15-816 Modal Logic
Lecture 24: Resource Semantics

In this lecture we continue our investigation of the resource semantics for linear logic from the previous lecture. We first consider the so-called additive connectives of linear logic. While we will be able to develop a resource sequent calculus which is still in bijective correspondence with the linear sequent calculus, it suggests a more elementary resource semantics which also has an elegant natural deduction formulation. This can be accomplished by ``untethering'' the left rules of the resource sequent calculus as much as possible. We also sketch how this technology can be applied to specify ordered logic, in which the structural rule of exchange is repudiated (in addition to weakening and contraction, as in linear logic).

Much of the contents of this last lecture on intuitionistic modal logic is speculative.

• Reading: 24-ressemantics.pdf
• Key concepts:
  • Additives connectives
  • Untethering
  • Ordered logic
• Previous lecture: Linear Logic
• Next lecture: Propositional Dynamic Logic Theory

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fp@cs, aplatzer@cs
Frank Pfenning, André Platzer