The Fixed-Point Theorems of Priess-Crampe and Ribenboim in Logic Programming (1999) [13 citations — 10 self]
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by Pascal Hitzler, Anthony Karel Seda, Abstract Sibylla Priess-crampe, Paulo Ribenboim Recently Established
Proceedings of the International Conference and Workshop on Valuation Theory, University of Saskatchewan in
http://ogham.ucc.ie/~pascal/pcrinlp.ps.gz
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@INPROCEEDINGS{Hitzler99thefixed-point,author = {Pascal Hitzler and Anthony Karel Seda and Abstract Sibylla Priess-crampe and Paulo Ribenboim Recently Established},
title = {The Fixed-Point Theorems of Priess-Crampe and Ribenboim in Logic Programming},
booktitle = {Proceedings of the International Conference and Workshop on Valuation Theory, University of Saskatchewan in},
year = {1999},
pages = {1--17},
publisher = {American Mathematical Society}
}
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Abstract:
a general xed-point theorem for multivalued mappings dened on generalized ultrametric spaces, and introduced it to the area of logic programming semantics. We discuss, in this context, the applications which have been made so far of this theorem and of its corollaries. In particular, we will relate these results to Scott-Ershov domains, familiar in programming language semantics, and to the generalized metrics of Khamsi, Kreinovich and Misane which have been applied, by these latter authors, to logic programming. Amongst other things, we will also show that a unied treatment of the xed-point theory of wide classes of programs can be given by means of the theorems of Priess-Crampe and Ribenboim. 1
