According to the balancing view of obligation, one ought to do something iff doing so is favoured by the balance of reasons, i.e., iff one’s reasons for doing it outweigh one’s reason for not doing it. According to standard views in deontic logic, what one ought to do is governed by substantive logical rules. Combining such a view with the balancing view then allows us to derive broadly logical principles governing the balance of reasons for logically related actions. Such principles, however, cry out for explanation in terms of corresponding principles governing individual reasons, their weights, and the ways they combine. A pressing question therefore emerges for proponents of the balancing view: Is there a plausible set of such principles which generates a plausible logic of obligation? My talk addresses the special case of that question which targets so-called standard deontic logic and argues for an optimistic conclusion: I identify a set of natural, though not uncontroversial principles governing reasons that generates, via the balancing view, an essentially standard deontic logic. I go on to briefly consider possible variations on the principles and discuss their relation to similar principles that have been proposed in the literature.

The idea that impossibilities have a role to play in a semantic analysis of validity is becoming widely accepted on various grounds, including grounds of relevance. I argue that this is a mistake, that it has led to various foundational objections to relevance logic, and that these objections are avoidable given a semantics that clearly distinguishes two types of conditional or inferential fallacies, namely, those concerning truth preservation from those concerning a relation between content or subject matter. I argue that we should avoid the use of impossibilities employed in the standard Kripke semantics for relevance logic in favor of a coarse-grained notion of content, and argue for the benefits of such an approach. Since this discussion generalizes to more than relevance logic, I discuss the the role that impossibilities might have to play more generally in logical analysis.

In previous publications, it was shown that finite non-deterministic matrices are quite powerful in providing semantics for a large class of normal and non-normal modal logics. However, some modal logics, such as those whose axiom systems contained the Löb axiom or the McKinsey formula, were not be analyzed via non-deterministic semantics. Furthermore, other modal rules than the rule of necessitation were not yet characterized in the framework.

In this presentation, we will overcome this shortcoming and present a novel approach for constructing semantics for normal and non-normal modal logics that is based on restricted non-deterministic matrices. This approach not only offers a uniform semantical framework for modal logics, while keeping the meaning of the involved modal operators the same, and thus making different systems of modal logic comparable. It might also lead to a new understanding of the concept of modality.