Contingency and knowing whether

Review of Symbolic Logic 8 (1):75-107 (2015)

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.

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Citations of this work

A Logic of Goal-Directed Knowing How.Yanjing Wang - 2018 - Synthese 195 (10):4419-4439.
Bimodal Logics with Contingency and Accident.Jie Fan - 2019 - Journal of Philosophical Logic 48 (2):425-445.
A Family of Neighborhood Contingency Logics.Jie Fan - 2019 - Notre Dame Journal of Formal Logic 60 (4):683-699.
A Modal Logic of Supervenience.Jie Fan - 2019 - Notre Dame Journal of Formal Logic 60 (2):283-309.

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