15-816 Modal Logic
Lecture 16: Kripke Semantics for Validity

In this lecture we continue the analysis of distributed computation in the multiple-worlds interpretation of intuitionistic modal logic. We then attempt to give a multiple-worlds interpretation of validity, which turns out to be IS4. When we add possibility, however, we find the semantics to be sound but not complete with respect to our judgmental formulation of validity and possibility.

• Reading: 16-vkripke.pdf
• Key concepts:
  • Non-local actions
  • Distributivity of possibility over disjunction
  • Multiple-world sequent calculus
  • Incompleteness for JS4 with respect to IS4
  • Axiomatic presentations of intutionistic modal logics
• Previous lecture: Intuitionistic Kripke Semantics
• Next lecture: Tethered Semantics

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Frank Pfenning, André Platzer