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
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