Karl Nygren

Many traditional semantic theories of conditionals can be seen as determining how to assign propositions to conditional sentences based on the propositions expressed by their antecedents and consequents. As shown by Ciardelli (Semantics and Linguistic Theory (SALT), 26, 732–752, 2016b), such traditional semantic theories of conditionals are naturally lifted to the setting of inquisitive semantics. In the resulting account, antecedents and consequents may be associated with multiple alternative propositions. A conditional sentence is then taken to express that for each alternative for the antecedent, if that alternative were to obtain, then some corresponding alternative for the consequent would also obtain. This paper studies the inquisitive conditional logics that result from applying Ciardelli’s lifting recipe to a Kripke-style semantics for conditional logic that interprets conditionals in terms of relative necessity. The main results of the paper are sound and complete axiomatizations, both for the inquisitive conditional logic over the class of all models, and for various stronger logics obtained by imposing additional semantic conditions. Among the logics considered in the paper are inquisitive versions of conditional logics due to Lewis and Stalnaker.

In recent work, Richard Booth develops a semantics for deontic modals based on inquisitive semantics that validates ‘independence inferences’: from a necessity or possibility modal with an embedded disjunction, one can infer that each disjunct can obtain without any of the other disjuncts obtaining. This paper investigates an extension of propositional inquisitive logic with a modal operator interpreted using Booth’s key semantic construction. The modal operator is used to express that all alternatives for the formula within the scope the operator are independently possible, in the sense that for each alternative, there is an accessible world where that alternative is true, whereas all other alternatives are false. Two versions of the semantics are considered: a local version where the modal operator quantifies over alternatives in submodels generated from the state of evaluation, and a global version where the modal operator quantifies over the alternatives in the full model of evaluation. The main results are sound and strongly complete axiom systems, both with respect to the local version, and with respect to the global version.

This paper develops a deontic logic based on dynamic logic for reasoning about permission and prohibition of sequential actions. Our approach is characterized by two main features. First, permission and prohibition of sequential actions are not necessarily reduced to permission and prohibition of the actions’ constituent parts. Second, we incorporate the idea that actions may be permitted or prohibited conditional on another action being performed first. The logic interprets actions in terms of sequences of states, and the deontic component of the logic is introduced by relating sequences of states to their legal and illegal future continuations. We consider various different logics obtained by imposing natural constraints on models, and formulate complete axiom systems for several of these logics.

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.