Beyond knowing that: a new generation of epistemic logics

Yanjing Wang
Peking University


ABSTRACT:
Epistemic logic is a major field of philosophical logic studying reasoning patterns about knowledge and belief. 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 new epistemic logics of know-wh motivated by questions in philosophy, AI and linguistics. The new epistemic modalities introduced in those logics usually 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. Therefore they are natural fragments of first-order modal logic. The new axioms of those logics intuitively capture the essential interactions of know-that and other know-wh operators, and the resulting logics are non-normal but decidable.

In this talk, I will first explain the core ideas behind this new research program with some examples, and then propose a more general framework inspired by the concrete know-wh logics, which leads to the discovery of new decidable fragments of first-order modal logic.