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QNT ClassificationQNT Classification- A New Approach to Knowledge - A New Approach to Knowledge

RepresentationRepresentation

US and International patents pending

Pavel Babikov, Oleg Gontcharov,Pavel Babikov, Oleg Gontcharov,and Maria Babikovaand Maria Babikova

QNT Software Development Inc.QNT Software Development Inc.528 Victoria Ave., Windsor, ON Canada N9A 4M8528 Victoria Ave., Windsor, ON Canada N9A 4M8Tel: 1-519-253-3889 Fax: 1-519-253-5389Tel: 1-519-253-3889 Fax: 1-519-253-5389

www.quasinewtonian.comwww.quasinewtonian.com

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Requirements to Classification SchemeRequirements to Classification Scheme General polyhierarchical structure – General polyhierarchical structure – no global no global

separation of classification aspectsseparation of classification aspects Persistence of the polyhierarchy –Persistence of the polyhierarchy – no no

dependence on actual set of classified objectsdependence on actual set of classified objects Compactness of description –Compactness of description – no explicit no explicit

enumeration of categoriesenumeration of categories Intrinsic support of set theory operations Intrinsic support of set theory operations

when forming classification categorieswhen forming classification categories Efficient realization of test for distance Efficient realization of test for distance

inheritance – inheritance – no combinatorial searchno combinatorial search Conceptual simplicity – Conceptual simplicity – no application-specific no application-specific

program codes or cumbersome descriptionsprogram codes or cumbersome descriptions

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Classification Criterion –Classification Criterion –Atomic Specialization AspectAtomic Specialization Aspect

Ck ≡ { Pk(i), i = 1,2,...,Nk }i – branch numberNk – cardinality

Pk(i) = { true / false }Pk(i) Λ Pk(j) ≡ false for i ≠ j

Elementary attributes:ak(i) ≡ { Ck, i } ~ Pk(i) = true

Criterion Ck

1kP

1 2 . . . Nk

Criterion branches

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Classification by criterion C1

a1(1)a1(2)

a1(4)a1(3)

Conjunctive ClassificationsConjunctive Classificationsby Systems of Criteriaby Systems of Criteria

1kP

Classification by conjunctive superposition of C1 and C2

{ak(i), an(j)} ~ Pk(i) Λ Pn(j)

{a1(1), a2(1)}{a1(3), a2(1)}

{a1(4), a2(1)}

{a1(1), a2(2)}{a1(2), a2(2)} {a1(3), a2(2)}

{a1(4), a2(2)}

{a1(2), a2(1)}

Classification by criterion C2

a2(1)

a2(2)

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Trees and Facets - ClassicTrees and Facets - ClassicConjunctive SchemesConjunctive Schemes

1kP

{a1(1),a2(2)}{a1(1),a2(1)}

{a1(1),a2(2),a5(1)}

{ }

{a1(1)} {a1(2)} {a1(3)}

{a1(1),a2(2),a5(3)} {a1(3),a4(2),a6(2)}

{a1(3),a4(2)}{a1(3),a4(1)}

{a1(1),a2(2),a5(2)} {a1(3),a4(2),a6(1)}

C1

C2

C6C5

C4C3

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Common Disadvantages of TreesCommon Disadvantages of Trees

Mandatory ranking classification criteria – Mandatory ranking classification criteria – the “predefined path” problemthe “predefined path” problem

Massive duplication of criteria inMassive duplication of criteria in parallel parallel sub-trees –sub-trees – the “subtrees multiplication” the “subtrees multiplication” problemproblem

Purely conjunctivePurely conjunctive logical structure –logical structure – no no intrinsic support for disjunctions and intrinsic support for disjunctions and negationsnegations

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Common Disadvantages of FacetsCommon Disadvantages of Facets

Global separation of classification aspects Global separation of classification aspects The same “The same “predefined pathpredefined path” and ” and

““subtrees multiplicationsubtrees multiplication” problems within ” problems within facetsfacets

Purely conjunctive intrinsic logical Purely conjunctive intrinsic logical structure within facetsstructure within facets

Inelegant and cumbersome formalism Inelegant and cumbersome formalism supporting non-intrinsic featuressupporting non-intrinsic features

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Our Approach:Our Approach:

Generalize formalism for building Generalize formalism for building classification in terms of elementary classification in terms of elementary specializations by criteriaspecializations by criteria

Develop purely synthetic poly-Develop purely synthetic poly-hierarchical classification scheme hierarchical classification scheme based on partially ordered criteriabased on partially ordered criteria

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Category can introduce more than one Category can introduce more than one classification criterionclassification criterion

Any applicable criterion can be used for Any applicable criterion can be used for further specializationfurther specialization

{ }

{a1(1)}

C2

{a1(3)} {a2(1)} {a3(1)}

C2 C2C1

{a1(3),a2(1),a3(1)}

C6

C3C1

C1

C5

{a1(1),a2(1)}

C4C3

{a1(3),a2(1),a3(1) a5(3),a6(1)}{a1(1),a2(1),a3(2)} {a1(1),a2(1),a4(2)}

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Classification categories are described by Classification categories are described by logical formulae containing conjunctions, logical formulae containing conjunctions, disjunctions and negationsdisjunctions and negations

{ }

C2

C2

C3

C1

C3

{[a1(1),a1(2)]}

C2

C4

{a2(2)}

{[a1(1),a1(2)],a3(3)}

{[a1(2),a1(3)]}

{[a1(2),a1(3)],a2(2)}

C1

{a1(3)}{a1(1)} {a1(2)}

{ }

{a1(2)}

(P1(1) V P1(2)) Λ

Λ P3(3)

(P1(2) V P1(3)) Λ

Λ P2(2)

(P1(2) Λ P3(2)) VV (P2(2) Λ P4(1))

[{a1(2),a3(2)}, {a2(2),a4(1)}]

{a1(2),a3(2)} {a2(2),a4(1)}

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Generating Polyhierarchy is Generating Polyhierarchy is Established by Dependence Established by Dependence

Relationships Between CriteriaRelationships Between Criteria

C3

{[a1(2),a1(3)],a2(2),a3(1)}

{ }

C2

C4

{a1(3)}{a1(2)}

C1

{a2(2)}

C2 C3C1

{[a1(2),a1(3)],a2(2),a3(1)} ~

(P1(2)VP1(3)) Λ P2(2) Λ P3(1) ~

~ root (C4), hence

C4 C1, C4 C2, C4 C3

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Generating Polyhierarchy of Criteria Generating Polyhierarchy of Criteria Implicitly Defines Induced Implicitly Defines Induced

Polyhierarchy of CategoriesPolyhierarchy of Categories

{[a1(2),a1(3)],a2(1)}

C6

C3

{a1(3),a2(2)}

C4

{[a1(1),a1(2)],a2(1)}

C5

{ }

C1 C2

Total number of categories

(collections with branch unions) =

98

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A Fragment of Generating Polyhierarchy A Fragment of Generating Polyhierarchy for Classification of Means of Conveyancefor Classification of Means of Conveyance

More Complex Example:More Complex Example:

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Advantages of the MethodAdvantages of the Method It satisfies all six requirements to It satisfies all six requirements to

classification scheme, listed aboveclassification scheme, listed above It provides very general and mathematically It provides very general and mathematically

rigorous formalism for manipulating complex rigorous formalism for manipulating complex hierarchical information structureshierarchical information structures

It uses very simple system of basic notions, It uses very simple system of basic notions, without requiring special knowledge for without requiring special knowledge for implementationimplementation

Target polyhierarchical classification is Target polyhierarchical classification is directly representable by DB structure – directly representable by DB structure – no no programming required!programming required!

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Fields of ApplicationFields of Application Taxonomical, expert, logistic, and content Taxonomical, expert, logistic, and content

management systemsmanagement systems Enterprise resource planning and project Enterprise resource planning and project

management systemsmanagement systems Application-specific data and knowledge Application-specific data and knowledge

basesbases Machine learning and AI systemsMachine learning and AI systems Intelligent control systems and robotsIntelligent control systems and robots Electronic lists, catalogues and directoriesElectronic lists, catalogues and directories Internet search enginesInternet search engines Online documentation and help subsystemsOnline documentation and help subsystems Components of computer OS and compilersComponents of computer OS and compilers

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Contact InformationContact InformationQNT Software Development Inc.QNT Software Development Inc.

528 Victoria Ave.,528 Victoria Ave.,Windsor, OntarioWindsor, OntarioCanada N9A 4M8Canada N9A 4M8Tel: 1-519-253-3889Tel: 1-519-253-3889Fax: 1-519-253-5389Fax: 1-519-253-5389

babikov@quasinewtonian.combabikov@quasinewtonian.comgontcharov@quasinewtonian.comgontcharov@quasinewtonian.com