: Peter Baumgartner.
Logical Engineering with Instance-Based Methods.
In Frank Pfenning, editor, CADE-21 -- The 21st International Conference on Automated Deduction, volume 4603 of Lecture Notes in Artificial Intelligence, pages 404--409. Springer, July 2007. [ bib | .pdf ]
: Frank Pfenning, editor.
Automated Deduction -- CADE-21, volume 4603 of Lecture Notes in Artificial Intelligence. Springer, 2007. [ bib ]
: Peter Baumgartner, Ulrich Furbach, and Björn Pelzer.
Hyper Tableaux with Equality.
In Frank Pfenning, editor, CADE-21 -- The 21st International Conference on Automated Deduction, volume 4603 of Lecture Notes in Artificial Intelligence, pages 492--507. Springer, 2007. [ bib | .pdf ]
In most theorem proving applications, a proper treatment of equational theories or equality is mandatory. In this paper we show how to integrate a modern treatment of equality in the hyper tableau calculus. It is based on splitting of positive clauses and an adapted version of the superposition inference rule, where equations used for paramodulation are drawn (only) from a set of positive unit clauses, the candidate model. The calculus also features a generic, semantically justified simplification rule which covers many redundancy elimination techniques known from superposition-style theorem proving. Our main theoretical result is the soundness and completeness of the calculus. The calculus is implemented, and we also report on practical experiments.