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SD : Natural Deduction in S

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

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  1. SD: Natural Deduction in S Gregory Chapter 4

  2. Anatomy of a Proof Primary Assumptions Target (conclusion) Scope Line

  3. 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 (⊢)

  4. 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.

  5. ∧I: Example

  6. ∧E: Example

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