As a new type of epistemic logic, the logic of knowing how essentially captures the high-level epistemic reasoning about the knowledge of various plans to achieve certain goals. Existing work focuses on the axiomatizations of such logics. This paper makes the first study of their model theoretical properties, by introducing suitable notions of bisimulation for a family of five logics of knowing how based on various notions of plans. As an application of these notions of bisimulation, we study and compare the expressive power of these logics.
(A preliminary version of this paper was first presented at SR2017.)
Abstract: A proposition is noncontingent, if it is necessarily true or it is necessarily false. In an epistemic context, ‘a proposition is noncontingent’ means that you know whether the proposition is true. In this paper, we study contingency logic with the noncontingency operator ? but without the necessity operator 2. This logic is not a normal modal logic, because is not valid. Contingency logic cannot define many usual frame properties, and its expressive power is weaker than that of basic modal logic over classes of models without reflexivity. These features make axiomatizing contingency logics nontrivial, especially for the axiomatization over symmetric frames. In this paper, we axiomatize contingency logics over various frame classes using a novel method other than the methods provided in the literature, based on the ‘almost-definability’ schema AD proposed in our previous work. We also present extensions of contingency logic with dynamic operators. Finally, we compare our work to the related work in the fields of contingency logic and ignorance logic, where the two research communities have similar results but are apparently unaware of each other’s work. One goal of our paper is to bridge this gap.