Abstract
AbstractThe material presented in this paper contributes to establishing a basis deemed essential for substantial progress in Automated Deduction. It identifies and studies global features in selected problems and their proofs which offer the potential of guiding proof search in a more direct way. The studied problems are of the wide-spread form of “axiom(s) and rule(s) imply goal(s)”. The features include the well-known concept of lemmas. For their elaboration both human and automated proofs of selected theorems are taken into a close comparative consideration. The study at the same time accounts for a coherent and comprehensive formal reconstruction of historical work by Łukasiewicz, Meredith and others. First experiments resulting from the study indicate novel ways of lemma generation to supplement automated first-order provers of various families, strengthening in particular their ability to find short proofs.
Highlights
Research in Automated Deduction, known as Automated Theorem Proving (ATP), has resulted in systems with a remarkable performance
In order to find out more global features for directing proof search we start out here to study the structures of proofs for complex formulas in some detail and compare human proofs with those generated by systems. Complex formulas of this kind have been considered by Łukasiewicz in [19]. They are complex in the sense that current systems require tens of thousands or even millions of search steps for finding a proof if any, the length of the formulas is very short
How come that Łukasiewicz found proofs for those formulas he could never carry out more than, say, a few hundred search steps by hand? Which global strategies guided him in finding those proofs? Could we discover such strategies from the formulas’ global features?
Summary
Research in Automated Deduction, known as Automated Theorem Proving (ATP), has resulted in systems with a remarkable performance. In order to find out more global features for directing proof search we start out here to study the structures of proofs for complex formulas in some detail and compare human proofs with those generated by systems. Complex formulas of this kind have been considered by Łukasiewicz in [19]. This investigation analyzes structures of, and operations on, proofs for formulas of the form “axiom(s) and rule(s) imply goal(s)” It renders condensed detachment, a logical rule historically introduced in the course of studying these complex proofs, as a restricted form of the Connection Method (CM) in ATP. Data and tools to reproduce the experiments are available at http://cs.christophwernhard.com/cd
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
