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QNT Classification

QNT Classification. - A New Approach to Knowledge Representation US and International patents pending Pavel Babikov, Oleg Gontcharov, and Maria Babikova QNT Software Development Inc. 528 Victoria Ave., Windsor, ON Canada N9A 4M8 Tel: 1-519-253-3889 Fax: 1-519-253-5389

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QNT Classification

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  1. QNT Classification - A New Approach to Knowledge Representation US and International patents pending Pavel Babikov, Oleg Gontcharov, and Maria Babikova QNT Software Development Inc. 528 Victoria Ave., Windsor, ON Canada N9A 4M8 Tel: 1-519-253-3889 Fax: 1-519-253-5389 www.quasinewtonian.com

  2. Requirements to Classification Scheme • General polyhierarchical structure – no global separation of classification aspects • Persistence of the polyhierarchy –no dependence on actual set of classified objects • Compactness of description –no explicit enumeration of categories • Intrinsic support of set theory operations when forming classification categories • Efficient realization of test for distance inheritance – no combinatorial search • Conceptual simplicity – no application-specific program codes or cumbersome descriptions

  3. 12 . . . Nk Classification Criterion –Atomic Specialization Aspect CriterionCk Ck≡{Pk(i), i = 1,2,...,Nk} i – branch number Nk– cardinality Pk(i)={true/false} Pk(i)ΛPk(j) ≡ false for i≠j Elementary attributes: ak(i)≡{ Ck, i }~ Pk(i) = true Criterion branches

  4. a1(2) a1(3) a2(1) a1(1) a1(4) {a1(2), a2(1)} {a1(3), a2(1)} {a1(1), a2(1)} {a1(4), a2(1)} a2(2) Classification by criterion C1 {a1(1), a2(2)} {a1(4), a2(2)} {a1(2), a2(2)} {a1(3), a2(2)} Classification by conjunctivesuperposition of C1and C2 {ak(i),an(j)}~Pk(i) ΛPn(j) Classification by criterion C2 Conjunctive Classificationsby Systems of Criteria

  5. {} C1 C2 C3 C4 {a1(3),a4(1)} {a1(3),a4(2)} {a1(2)} {a1(3)} {a1(1),a2(1)} {a1(1),a2(2)} {a1(1)} C5 C6 {a1(3),a4(2),a6(1)} {a1(3),a4(2),a6(2)} {a1(1),a2(2),a5(2)} {a1(1),a2(2),a5(3)} {a1(1),a2(2),a5(1)} Trees and Facets - ClassicConjunctive Schemes

  6. Mandatory ranking classification criteria – the “predefined path” problem Massive duplication of criteria inparallel sub-trees –the “subtrees multiplication” problem Purely conjunctivelogical structure –no intrinsic support for disjunctions and negations Common Disadvantages of Trees

  7. Global separation of classification aspects The same “predefined path” and “subtrees multiplication” problems within facets Purely conjunctive intrinsic logical structure within facets Inelegant and cumbersome formalism supporting non-intrinsic features Common Disadvantages of Facets

  8. Our Approach: • Generalize formalism for building classification in terms of elementary specializations by criteria • Develop purely synthetic poly-hierarchical classification scheme based on partially ordered criteria

  9. {} C3 C6 C1 C2 C1 C1 C2 C2 {a1(1),a2(1),a3(2)} {a1(1)} {a1(3)} {a2(1)} {a1(1),a2(1)} {a1(1),a2(1),a4(2)} {a1(3),a2(1),a3(1)} {a3(1)} C5 {a1(3),a2(1),a3(1) a5(3),a6(1)} C3 C4 • Category can introduce more than one classification criterion • Any applicable criterion can be used for further specialization

  10. {} {} C1 C1 C2 C2 C4 C3 {[a1(2),a1(3)],a2(2)} {[a1(1),a1(2)]} {a2(2)} {[a1(1),a1(2)],a3(3)} {a1(2),a3(2)} {a1(3)} {a1(1)} {a1(2)} {a1(2)} {[a1(2),a1(3)]} {a2(2),a4(1)} C3 C2 [{a1(2),a3(2)}, {a2(2),a4(1)}] (P1(1) VP1(2)) Λ ΛP3(3) (P1(2) VP1(3)) Λ ΛP2(2) (P1(2) ΛP3(2)) V V(P2(2) ΛP4(1)) • Classification categories are described by logical formulae containing conjunctions, disjunctions and negations

  11. {} C1 C2 C3 C2 C1 {[a1(2),a1(3)],a2(2),a3(1)} ~ (P1(2)VP1(3)) ΛP2(2) ΛP3(1) ~ ~ root (C4), hence C4 C1, C4 C2, C4C3 C3 {[a1(2),a1(3)],a2(2),a3(1)} {a1(3)} {a1(2)} {a2(2)} C4 Generating Polyhierarchy is Established by Dependence Relationships Between Criteria

  12. {} C6 C4 C1 C2 C3 C5 {[a1(2),a1(3)],a2(1)} {a1(3),a2(2)} {[a1(1),a1(2)],a2(1)} Total number of categories (collections with branch unions) = 98 Generating Polyhierarchy of Criteria Implicitly Defines Induced Polyhierarchy of Categories

  13. A Fragment of Generating Polyhierarchy for Classification of Means of Conveyance More Complex Example:

  14. Advantages of the Method • It satisfies all six requirements to classification scheme, listed above • It provides very general and mathematically rigorous formalism for manipulating complex hierarchical information structures • It uses very simple system of basic notions, without requiring special knowledge for implementation • Target polyhierarchical classification is directly representable by DB structure – no programming required!

  15. Fields of Application • Taxonomical, expert, logistic, and content management systems • Enterprise resource planning and project management systems • Application-specific data and knowledge bases • Machine learning and AI systems • Intelligent control systems and robots • Electronic lists, catalogues and directories • Internet search engines • Online documentation and help subsystems • Components of computer OS and compilers

  16. Contact Information QNT Software Development Inc. 528 Victoria Ave., Windsor, Ontario Canada N9A 4M8 Tel: 1-519-253-3889 Fax: 1-519-253-5389 babikov@quasinewtonian.com gontcharov@quasinewtonian.com

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