15-317 Constructive Logic
Lecture 2: Natural Deduction

We define the meaning of the usual connectives of propositional logic (conjunction, implication, disjunction) by rules that allow us to infer when they should be true, so-called introduction rules. From these, we derive rules for the use of propositions, so-called elimination rules. The resulting system of natural deduction is the foundation of intuitionistic logic which has direct connections to functional programming and logic programming.

  • Reading: 02-natded.pdf
  • Previous lecture: Overview
  • Next lecture: Harmony
  • Key concepts:
    • Judgment
    • Proposition
    • Truth
    • Inference rule
    • Premise
    • Conclusion
    • Introduction rule
    • Elimination rule
    • Hypothetical judgment
    • Substitution principle

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Frank Pfenning