15-816 Modal Logic
Lecture 17: Tethered Semantics

In this lecture we present a new form of semantics which combines multiple worlds with multiple judgments at these worlds. We find that this so-called tethered semantics has local actions, and that its sequent calculus is in bijective correspondence with the sequent calculus JS4 for validity and possibility. Because antecedents are persistent and just become unusable instead of being erase, the tethered semantics is well-suited for implementation of JS4 in a logical framework.

• Reading: 17-tethered.pdf
• Code (in Twelf):
  • tether-seq.elf - tethered sequent calculus and cut elimination.
  • tether-nd.elf - tethered natural deduction.
• Key concepts:
  • Tethering rules
  • Tethered sequent calculus
  • Tethered cut and identity
  • Strengthening
  • Tethered natural deduction
• Previous lecture: Kripke Semantics for Validity
• Next lecture: Model Checking

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Frank Pfenning, André Platzer