Topics in Logic

A Journey through Epistemic Logic

Epistemic logic is currently considered one of the best general formal ap- proaches to the study of the structure of knowledge, its static and dynamic aspects, its limits and possibilities. At the beginning of this century we have witnessed an impressive revival of interest in this field, related both to the ex- ploration of new formal tools for studying the epistemic attitudes of ideal and ordinary agents and to the application of these tools to classical epistemological problems. The present course aims to provide a general introduction to the ba- sic concepts in the intersection between epistemology and epistemic logic and to develop systems of logic where these concepts are studied both from a semantic and from an axiomatic point of view. We will start with reviewing a standard possible world semantics for knowledge and justification. Then, we will go on by highlighting the limits of this kind of semantics for modeling the way in which ordinary agents argue based on what they know. Finally, we will consider how these limits can be overcome by refining the our initial semantic apparatus. In doing this we will constantly refer to some basic issues in epistemology, such as the problem of providing a correct definition of knowledge, the problem of avoiding logical omniscience, and the problem of solving the knowability para- dox, so as to check whether the systems we propose are acceptable. This will lead us to study a rich family of modal systems and to become familiar with a wide range of tools and techniques in intensional and hyperintentional logic.

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