## ADVANCED LOGIC: MODAL AND NON-CLASSICAL LOGICS

In a first logic course, one learns about two kinds of logic: propositional logic (sometimes called sentential logic) and first-order logic (sometimes called predicate or quantifier logic). These kinds of logic provide models for reasoning, and they are used to represent philosophical arguments. Specifically, these logics model reasoning about things that are true or false. But many philosophical arguments go beyond questions of what is true and what is false. Often one must reason about, for example, what is possible or what is necessary. Modal logic provides the framework required to model reasoning with these concepts. Furthermore, there are reasons to think that some sentences are neither true nor false, or both true and false. Non-classical logic provides the framework required to model reasoning in these situations.

Course Text:

An Introduction to Non-Classical Logic, second edition, by Graham Priest

Assessment:

Exercise sets, one mid term, and one final examination.

Course Schedule:

Week 1: Review of classical propositional logic, tableaux methods

Week 2: Introduction to modal logic

Week 3: Translations from English to the language of propositional modal logic

Week 4: Absolute modality

Week 5: Relative modality: System K

Week 6: Systems T, D, B

Week 7: Systems S4, S5

Week 8: Intuitionistic Logic

Week 9: Non-classical propositional logic: K3

Week 10: Non-classical propositional logic: FDE

Week 11: First-order modal logic: constant domains

Week 12: First-order modal logic: variable domains