Mathematical Logic

Overview

Contents:
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, Resoltion in FL.

Proof Systems for FL : Axiomatic system FC, Analytic tableau FT, Adequacy of FC and FT, Compactness in FL.
Axiomatic Theories : Undecidabilty of FL, Godel's incompleteness theorems.