15-816 Modal Logic
Lecture 9: Combinatory Modal Logic

In this lecture we establish an axiomatic system for intuitionistic modal logic and relate it to natural deduction. Computationally, the axiomatic system corresponds to combinatory logic due to Curry.

• Reading: 09-combinators.pdf
• Key concepts:
  • Modus ponens
  • Hilbert systems
  • Axioms S, K, and I
  • Rule of necessitation
  • Axioms T, K, and 4
  • Bracket abstraction
  • Combinatory reduction
• Previous lecture: Sequent Calculus
• Next lecture: Modal Tableaux

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Frank Pfenning, André Platzer