15-816 Linear Logic
Lecture 11: Unification

Focusing removes some unnecessary non-determinism from search, but other sources of inefficiency remain. In this lecture we talk about how to resolve existential non-determinism which arises in the choice of a substitution for the existential right or universal left rule.

The non-determinism is resolved by substitution an existential variable (also called meta-variable or logic variable) and then collecting constraints on this variable. Solving these constraints is referred to as unification. Unification is at the heart of almost all theorem provers and logic programming languages.

We present the relationship between search and unification using residuation which collects constraints in the form of a proposition in a simpler logic. Propositions in this simpler logic can be solved by unification. Time permitting, we will give a new presentation of a unification algorithm in linear logic (presently not in the notes).

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Frank Pfenning