Logic as a Tool: A Guide to Formal Logical Reasoning
1 Understanding Propositional Logic
1.1 Propositions and logical connectives: truth tables and tautologies
1.2 Propositional logical consequence: logically correct inferences
1.3 Logical equivalence: negation normal form of propositional formulae
1.4 Supplementary: Inductive definitions and structural induction and recursion
2 Deductive Reasoning in Propositional Logic
2.1 Deductive systems: an overview
2.2 Axiomatic systems for propositional logic
2.3 Semantic Tableaux
2.4 Natural Deduction
2.5 Normal forms and Propositional Resolution
2.6 Supplementary: The Boolean satisfiability problem and NP-completeness
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2.7 Supplementary: Completeness of the propositional deductive systems
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3 Understanding First-order Logic
3.1 First-order structures and languages: terms and formulae of first-order logic
3.2 Semantics of first-order logic
3.3 Basic grammar and use of first-order languages
3.4 Logical validity, consequence, and equivalence in first-order logic
3.5 Syllogisms
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4 Deductive Reasoning in First-order Logic
4.1 Axiomatic system for first-order logic
4.2 Semantic Tableaux for first-order logic
4.3 Natural Deduction for first-order logic
4.4 Prenex and clausal normal forms
4.5 Resolution for first-order logic
4.6 Supplementary: Soundness and completeness of the deductive systems for first-order logic
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5 Applications: Mathematical Proofs and Automated Reasoning
5.1 Logical reasoning and mathematical proofs
5.2 Logical reasoning on sets, functions, and relations
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5.3 Mathematical Induction and Peano Arithmetic
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5.4 Applications: automated reasoning and logic programming
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Logic as a tool 