Room 327

Beyond "knowing that": A new framework for epistemic logic

Yanjing Wang

Peking University

Epistemic logic is a major field of philosophical logic studying reasoning patterns about knowledge. Despite its various applications in
epistemology, theoretical computer science, AI, and game theory, the technical developments in the field have been mainly focusing on the
propositional part, i.e., the propositional modal logics of "knowing that". However, knowledge is also expressed in everyday life by "knowing whether", "knowing what", "knowing how", "knowing why" and so on (know-wh hereafter).
Recent years witnessed a growing interest in non-standard epistemic logics
of know-wh motivated by questions in philosophy, AI and linguistics. The new epistemic modalities introduced in those logics all share, in their
semantics, the general schema of ‘exists x [] phi’ (where [] is a box-modality), e.g., knowing how to achieve phi roughly means that there
exists a way such that you know that it is a way to make sure that phi. The axioms of those logics intuitively capture the essential interactions of
know-that and other know-wh operators, and the resulting logics are decidable.

In this talk, I will first briefly explain the core ideas behind this new research program, and then propose a very general and powerful framework based on a predicate language extended by a new modality which packs exactly ‘exists x []’ together. We show that the resulting logic, though
more expressive, shares many good properties of the basic propositional modal logic, such as the finite-tree-model property and van Benthem-like
characterization w.r.t. first-order modal logic. This will also pave a new way to the discovery of new decidable fragments of first-order modal logic.

The talk is mainly based on the following papers:

Yanjing Wang: Beyond knowing that: a new generation of epistemic logics, to
appear in the Hintikka volume of Outstanding Contributions to Logic, Springer (arxiv.org/abs/1605.01995)

Yanjing Wang: A new modal framework for epistemic logic in Proceedings of 16th conference on Theoretical Aspects of Rationality and Knowledge (TARK2017) (arxiv.org/abs/1707.08764)