MA 209: Logic: classical, modal and intuitionistic
Credits: 3:0
Pre-requisites :
- No prior knowledge of logic is assumed.
- Background in reading and doing mathematical proofs will be assumed.
This course is an introduction to standard material in logic, based on classical first-order logic, after which it ventures into modern treatments of some non-classical logics. Although other proof methods will be discussed, the emphasis will be on proofs using tableaus.
Topics:
- First-order logic: First-order languages, deduction and truth, models, Smullyan-style tableaus, completeness and compactness theorems.
- Modal logics: Kripke frames, characterization of frame conditions, tableaus, completeness, finite model property, decision procedures for validity.
- First-order modal logics: Kripke frames with constant and varying domains, tableaus, rigid and flexible designators, non-designating terms, definite descriptions, ontological arguments.
- Intuitionistic logic: Kripke frames, tableaus, completeness.
Suggested books and references:
- I. Chiswell and W. Hodges, Mathematical logic, Oxford Univ Press, 2007.
- M.C. Fitting, First-order logic and automated theorem proving, Springer, 2nd edition, 1996.
- M.C. Fitting, Proof methods for modal and intuitionistic logics, Reidel, 1983.
- M.C. Fitting and R. Mendelsohn, First-order modal logic, Kluwer, 1998.