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 theorem proving. Our main results are soundness and completeness, but we briefly describe the implementation, too. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Baumgartner, P., Furbach, U., & Pelzer, B. (2007). Hyper tableaux with equality. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4603 LNAI, pp. 492–507). Springer Verlag. https://doi.org/10.1007/978-3-540-73595-3_36
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