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.

This paper investigates and develops generalizations of two-dimensional modal logics to any finite dimension. These logics are natural extensions of multidimensional systems known from the literature on logics for a priori knowledge. We prove a completeness theorem for propositional n-dimensional modal logics and show them to be decidable by means of a systematic tableau construction.

Our concern here is with the extent to which the expressive equivalence of Wehmeier’s Subjunctive Modal Language and the Actuality Modal Language is sensitive to the choice of background modal logic. In particular we will show that, when we are enriching quantified modal logics weaker than S5, AML is strictly expressively stronger than SML, this result following from general considerations regarding the relationship between operators and predicate markers. This would seem to complicate arguments given in favour of SML which rely (...) upon its being expressively equivalent to AML. (shrink)

We investigate and compare two major approaches to enhancing the expressive capacities of modal languages, namely the addition of subjunctive markers on the one hand, and the addition of scope-bearing actuality operators, on the other. It turns out that the subjunctive marker approach is not only every bit as versatile as the actuality operator approach, but that it in fact outperforms its rival in the context of cross-world predication.