Definability of Sentences in the Language of Boolean Algebras with Distinguished Ideals

D. E. Palchunov

Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 2, pp. 91-104

Résumé

Paper is devoted to model-theoretical methods of ontology formalization and knowledge representation. Questions, what methods of knowledge representation can be applied in all possible situations, and what methods can be used only in certain special cases, are investigated. It is shown that any information can be represented in the form of semantic network of first order predicate logic sentences. On the other hand, not each set of definitions of concepts can be represented by means of an explicit glossary; moreover concept definitions not always can be represented by a glossary defining concepts one by one. To prove these results we investigate model-theoretical properties of Boolean algebras with distinguished ideals.

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