# The hyper tableaux calculus with equality and an application to finite model computation

## Authors

Peter Baumgartner, Ulrich Furbach and Bjoern Pelzer

NICTA

Australian National University

Universitaet Koblenz-Landau

Germany

## Abstract

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 treat- ment 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 superposition are drawn (only) from a set of positive unit clauses, and superposition inferences into positive literals is restricted into (positive) unit clauses only. 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 of the calculus, but we also show how to apply the calculus for finite model computation, and we briefly describe the implementation.

## BibTeX Entry

@article{Baumgartner_FP_10,
title = {The Hyper Tableaux Calculus with Equality and an Application to Finite Model Computation},
month = feb,
keywords = {automated theorem proving, equality},
journal = {Journal of Logic and Computation},
volume = {20},
number = {1},
author = {Baumgartner, Peter and Furbach, Ulrich and Pelzer, Bjoern},
year = {2010},
pages = {77--101},
paperurl = {https://trustworthy.systems/publications/nicta_full_text/662.pdf}
}

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