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):
- 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