Theorem Proving with Transitive Relations from a Practical Point of View (1995)
| Venue: | Research Report IIIA 95/12, Institut d'Investigaci'o en Intel\Deltalig`encia Artificial (CSIC |
| Citations: | 3 - 3 self |
BibTeX
@INPROCEEDINGS{Schorlemmer95theoremproving,
author = {W. Marco Schorlemmer and Jaume Agusti},
title = {Theorem Proving with Transitive Relations from a Practical Point of View},
booktitle = {Research Report IIIA 95/12, Institut d'Investigaci'o en Intel\Deltalig`encia Artificial (CSIC},
year = {1995}
}
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Abstract
Rewrite techniques have been typically applied to reason with the equality relation and have turned out to be among the more successful approaches to equational theorem proving. In fact, it is not only in reasoning with the equality relation where these techniques naturally apply, but in reasoning with arbitrary, probably non-symmetric, transitive relations, being the equality relation just a special case of monotone transitive relation, which is also symmetric. The work done so far in applying rewrite techniques to arbitrary transitive relations showed several important differences with the equational case. Although most equational results can be extended to non-symmetric relations, new problems appear which must be solved in a quite different way. In this paper we review the use of rewrite techniques for reasoning with arbitrary possibly non-symmetric transitive relations and we analyze the reasons why an efficient treatment of this generalization to nonsymmetric transitive relations...
