A New Modal Framework for Epistemic Logic
This work provides a foundational framework for epistemic logic researchers, enabling the study of diverse knowledge modalities in a unified way, though it is incremental as it builds on existing logics.
The authors tackled the challenge of unifying various non-standard epistemic logics (e.g., knowing whether, how, what, why) by proposing a general modal framework based on a new modality that encapsulates the shared semantic schema of ∃x□φ, and they showed that this more expressive language retains desirable properties like decidability and axiomatization over S5 frames.
Recent years witnessed a growing interest in non-standard epistemic logics of knowing whether, knowing how, knowing what, knowing why and so on. The new epistemic modalities introduced in those logics all share, in their semantics, the general schema of $\exists x \Box φ$, e.g., knowing how to achieve $φ$ roughly means that there exists a way such that you know that it is a way to ensure that $φ$. Moreover, the resulting logics are decidable. Inspired by those particular logics, in this work, we propose a very general and powerful framework based on quantifier-free predicate language extended by a new modality $\Box^x$, which packs exactly $\exists x \Box$ together. We show that the resulting language, though much more expressive, shares many good properties of the basic propositional modal logic over arbitrary models, such as finite-tree-model property and van Benthem-like characterization w.r.t.\ first-order modal logic. We axiomatize the logic over S5 frames with intuitive axioms to capture the interaction between $\Box^x$ and know-that operator in an epistemic setting.