maintain the intuitions behind relevant logics. I close by exploring some of the philosophical consequences of the addition. 1. See Dunn and Restall (2002) or Bimbó (2006) for reader-friendly overviews of relevant logics. 2. How to understand the connection at issue is a delicate matter. Anderson and Belnap (1975) suggest a kind of connection based on use. An alternative conception is the sufficiency view of Routley (1977: 895ff.). A different approach to relevance is offered by Tennant (2017).

The Logic of Sequence Frames

“…So, in case there is a translation, it has to be modified accordingly, for the procedure described by Antonelli and Thomason does not seem to generalize for (or ) with propositional quantification. Still, is there any recursive translation with full second-order logic, such as in Antonelli and Thomason’s case, that shows second-order and hence ( ) to be undecidable? Even though the validity problem for n -dimensional sequence modal logics was shown to be decidable, what is its complexity? Is the sequence modal logic of -dimensions complete or decidable? Standefer (forthcoming) investigates relevant logics with the actuality operator. It would be interesting to see the relevant counterparts of multidimensional modal logics with, possibly, many actuality operators. …”

“…Standefer (forthcoming) investigates relevant logics with the actuality operator. It would be interesting to see the relevant counterparts of multidimensional modal logics with, possibly, many actuality operators.…”

The Logic of Hyperlogic. Part A: Foundations

“…For example, Braüner & de Paiva [12] observe that there are multiple ways to develop intuitionistic hybrid logic. Standefer [57] makes a similar observation about relevant logic. In fact, Standefer observes that the “naïve” way of adding an “actually” operator (a close relative of hybrid operators) to Routley–Meyer semantics for relevant logic results in violations of relevance; e.g., it would validate , which “flagrantly violates relevance intuitions” (p. 254).…”