15-815 Automated Theorem Proving
Lecture 17: Labeled Deduction
The system of focusing, when used for backwards search, significantly
reduces non-determinism. Yet, many choice points remain which can be
especially prohibitive in complex, non-Horn theories. In this lecture
we present another approach which, in the end result, will make all
rules of the logic invertible, just as they are for classical
(propositional) logic.
The first fundamental idea is to label propositions in order to track
dependencies between the order in which inference rules are applied in
bottom-up search. The second idea is to replace certain labels by
variables (instead of guessing them) and use a specialized form of
unification. In this lecture we present a system of labeled deduction
for intuitionistic propositional logic, paving the way for later
optimization via the use of variables.
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Frank Pfenning
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