15-317 Constructive Logic
Lecture 5: Quantification

In this lecture we introduce universal and existential quantification, making the transition from purely propositional logic to first-order intuitionistic logic. At the moment, the domain of quantification remains unspecified: we reason with the quantifiers abstractly, isolating what should be true without regard to any particular set of object. What emerges as a important judgmental principle is that of a parametric judgment and the associated substitution principle for objects.

  • Reading: 05-quant.pdf
  • Key concepts:
    • Universal quantification
    • Existential quantification
    • Parametric judgments
    • Substitution principle for parametric judgments
  • Previous lecture: Proofs as Programs
  • Next lecture: Natural Numbers

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Frank Pfenning