15-816 Modal Logic
Lecture 15: Intuitionistic Kripke Semantics

In this lecture we present the intutionistic approach to understanding Kripke semantics. This consists of a logical system based on two judgments: truth at a world, and accessibility between worlds. We present natural deduction and a sequent calculus and begin the discussion of potential operational interpretations. This view of intuitionistic modal logic goes back to the seminal work by Simpson [Sim94].

• Reading: 15-ikripke.pdf
• Original sources (accessible from at CMU only):

  [Sim94]

  Alex K. Simpson.
  The Proof Theory and Semantics of Intuitionistic Modal Logic. PhD thesis, University of Edinburgh, 1994.

• Key concepts:
  • Multiple world semantics
  • Accessibility relation
  • Distributed computation
• Previous lecture: Reconciliation
• Next lecture: Kripke Semantics for Validity

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Frank Pfenning, André Platzer