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.
An Introduction to Non-Classical Logic, second edition, by Graham Priest
Exercise sets, one mid term, and one final examination.
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