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