A Tableaux Calculus for Reducing Proof Size

Abstract

A tableau calculus is proposed, based on a compressed representation of clauses, where literals sharing a similar shape may be merged. The inferences applied on these literals are fused when possible, which reduces the size of the proof. It is shown that the obtained proof procedure is sound, refutationally complete and allows to reduce the size of the tableau by an exponential factor. The approach is compatible with all usual refinements of tableaux.

Synthetic Tableaux with Unrestricted Cut for First-Order Theories

“…A step in the same direction has been made before in [34]. The authors proposed a proof procedure for First-Order Logic based on tableaux method with the cut rule.…”

“…Our work is similar to this proposal in the sense that the cut rule is used while proving theorems and not as the post-processing tool employed to transform already existing derivations to reduce their size. The main difference between the approach in [34] and our approach concerns the proof method used and the form of syntactic structures being processed-in the cited work, the rules act on clauses, whereas our solution does not assume deriving a clausal form.…”