Karl Nygren

In this thesis, I develop and investigate various novel semantic frameworks for deontic logic. Deontic logic concerns the logical aspects of normative reasoning. In particular, it concerns reasoning about what is required, allowed and forbidden. I focus on two main issues: free-choice reasoning and the role of norms in deontic logic. Free-choice reasoning concerns permissions and obligations that offer choices between different actions. Such permissions and obligations are typically expressed by a disjunctive clause in the scope of a deontic operator. For instance, the sentence "Jane may take an apple or a pear" intuitively offers Jane a choice between two permitted courses of action: she may take an apple, and she may take a pear. In the first part of the thesis, I develop semantic frameworks for deontic logic that account for free-choice reasoning. I show that the resulting logics avoid problems that arise for other logical accounts of free-choice reasoning. The main technical contributions are completeness results for axiomatizations of the different logics. Semantic frameworks for deontic logic typically only talk about norms implicitly. In the second part of the thesis, I clarify the role of norms in deontic logic. I develop a formal model of normative systems where norms are represented explicitly. The model takes into account both the hierarchical structure of normative systems, and the function of norms to regulate agent behavior. I show how the model can be used to clarify issues in the study of normative systems. I also develop a norm-based semantics for deontic action logic based on the model.

This paper investigates inquisitive extensions of normal modal logic with an existential modal operator taken as primitive. The semantics of the existential modality is generalized to apply to questions, as well as statements. When the generalized existential modality is applied to a question, the result is a statement that roughly expresses that each way of resolving the question is consistent with the available information. I study the resulting logic both from a semantic and from a proof-theoretic point of view. I argue that it can be used for reasoning about a general notion of ignorance, and for reasoning about choice-offering permissions and obligations. The main technical results are sound and complete axiomatizations, both for the class of all Kripke frames, and for any class of frames corresponding to a canonical normal modal logic.

This paper introduces deontic logic based on inquisitive semantics. A semantics for action formulas is introduced where each action formula is associated with a set of alternatives. Deontic operators are then interpreted as quantifying over all alternatives associated with the action formulas within their scope. It is shown how this construction provides solutions to problems related to free choice permissions and obligations, including issues concerning Hurford disjunctions. The main technical result is a complete axiomatization of the logic.

Conflicts between legal norms are common in reality. In many legislations, legal conflicts between norms are resolved by applying ordered principles. This work presents a formalization of the conflict resolution mechanism and introduces action legal logic (⁠ALL) to reason about the normative consequences of possibly conflicting legal systems. The semantics of ALL is explicitly based on legal systems consisting of norms and ordered principles. Legal systems specify the legal status of transitions in transition systems and the language of ALL describes the legal status of paths in transition systems. The formalization is used to study abstract revisions of legal systems. The expressivity of ALL is studied and its completeness is proved.

The semantics for a deontic action logic based on Boolean algebra is extended with an interpretation of action expressions in terms of sets of alternative actions, intended as a way to model choice. This results in a non-classical interpretation of action expressions, while sentences not in the scope of deontic operators are kept classical. A deontic structure based on Simons’ supercover semantics is used to interpret permission and obligation. It is argued that these constructions provide ways to handle various problems related to free choice permission. The main result is a sound and complete axiomatization of the semantics.