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*To*: cg@cs.uah.edu, SUO <standard-upper-ontology@ieee.org>*Subject*: SUO: Re: maximum number of semantical relations*From*: "John F. Sowa" <sowa@bestweb.net>*Date*: Tue, 16 Dec 2003 10:52:09 -0800*In-Reply-To*: <200312160901.hBG91ed18505@mail.cerist.dz>*References*: <200312160901.hBG91ed18505@mail.cerist.dz>*Reply-To*: "John F. Sowa" <sowa@bestweb.net>*Sender*: owner-standard-upper-ontology@majordomo.ieee.org*User-Agent*: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.4) Gecko/20030624 Netscape/7.1 (ax)

In any kind of design or analysis, there are only three numbers that require no further explanation: zero, one, and infinity. Any number N greater than 1 is probably an inadequate approximation to infinity -- unless there is a convincing explanation of why N should be considered a natural stopping point before infinity. Following are some sample explanations: - Dichotomy: If a distinction divides a class of possibilities into A and not-A, then there are exactly two classes. - Trichotomy: Peirce showed that it is possible to transform any graph that contains a node with 4 or more attached arcs into a graph that contains no node with more than 3 attached arcs. See the diagram nodes.gif for a transformation that splits the node X with four arcs into two nodes X1 and X2, which have three arcs each; similar transformations can be used to split nodes with any number of arcs to additional nodes that have no more than 3. - Four-color theorem: Any map of countries (i.e., connected areas) drawn on a plane can colored with at most 4 colors so that no two contiguous contries have the same color. Any claim that some number N is a maximum should be supported with such an explanation. Otherwise, we should regard N as merely the point at which somebody stopped counting. Yalaoui asked: > I want to estimate a maximum number of relations that can > be used in a knowledge representation in an ontology. I > think that is no more then 16. What do you think about this? Meena responded: > To my knowledge the semantic relations are --- inclusion, > possession, attachment, attribution, antonym, synonym, case. > The inclusion is further divided as class inclusion, meronymic > inclusion, and spatial inclusion. (Winston, Chaffin, Hermann, 1987). Winston, Chaffin, and Hermann had a good analysis and classification of relations, which is well worth reading. But I would regard any of those numbers -- 16, 7, 3, or whatever -- as inadequate approximations to infinity unless or until somebody can provide a good explanation of why that subdivision should be considered exhaustive. John Sowa

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