We introduce a natural sequent calculus for preferential conditional logic PCL via embeddings into provability logic GL, achieving optimal complexity and enabling countermodel extraction. Extending the method to PCL with reflexivity and absoluteness – corresponding to Åqvist’s deontic system F with cautious monotony – we employ hypersequents to capture the S5 modality; the resulting calculus subsumes the known calculi for the weaker systems E and F within Åqvist family.

We propose a logic-based formalization of deontic explanations, which aim to address questions about obligations and permissions such as “Why does this norm apply?” or “Why should I perform A rather than B?”. Our framework is designed to be flexible, accommodating various deontic logics. In this work, we build on Åqvist’s dyadic deontic logics, extending them by introducing an obligation operator that supports Factual Detachment along with mechanisms for non-monotonic reasoning. Applying our framework to legal examples, we demonstrate its effectiveness in explaining normative statements while also identifying its limitations.

The traditional definition of permission as the dual of obligation oversimplifies its many applications, often yielding undesirable consequences. Recent literature recognizes the need to distinguish various types of permissions but often overlooks potential preferences associated with them. In contrast, the Sanskrit philosophical school of Mīmāṃsā refutes the interdefinability of deontic concepts, and asserts that permissions always refer to less desirable actions (‘better-not’ permissions), and are exceptions to prohibitions or negative obligations. This article analyzes the concept of Mīmāṃsā permission, compares it with contemporary theories and formalizes it while carefully preserving its essential characteristics. We transform Mīmāṃsā’s reasoning principles for permission into Hilbert axioms and introduce neighbourhood semantics, incorporating ceteris-paribus preferences. The resulting logic is evaluated against various paradoxes from contemporary deontic logic and applied to a scenario from Sanskrit jurisprudence.

The theme of extensionality in first-order deontic logic has been thoroughly studied in the past, but not in the context of a combination of different types of modalities. An operator is extensional if it allows substitution salva veritate of co-referential terms within its scope and intensional if it does not. It can be argued that one distinctive feature of “ought” (as opposed to the other modalities) is that it is extensional. The question naturally arises as to whether it is possible to combine extensionality and intensionality of different modal operators in the same semantics without creating the deontic collapse. We answer this question within a particular framework, Åqvist’s system F for conditional obligation. We develop in full detail a perspectival account of obligation (and related notions), as was done for Standard Deontic Logic (SDL) by Goble. It is called “perspectival”, because one always evaluates the content of an obligation in one world from the perspective of another one. This requires using some form of cross-world evaluation to handle non-rigid terms like definite descriptions. The proposed framework allows for a more nuanced way of approaching first-order deontic principles.