Table of Contents
Introduction to Formal Logic
Introduction to Formal Logic
I. Propositional Logic
1. Formulas
1.1. Definition
1.2. Object language and metalanguage
1.3. Notations
2. Models
2.1. Two element Boolean algebra
2.2. Definition
2.3. Satisfiability and validity
2.4. Truth tables
2.5. Substitution and validity
3. Axiomatic system
3.1. Axiom schemes
3.2. Inference rules
3.3. Provable formulas
4. Deduction theorem
4.1. Formulas provable under a set of hypotheses
4.2. Inference rules under sets of hypotheses
4.3. Deduction theorem
5. Derived rules
5.1. Identity, cut, and weakening
5.2. Introduction and elimination rules
5.3. Left and right introduction rules
6. Correctness and completeness
6.1. Correctness
6.2. Theories
6.3. Lindebaum lemma
6.4. Completeness
II. Predicate Logic
1. Terms and formulas
1.1. First-order languages
1.2. Terms
1.3. Formulas
1.4. Free and bound variables
2. Models
3. Axiomatic system
4. Deduction theorem
5. Derived rules
6. Correctness and completeness