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Learn about the principles of natural deduction, including a brief history of logic, Aristotelian logic and its elaborations, axiomatic systems, and the rules of inference. Explore how the introduction and elimination rules and the reiteration rule contribute to truth-preserving proofs. Understand the concepts of semantic entailment and derivability. Examples of the ∧I (and introduction) and ∧E (and elimination) rules are provided.
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SD: Natural Deduction in S Gregory Chapter 4
Anatomy of a Proof Primary Assumptions Target (conclusion) Scope Line
What is Natural Deduction? • A (very) brief history of logic (cultural enrichment) • Aristotelian Logic and its elaborations • Boole, Peirce, Frege, Principia and beyond: Axiomatic Systems & Natural Deduction • The Rules of Inference • Each of the 5 connectives has an introduction rule and an elimination rule. • The Reiteration Rule allows lines of the proof to be repeated. • The Rules are truth-preserving! • Two concepts of validity: semantic entailment (⊨ ) and derivability (⊢)
Wedge Rules - ∧I and ∧E • Note: like all the Rules of Inference they can only be applied to whole lines. • Note: Like all the Rules they can be shown to be truth preserving via truth tables.
