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Mathematical Induction:Inductive definitions and inductive proofs, Proving programs correct

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Advanced Topics in Propositional Logic:Completeness for propositional logic, Horn sentences >>



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Table of Contents:
  1. Atomic Sentences:Individual constants, Predicate symbols, General ¯rst-order languages
  2. The Logic of Atomic Sentences:Valid and sound arguments, Methods of proof
  3. The Boolean Connectives:Negation symbol, Conjunction symbol, Remarks about the game
  4. The Logic of Boolean Connectives:Tautologies and logical truth, Logical and tautological equivalence
  5. Methods of Proof for Boolean Logic:Valid inference steps, Proof by cases
  6. Formal Proofs and Boolean Logic:Conjunction rules, Negation rules, Strategy and tactics
  7. Conditionals:Material conditional symbol, Conversational implicature, Alternative notation
  8. The Logic of Conditionals:Informal methods of proof, Soundness and completeness, Valid arguments: some review exercises
  9. Introduction to Quantification:Variables and atomic w®s, W®s and sentences
  10. The Logic of Quantifiers:First-order validity and consequence, Other quanti¯er equivalences
  11. Multiple Quantifiers:Multiple uses of a single quantifier, Ambiguity and context sensitivity
  12. Methods of Proof for Quantifiers:The method of existential instantiation, Axiomatizing shape
  13. Formal Proofs and Quantifiers:Universal quantifier rules, Soundness and completeness
  14. More about Quantification:Proving numerical claims, Adding other determiners to fol
  15. First-order Set Theory:Singletons, the empty set, subsets, Intersection and union
  16. Mathematical Induction:Inductive definitions and inductive proofs, Proving programs correct
  17. Advanced Topics in Propositional Logic:Completeness for propositional logic, Horn sentences
  18. Advanced Topics in FOL:Truth and satisfaction, revisited, Uni¯cation of terms
  19. Completeness and Incompleteness:Adding witnessing constants, The Henkin Construction
  20. Summary of Formal Proof Rules:Propositional rules, First-order rules, Inference Procedures
  21. Glossary:Ambiguity, Antecedent, Argument, Arity, Atomic sentences, Axiom
  22. General Index
  23. Exercise Files Index