MA 209: Logic: classical, modal and intuitionistic
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.
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
First-order modal logics: Kripke frames with constant and varying domains,
tableaus, rigid and flexible designators, non-designating terms,
definite descriptions, ontological arguments.