Logic for Computer Science

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3 STUDENTS

Contents:
Introduction – Propositional Logic Syntax – Semantics of Propositional Logic – Logical and Algebraic Concepts – Identities and Normal forms – Tautology Checking – Propositional Unsatisfiability – Analytic Tableaux – Consistency and Completeness – The Completeness Theorem – Maximally Consistent Sets – Formal Theories – Proof Theory : Hilbert-style – Derived Rules – The Hilbert System : Soundness – The Hilbert System :Completeness – Introduction to Predicate Logic – The Semantic of Predicate Logic – Subsitutions.

Models – Structures and Substructures – First – Order Theories – Predicate Logic: Proof Theory (Contd..) – Existential Quantification – Normal Forms – Skalemization – Substitutions and Instantiations – Unification – Resolution in FOL – More on Resolution in FOL – Resolution : Soundness and Completeness – Resolution and Tableaux – Completeness of Tableaux Method – Completeness of the Hilbert System – First -Order Theories – Towards Logic Programming – Verification of Imperative Programs – Verification of WHILE Programs.

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