Realizing impossibilities

Abstract

It is common in epistemic modal logic to model the epistemic states of agents via box operators in the normal logic S5. However, this approach treats agents as logically omniscient by requiring their knowledge to be closed under classical logical consequence. A promising way of avoiding logical omniscience consists in extending epistemic models with impossible states, that is states, where complex formulas are not evaluated recursively. However, this approach faces the dual problem of logical ignorance by modeling agents as not even minimally logically competent. In this paper I will outline an epistemic logic that combines impossible states with dynamic realization modalities akin to the dynamic announcement operators from public announcement logic (PAL). I will show that this epistemic logic avoids both the problem of logical omniscience and the problem of logical ignorance. Furthermore, I prove that so-called successful updates in my logic can be characterized in the same way as in PAL and that a similar logic due to Johan van Benthem can be simulated in my logic. Finally, I will compare my epistemic logic with a similar one, which has recently been advanced by JC Bjerring and Mattias Skipper.