Alternative Semantics for Normative Reasoning with an Application to Regret and Responsibility

We provide a fine-grained analysis of notions of regret and responsibility (such as agent-regret and individual responsibility) in terms of a language of multimodal logic. This language undergoes a detailed semantic analysis via two sorts of models: (i) relating models, which are equipped with a relation of propositional pertinence, and (ii) synonymy models, which are equipped with a relation of propositional synonymy. We specify a class of strictly relating models and show that each synonymy model can be transformed into an equivalent strictly relating model. Moreover, we define an axiomatic system that captures the notion of validity in the class of all strictly relating models.