15-816 Linear Logic
Lecture 1: Introduction
We give a general introduction to linear logic, the organization of the
class, and the topics we plan to cover.
We demonstrate by means of an extended example the problems that arise if we
formulate problems involving state in logic. A prototypical example is the
Blocks World that is used in artificial intelligence to illustrate
planning problems. One of the essential difficulties is called
the frame problem: how can we specify that some aspects of
the state change while all others stay the same.
Linear logic solves the frame problem in an ingenious way by requiring
that assumptions must be used exactly once. Then assumptions may be
viewed as resources that are consumed during a proof. This gives rise
to some interesting new connectives that could not be distinguished
in ordinary logic where assumptions may be used arbitrarily many times.