Redirecting Proofs by Contradiction
نویسنده
چکیده
This paper presents an algorithm that redirects proofs by contradiction. The input is a refutation graph, as produced by an automatic theorem prover (e.g., E, SPASS, Vampire, Z3); the output is a direct proof expressed in natural deduction extendedwith case analyses and nested subproofs. The algorithm is implemented in Isabelle’s Sledgehammer, where it enhances the legibility of machine-generated proofs.
منابع مشابه
Comparative commentary of Anfal verse
What is meant by anfal in Quran, its ownership and the abrogation of anfal verse is a position of disagreement between Shiite and Sunni`s commentators. As is clearly understood by the first verse of chapter Anfal, anfal has been known as one of the great financial sources for Islamic government. Some commentators have viewed the verse to be in contradiction with the verse of khums and, therefor...
متن کامل4 Kolmogorov Complexity
One can prove X1 is not regular using the pumping lemma. One can prove X2 is not regular either by using the pumping lemma (a version with bounds on the prefix) or by contradiction: if X2 is regular than X2 ∩ a∗b∗ = X1 is regular. One cannot prove X3 non-regular with the pumping theorem directly; however one can prove its regular by contradiction: if X3 is regular than X3 = X2 is regular. We wi...
متن کاملContradiction: When Avoidance Equals Removal - Part II
This paper is the continuation of 1] in this volume. There we present a sceptical semantics which avoids contradiction for extended logic programs plus integrity contraints in the form of denials, based on the notion of optative hypotheses {an abductive approach. In this part we deene a program revision method for removing contradiction from contradictory programs under WFSX, based on the notio...
متن کاملSeki Report Planning Diagonalization Proofs Planning Diagonalization Proofs
This report is a rst attempt of formalizing the diagonalization proof technique. We give a strategy how to systematically construct diagonalization proofs: (i) nding an indexing relation, (ii) constructing a diagonal element, and (iii) making the implicit contradiction of the diagonal element explicit. We suggest a declarative representation of the strategy and describe how it can be realized i...
متن کاملRobust, Semi-Intelligible Isabelle Proofs from ATP Proofs
Sledgehammer integrates external automatic theorem provers (ATPs) in the Isabelle/HOL proof assistant. To guard against bugs, ATP proofs must be reconstructed in Isabelle. Reconstructing complex proofs involves translating them to detailed Isabelle proof texts, using suitable proof methods to justify the inferences. This has been attempted before with little success, but we have addressed the m...
متن کامل