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.

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Frank Pfenning