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Language, Proof and Logic

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

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