SE 354. Mathematical Logic
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Formal theories, consequence and deduction. Classical Propositional Calculus: Syntax, truth, validity, Adequacy of connectives, normal forms, applications to circuit design, Axiomatic treatment, deduction theorem, derived rules of inference, Soundness, Independence of axioms, Consistency, completeness, Completeness w.r.t. Boolean algebras, Computer-assisted formal proofs: tableaux, resolution. Classical first order theories: Syntax, satisfaction, truth validity, Axiomatic treatment, Equality, Examples of first-order theories : Peano arithmetic, Groups, Orderings, Basis of axiomatic set theory, Deduction theorem, derived rules of inference, soundness, Consistency, completeness, Lowenheim-Skolem theorems, compactness, First-order theories with equality, Decidability, Computer-assisted formal proofs: tableaux, resolution. Godel's incompleteness theorems. Examples of other/non-classical logics. Other proof techniques - natural deduction, sequent calculus.
- REFERENCES:
- J. Kelly, The essence of logic, Prentice-Hall 1997.
- H.D. Ebbinghaus, T. Flum and W. Thomas, Mathematical logic, Springer 1994.
- E. Mendelson, Introduction to mathematical logic, Van Nostrand 1979.
- A. Margaris, First order mathematical logic, Blaisdell 1967.
- J.R. Shoenfield, Mathematical logic, Addison-Wesley 1967.
- Concerned Department: Mathematics