Preface

Modal logic extends the language of propositional and quantificational logic with a sentential operator for necessity. This course will cover basic elements of propositional and quantified modal logic and selected philosophical applications, which may include the logic of belief and knowledge, provability logic, tense logic, and the logic of preference and obligation.

The semester will be divided into four main parts:

  1. The Metatheory of Propositional Logic

    We will look at an axiomatic presentation of propositional logic for which we prove a completeness theorem.

  2. Propositional Modal Logic

    We will focus on normal systems of propositional modal logic, completeness and decidability.

  3. Applications of Propositional Modal Logic

    We will discuss selected applications of modal logic and the possible worlds model theory in philosophy. They may include the logic of belief and knowledge, deontic logic, and the logic of conditionals.

  4. Quantified Modal Logic

    We cover the de re and de dicto distinction; different approaches to quantified modal logic and the question of whether existence is ever contingent.