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
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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
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Classification Criterion –
Atomic Specialization Aspect
Criterion Ck
P1
k
Ck ≡ { Pk(i), i = 1,2,...,Nk }
i – branch number
Nk – cardinality
1 2 . . . Nk
Pk(i) = { true / false }
Pk(i) Λ Pk(j) ≡ false for i ≠ j
Criterion
branches
Elementary attributes:
ak(i) ≡ { Ck, i } ~ Pk(i) = true
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Conjunctive Classifications
by Systems of Criteria
a1(2)
a1(1)
P1
k
a1(3)
a1(4)
{a1(2), a2(1)}
{a1(1), a2(1)}
{a1(3), a2(1)}
{a1(4), a2(1)}
{a1(1), a2(2)}
{a1(2), a2(2)}
{a1(4), a2(2)}
{a1(3), a2(2)}
Classification by criterion C1
a2(1)
a2(2)
Classification by criterion C2
Classification by conjunctive
superposition of C1 and C2
{ak(i), an(j)} ~ Pk(i) Λ Pn(j)
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Trees and Facets - Classic
Conjunctive Schemes
{}
C1
{a1(1)}
P1
k
{a1(2)}
C2
{a1(1),a2(1)}
{a1(3)}
C3
{a1(1),a2(2)}
{a1(3),a4(1)}
C5
{a1(1),a2(2),a5(1)}
{a1(3),a4(2)}
C6
{a1(1),a2(2),a5(3)}
{a1(1),a2(2),a5(2)}
C4
{a1(3),a4(2),a6(2)}
{a1(3),a4(2),a6(1)}
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Common Disadvantages of Trees

Mandatory ranking classification criteria –
the “predefined path” problem

Massive duplication of criteria in parallel
sub-trees – the “subtrees multiplication”
problem

Purely conjunctive logical structure – no
intrinsic support for disjunctions and
negations
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Common Disadvantages of Facets


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
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Our Approach:


Generalize formalism for building
classification in terms of elementary
specializations by criteria
Develop purely synthetic polyhierarchical classification scheme
based on partially ordered criteria
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

Category can introduce more than one
classification criterion
Any applicable criterion can be used for
further specialization
{}
C1
{a1(1)}
{a1(3)}
{a2(1)}
C2
{a3(1)}
C1
{a1(1),a2(1)}
C3
{a1(1),a2(1),a3(2)}
C3
C2
C1
C2
{a1(3),a2(1),a3(1)}
C4
{a1(1),a2(1),a4(2)}
C5
C6
{a1(3),a2(1),a3(1) a5(3),a6(1)}
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
Classification categories are described by
logical formulae containing conjunctions,
disjunctions and negations
{}
{}
C2
C1
{a1(1)}
{a2(2)}
C3
{[a1(1),a1(2)]}
{[a1(2),a1(3)]}
C3
C2
{a1(2)}
{a1(3)}
{a1(2)}
C1
{a1(2),a3(2)}
C4
{a2(2),a4(1)}
C2
{[a1(1),a1(2)],a3(3)}
{[a1(2),a1(3)],a2(2)}
[{a1(2),a3(2)}, {a2(2),a4(1)}]
(P1(1) V P1(2)) Λ
Λ P3(3)
(P1(2) V P1(3)) Λ
Λ P2(2)
(P1(2) Λ P3(2)) V
V (P2(2) Λ P4(1))
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Generating Polyhierarchy is
Established by Dependence
Relationships Between Criteria
C1
{}
C1
{a1(2)}
{a1(3)}
C2
C3
{[a1(2),a1(3)],a2(2),a3(1)} ~
{a2(2)}
C3
(P1(2)VP1(3)) Λ P2(2) Λ P3(1) ~
~ root (C4), hence
{[a1(2),a1(3)],a2(2),a3(1)}
C4
C2
C4
C1, C4
C2, C4
C3
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Generating Polyhierarchy of Criteria
Implicitly Defines Induced
Polyhierarchy of Categories
{}
C1
{[a1(1),a1(2)],a2(1)}
C2
{[a1(2),a1(3)],a2(1)}
C6
C5
{a1(3),a2(2)}
C3
C4
Total number of
categories
(collections with
branch unions) =
98
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More Complex Example:
A Fragment of Generating Polyhierarchy
for Classification of Means of Conveyance
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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!
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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
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Contact Information
QNT Software Development Inc.
528 Victoria Ave.,
Windsor, Ontario
Canada N9A 4M8
Tel: 1-519-253-3889
Fax: 1-519-253-5389
[email protected]
[email protected]
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