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15-815 Automated Theorem Proving

Lecture 16: Towards Tableaux

The considerations introduced into proof search so far are mostly motivated by backward theorem proving, where we start with a proposed theorem and work towards the initial sequents. Nonetheless, with some modifications, the principal ideas and techniques are shared between different styles of theorem provers and apply to forward theorem proving as well.

In this lecture we introduce a further improvement which postpones disjunctive choices (don't know non-determinism) until later in the search, in the hope they may become irrelevant or otherwise shorten the proof. This is achieved by postponing the choice of either proving either A or B when the succedent is the disjunction A v B, leading to a sequent with multiple conclusions. A similar idea can be applied to delay the choice for existential instantiation.

Taken a step further, these ideas lead to tableaux provers, such as those developed Otten and Kreitz, following earlier ideas by Wallen.


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Frank Pfenning