NASSLLI18 Course : Beyond "knowing that": a new generation of epistemic logics

Lecturer: Yanjing Wang (王彦晶) Department of Philosophy, 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 natural language 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. Inspired by linguistic discussions on the semantics of questions, the new epistemic modalities introduced in those logics often share, in their formal semantics, the general schema of ‘exists x K phi’ (where K is the knowledge modality). For example, knowing how to achieve phi roughly says 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 course, I will survey the recent developments of this new research program on non-standard epistemic logics of know-wh and its various connections with existing logics and philosophical/AI/linguistic questions in the literature. Inspired by those logics, we will also discuss a very general and powerful framework based on a predicate language extended by new modalities which pack a quantifier and a modality 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. This may also pave a new way to the discovery of new decidable fragments of first-order modal logic.

Check the website of the previous
ESSLLI15 course for an (outdated) preview of the course. Note that we have much much more to tell you now after three fruitful years! We will try to present a balanced view on the technical theory and potential applications of this fascinating new field.

The detailed schedule and reading materials will be announced here.