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.