Mathematical Logic. Instructor: Prof. Arindama Singh, Department of Mathematics, IIT Madras. Propositional Logic: Syntax, Unique parsing, Semantics, Equivalences, Consequences, Calculations, Informal proofs. Normal Forms and Resolution: Clauses, CNF and DNF representations, Adequacy of calculations, SAT, Resolution refutation, Adequacy of resolution. Proof Systems: Axiomatic system PC, Adequacy of PC, Analytic tableau PT, Adequacy of PT, Compactness of PL. First Order Logic: Syntax of FL, Scope and binding, Substitutions, Semantics of FL, Quantifier laws, Equivalences, Consequences. Normal Forms in FL: Calculations, Informal proofs, Prenex forms, Skolem forms, Herbrand's Theorem, Skolem-Lowenheim theorem, Resolution in FL. Proof Systems for FL: Axiomatic system FC, Analytic tableau FT, Adequacy of FC and FT, Compactness in FL. Axiomatic Theories: Undecidability of FL, Godel's incompleteness theorems. (from nptel.ac.in)
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Instructor: Prof. Arindama Singh, Department of Mathematics, IIT Madras. Propositional logic, normal forms and resolution, proof systems, first order logic, normal forms in first order logic, proof systems for first order logic, axiomatic theories.