Lecture 2: Natural Deduction

We introduce the calculus of natural deduction due to Gentzen. We take Martin-Löf's point of view that this provides a definition of the logical connectives and quantifiers.

Key Concepts

• Judgment
• Evident judgment
• Proposition
• Truth
• Proof
• Inference rule
• Premises and conclusion
• Hypothesis
• Hypothetical judgment
• Substitution
• Orthogonality of logical connectives
• Introduction and elimination rules
• Local soundness and completeness
• Conjunction, implication, disjunction, truth, falsehood

Reading

• Pages 3-16 of Handout 1 on Natural Deduction (also available in DVI and PDF formats).

Links

• Previous lecture: Introduction
• Next lecture: Proof Terms