Course Description: Classical logic was developed to formalize the reasoning used by (most) mathematicians. It is very good at this, but it is not a satisfactory fit with most of the other kinds of reasoning we do. To take its place a very large number of non-classical logics have been created, primarily by philosophical logicians and by logicians in computer science. This course will study the main examples of such logics. We will confine things to the propositional level since, generally, adding quantification is less traumatic than one might think.
We will study modal logics, tense logics, intuitionistic logic, relevance logics, first degree entailment, substructural logics, conditional logics, many-valued logics, fuzzy logics. Non-classical logics generally fall into families whose members have significant resemblances to each other. Modal logics are such a family. Intuitionistic logic is a single item but it, along with several other items in the list fall into the family of substructural logics. All this will be sorted out as we proceed. Non-classical logics constitute a rich and complex realm, and we must concentrate on a relatively small number of most significant examples.
For each logic we need a formal language, a semantics, and a proof procedure. And of course we need some informal motivation for considering this particular logic. In general, semantics and proof procedures will be plural. There often are more than one semantics for a given logic, and more than one proof procedure. Among the proof procedures we will favor tableaus, but other kinds will be mentioned. And it should also be mentioned that tableaus themselves are a multiplicity‹a variety of kinds exists.
There will be no official textbook for the course, but the book An Introduction to Non-Classical Logic, by Graham Priest is strongly recommended. Most of what we cover can be found there. The book exists in a first and a second edition. They differ primarily in that the second edition covers quantification. Since we will not be discussing this, if you already have the first edition, this should be fine.