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Tag Archives: Russell paradox
Set Theory in KIF 3.0
Regarding Russell Paradox, KIF 3.0 set up a special set theory that is based on von NeumannBernaysGödel (NBG). The 7th chapter of the reference manual, which is titled “Sets” starts with the description as follows. “In many applications, it is … Continue reading
Posted in RDF
Tagged bounded set, KIF, NBG set theory, principle of restricted set abstraction, Russell paradox, unbounded set
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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 (ZermeloFraenkel) set theory, which forbids … Continue reading
Posted in RDF, Semantic Web
Tagged axiom of foundation, cumulative sets, KIF, Russell paradox, ZermeloFraenkel set theory, ZF set theory
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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 comprehension principle, ramified type theory, Russell paradox, separation principle, ZF set theory
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