Dynamic extensions for the logic of knowing why with public announcements of formulas

TL;DR

This paper extends the non-standard epistemic logic of knowing why with dynamic public announcements, analyzing two variants and their expressivity, and discusses challenges in proving completeness for these logics.

Contribution

It introduces dynamic extensions of the logic of knowing why with public announcements and examines their axiomatization and expressivity properties.

Findings

Two variants of public announcement extensions are considered.

The logic's expressivity is compared among different extensions.

Challenges in proving completeness via translation are identified.

Abstract

In this paper, we address the logic of knowing why, an example of a non-standard epistemic logic dealing with justified knowledge via a new epistemic operator, under the extensions with ideas from dynamic epistemic logic, namely public announcements. Through the additional notions present in the knowing why context, we consider two possible variants, namely the extensions by (i): public announcements of a formula and by (ii): public announcements of reasons, although the deeper analysis of the latter is left for future work. We consider another logical operator, the conditional knowing-why operator, for which we study the applications to the axiomatization of public announcements as well as the solely framework. At the end, we consider the logical expressivity of these different logics in comparison to each other, and thus we show one of the main problems with the usual process of proving completeness through translation in the context of logics with public announcements.