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By Caldiroli P., Musina R.

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Statements of the theory of sets can be derived from its axioms, which can be viewed as semantic postulates specifying the properties of a theoretical notion of a set. On this example we can see that propositions in analytical knowledge need not be just trivial logical consequences of semantic postulates; on the contrary, obtaining such propositions may be very difficult. Analytical knowledge also includes statements whose validity can be derived by purely logical means without using semantic postulates.

In other words, a reasonable measure of uncertainty reduction by obtaining a piece of knowledge should be proposed. We will propose such a measure below, and call it information content in knowledge (Vajda, Veselý, Zvárová, 2005). 27 Data, Information and Knowledge Let us suppose that language J describes ontology Ω and contains predicates π1 , . . , πr describing properties of objects within ontology Ω, as well as individual constants ω1, . . ,ωs representing individual objects Ω. States of ontology Ω can be described by conjunctions α: α = α (ω1) ∧ .

3, will not make such decision-making possible, and a loss of source data might cause a costly lawsuit. The last three examples show that sufficiency or insufficiency of derived data depends on the source and on the actual decision-making problem to be resolved on the basis of the given source. In Example 6, a situation was mentioned in which the derived data of Example 3, (1, 1, 1, 0, 0, 0), was sufficient. On the other hand, Example 8 refers to a situation in which only extended derived data, (h, 1, 1 ,1, 0, 0, 0), was sufficient.

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H-bubbles in a perturbative setting the finite-dimensional reductions method by Caldiroli P., Musina R.

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