Abstract We introduce classical term-modal logics and argue that they are useful for modelling agent-relative notions of obligation, evidence and abilities, and their interaction with properties of and relations between the agents in question. We spell out the semantics of these logics in terms of neighborhood models, provide sound and strongly complete axiomatizations and establish the decidability of specific (agent-finite) variants.

Cariani (Ought and resolution semantics) has proposed a semantics for ought that combines two features: (i) it invalidates Inheritance, i.e. the inference from ought|$(\varphi )$| to ought|$(\psi )$| whenever |$\psi $| is logically weaker than |$\varphi $|⁠, and it does so in a principled manner; (ii) it allows for coarseness, which means that ought|$(\varphi )$| can be true even if there are specific ways of making |$\varphi $| true that are (intuitively speaking) impermissible.we present a family of multi-modal logics based on Cariani’s proposal and a more recent criticism by Bronfmann and Dowell (2018, Oxford Handbook of Reasons). We study the formal properties of these logics in detail and show how they can be translated into normal multi-modal logics. Using well-known techniques, we establish a sound and (strongly) complete axiomatisation for each of these and show them to satisfy the finite model property. In addition, we compare them to existing approaches in the deontic logic literature—most notably Anglberger et al.’s logic of obligation as weakest permission and Horty’s deontic STIT logic.

The standard format of adaptive logics makes use of two so-called strategies: reliability and minimal abnormality.While these are fairly well-known and frequently applied, the question of whether and when the two strategies are equi-epressive has so far remained unaddressed.In this paper, we show that for a specific, yet significant class of premise sets, the consequence set of an adaptive logic that uses the minimal abnormality strategy can be expressed by another adaptive logic that uses the reliability strategy.The basic idea is that we close the set of abnormalities under conjunction.We show that the consequence sets obtained by both logics from a premise set Γ is identical if and only if Γ is finite-conditional.The latter property is specified in terms of a well-known characterization of minimal abnormality.In addition, we discuss other (stronger) properties of premise sets that have been considered in the literature, showing each of them to imply finite-conditionality.

This article discusses Parikh's axiom of relevance in belief revision, and recalls some results from Kourousias and Makinson (2007, J. Symbolic Logic, 72, 994–1002) in this context. The crucial distinction is emphasized between the uniqueness of the finest splitting of K and the fact that K has several normal forms associated with that finest splitting. The main new result of this article is a new proof for the theorem that the set of prime implicates of K is a normal form for the finest splitting of K. It is explained how this proof avoids a mistake in an earlier proof from Wu and Zhang (2010, Knowledge-Based Syst., 23, 70–76). As a corollary, relevance can be re-defined without reference to the finest splitting, using the notion of path-relevance from Makinson (2009, J. Appl. Logic, 7, 377–387). Finally, a weak yet sufficient condition for irrelevance is presented.

In this article we present the logic MP⊏ that explicates reasoning on the basis of prioritized obligations. Although formal criteria to handle prioritized obligations have been formulated in the literature, little attention has been paid to the actual (non-monotonic) reasoning that makes use of these criteria. The dynamic proof theory of MP⊏ fills this lacuna. This article focuses on premise sets consisting of possibly conflicting prima facie obligations that have a modular order. MP⊏ allows to derive—inter alia—the actual, all-things-considered obligations from such premise sets. It is defined in the format of lexicographic adaptive logics from [34], whence a rich meta-theory is immediately available (e.g. soundness and completeness, idempotence, reflexivity, etc.). In addition, we establish some meta-theoretic results that are specific to the context of prioritized obligations. With the aid of concrete examples, we illustrate properties of MP⊏ which improve on other existing criteria for prioritized obligations.