Review of topics covered before the midterm exam Sections 1.1-1.4 [Mendelson] propositional connectives, truth tables, tautologies, logical implication or consequence, substitution, propositions as descriptions of truth functions, Axiom systems, well-formed formulas, proofs, theorems, decidable, Modus Ponens, Deduction theorem, soundness (every theorem is a tautology), completeness (every tautology is a theorem) Section 2.1-2.8 [Mendelson] quantifiers, free, bound variables, free for x in B, first-order language, interpretation, model, soundness, completeness for first-order logic, satisfiability, first-order theories, logical axioms, proper axioms, rules of inference. Generalization, Natural Deduction rules (see slides set ln6.pdf), proofs of soundness, completeness, consistent, deduction theorem, Equivalence theorem, replacement theorem, rule C (EI), closed form, complete theories, Lindenbaum's Lemma (complete extensions of consistent theories), scapegoat theories, Godel's completeness theorem, Skolem-Lowenheim theorem (denumerable models), theories with equality, testing whether a theory is a theory with equality, normal models, quantified quantifiers ("there exist exactly n entities such that ...", logical validity, logical inference, |=, |-