Monthly Archives: October 2011

Axiom of Foundation in Zermelo Fraenkel Set Theory

I pointed out, in the earlier page of my blog, that Pat and Brian said in RDF Semantics, “Such ‘membership loops’ might seem to violate the axiom of foundation, one of the axioms of standard (Zermelo-Fraenkel) set theory, which forbids … Continue reading

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What is Russell paradox?

Even if we restrict ourselves to select only sets that do not include the membership loop, we cannot avoid a paradox on a kind of naive formal systems such that contains inside the infinity or the totality. See the following … Continue reading

Posted in LOD, OWL, RDF, Semantic Web | Tagged , , , , | 1 Comment

Metaclass Framework of CLOS, Python, and RDF(S)

As shown in the RDF Schema file, rdfs:Resource is a superclass of all classes including rdfs:Class, and rdfs:Class is a class of all classes including rdfs:Resource. Surprisingly, two object oriented languages, Common Lisp Object System (CLOS) and Python3.x show the … Continue reading

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Universal Class

In the document of RDF Semantics, the term “universal class” appears only once in the discussion on membership loop. When classes are introduced in RDFS, they may contain themselves. … In particular, this use of a class extension mapping allows … Continue reading

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Universe of Discourse

What is the universe of discourse? Pat and Brian say, “The semantics treats all RDF names as expressions which denote. The things denoted are called ‘resources’, following [RFC 2396], … ; ‘resource’ is treated here as synonymous with ‘entity’, i.e. … Continue reading

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