On Thursday 2015-07-09, at 10:30, in room F102,
Speaker: Tsvetan Chavdarov Dunchev
Title: Automation of cut-elimination in proof schemata
Schematising sets of objects by abstracting their general structure is an important and frequently necessary task in mathematics. In this talk will be presented a method for cut-elimination by resolution for propositional and first-order proof schemata (CERESs). Cut-elimination, introduced by Gentzen, is the most prominent form of proof transformation in logic and plays an important role in automating the analysis of mathematical proofs. The removal of cuts corresponds to the elimination of intermediate statements (lemmas) from proofs resulting in a proof which is analytic in the sense, that all statements in the proof are sub-formulas of the result. Therefore, the proof of a combinatorial statement is converted into a purely combinatorial proof. For a given proof schemata we will extract a (schematic) set of clauses which is always unsatisfiable. A resolution refutation of this set will be constructed using the notion of the resolution schemata. The obtained refutation will be used as a skeleton of a proof in normal form with at most atomic cut-formulas.