Expressing Classification Schemes -- Part 3

Expressing Classification Schemes with OWL 2 Web Ontology Language

Considering basic functional requirements Can be done with many languages, e.g., SKOS, RDFs, OWL ISKO-2010, Rome ©ZengPanzerSalaba

3. WHEN OWL MEETS CLASSIFICATION 3.1 OWL for complex class expressions 3.2 OWL axioms for relationships between class expressions 3.3 OWL properties and restrictions for more complicated class expressions and relationships ISKO-2010, Rome ©ZengPanzerSalaba

Our interests in OWL Class expression Built classes Classes to be built according to rules and instructions Class : Class Class + Auxiliary Table Class + Added Table Class + implied example Relationship expression Typical Class-to-class SubClassOf DisjointClasses EquivelantClasses More complicated Class-to-class Class-to-topic Index terms Class-here Class-elsewhere See reference … ISKO-2010, Rome ©ZengPanzerSalaba

class identification the enumeration of individuals that form class instances the intersection and union of two or more class descriptions the complement of a class description property restrictions Class expression Built classes Classes to-be-built according to rules and instructions Class : Class Class + Auxiliary Table Class + Added Table Class + implied example OWL supports various ways of describing classes ISKO-2010, Rome ©ZengPanzerSalaba

OWL provides for the standard set-theoretic operations on class expressions. ObjectIntersectionOf ObjectUnionOf ObjectComplementOf 3.1 OWL for complex class expressions ISKO-2010, Rome ©ZengPanzerSalaba

Complex class expressions are needed for synthesized classes ISKO-2010, Rome ©ZengPanzerSalaba by adding numbers from other parts of the schedule, by adding numbers from a table, or by basing it on a pattern defined in another part of the schedule. Auxiliary tables rules combine add Subject schedule A Subject schedule B 1 2 2 follow 3 To accommodate new subjects and reflect the nature of interdisciplinary, instructions are provided to the classifier to construct a number in practice:

Classification numbers may be built according to rules Theoretically unlimited classes can be built Example from DDC: 821.008 Collections of English poetry is built with 82 (following the instruction at 820.1-828 Subdivisions of English literature ) plus 100 (following the instruction at T3B--1001-T3B--1009 Standard subdivisions; collections; history, description, critical appraisal ) plus 8 Collections of literary texts from the add table at T3B--1-T3B--8 Specific forms . 821 English poetry 821.008 English poetry--collections 821.00803543 Love--poetry--English literature--collections, . . . 821.0080355 English poetry--social themes--collections, . . . 821.008036 English poetry--nature--collections, . . . 821.0080382 English poetry--religious themes--collections, . . . 821.00 9 English poetry--history and criticism 821.04 English poetry--lyric poetry, . . . 821.0708 Humorous poetry--English literature--collections, . . . http://ddc.typepad.com/025431/ddc_tip_of_the_week/ Source: One Zero or Two? Dewey Blog. September 28, 2006 ISKO-2010, Rome ©ZengPanzerSalaba rules

The intersection of two classes ISKO-2010, Rome ©ZengPanzerSalaba

ObjectIntersectionOf DDC: 616.12 03 Heart diseases—rehabilitation built with: 616.12 Diseases of heart + 03 Rehabilitation from the add table under 616.1–616.9 Specific diseases following the add footnote at 616.12 : “Add as instructed under 616.1–616.9”. EquivalentClasses( :616.1203 ObjectIntersectionOf( :616.12 :03 ) ) [In Functional-Style Syntax] ISKO-2010, Rome ©ZengPanzerSalaba

The union of two classes --contains every individual which is contained in at least one of these classes ObjectUnionOf Union classes, e.g., 641 Food and Drink 020 Library & Information Science 025.24 Information Storage and Retrieval System Notes: “ class here” “ including” ISKO-2010, Rome ©ZengPanzerSalaba

“ including” “class here” “class elsewhere” Example from DDC 025.04 Information Storage and Retrieval Systems ISKO-2010, Rome ©ZengPanzerSalaba

The complement of a class -- corresponds to logical negation: It consists of exactly those objects which are not members of the class itself. ObjectComplementOf e.g., 025.24 Information Storage and Retrieval System Notes : For computer science aspects of information storage and retrieval systems, of databases, see 005.74 ISKO-2010, Rome ©ZengPanzerSalaba

Review: Our interests in OWL Class expression Built classes Classes to be built according to rules and instructions Class : Class Class + Auxiliary Table Class + Added Table Class + implied example Relationship expression Typical Class-to-class SubClassOf DisjointClasses EquivelantClasses More complicated Class-to-class Class-to-topic Index terms Class-here Class-elsewhere See reference … ISKO-2010, Rome ©ZengPanzerSalaba

3.2 AXIOMs for relationships between class expressions OWL 2 provides axioms (statements that say what is true in the domain) that allow relationships to be established between class expressions: SubClassOf EquivalentClasses DisjointClasses DisjointUnion ISKO-2010, Rome ©ZengPanzerSalaba

Overview: The Class Axioms of OWL 2 http://www.w3.org/TR/owl2-syntax/#Inverse_Object_Properties ISKO-2010, Rome ©ZengPanzerSalaba

SubClassOf axiom SubClassOf axiom: allows one to state that each instance of one class expression is also an instance of another class expression, and thus to construct a hierarchy of classes. Subclass axioms are a fundamental type of axioms in OWL 2 and can be used to construct a class hierarchy. ISKO-2010, Rome ©ZengPanzerSalaba

DisjointClasses axiom DisjointClasses axiom: allows one to state that several class expressions are pairwise disjoint — that is, they have no instances in common. DisjointUnion class expression: allows one to define a class as a disjoint union of several class expressions and thus to express covering constraints. Such axioms are sometimes referred to as covering axioms. ISKO-2010, Rome ©ZengPanzerSalaba

EquivalentClasses axiom EquivalentClasses axiom: allows one to state that several class expressions are equivalent to each other. Can be used in classifications for building equivalent classes expressing equivalent classes  see example etc. ISKO-2010, Rome ©ZengPanzerSalaba

EquivalentClasses axiom for Alternative Classes However this is not enough. There are also certain relationship types and constrains between the classes. EquivalentClasses ( :X17 : Q89) ISKO-2010, Rome ©ZengPanzerSalaba [ ] [Q89 Environmental Biology] Preferred class: X17 Example from Chinese Library Classification (CLC): X17 Environmental Biology …… ……

3.3 Properties and restrictions for more complicated class expressions and relationships More complicated relationships Class-to-class Class-to-topic Index terms Class-here Class-elsewhere See reference … ISKO-2010, Rome ©ZengPanzerSalaba

1) Symmetric Object Property [Q89 Environmental Biology] Preferred class: X17 CLC’s alternative classes X17 Environmental Biology …… …… EquivalentClasses ( :X17 S ymmertricbjectProperty ( :isAlternativeClass : Q89) ) ISKO-2010, Rome ©ZengPanzerSalaba [ ]

2) Inverse object properties inverse object properties -- allow for bidirectional navigation in class expressions and axioms. Could be useful for the expressions of a class and its related index entries e.g., we can establish such a property relation: InverseObjectProperties( :hasIndexTerm :isIndexTermOf ) ISKO-2010, Rome ©ZengPanzerSalaba

DDC: 616 Diseases: Clinical medicine Diseases—humans—-medicine Illness—medicine Internal medicine Physical illness—medicine Sickness—medicine InverseObjectProperties( :hasIndexTerm :isIndexTermOf ) EquivalentClasses( :616 ObjectInverseOf ( ObjectOneOf ( : Clinical medicine :Diseases—humans—- medicine :Illness—medicine :Internal medicine :Physical illness—medicine :Sickness—medicine) ) ) ISKO-2010, Rome ©ZengPanzerSalaba

3) Restrictions allValuesFrom someValuesFrom hasValue minCardinality maxCardinality cardinality Quantifier Restrictions ( Existential ∃ , Universal ∀) Cardinality Restrictions (Min ≥, Equal =, Max ≤) Has Value Restriction (∍) Define a condition for property values Classes are created by restricting the property values on its individuals ISKO-2010, Rome ©ZengPanzerSalaba

Restrictions can be applied to deal with class–topic relationships 370.113 Vocational education Class here career education , occupational training , vocational schools Class on-the-job training , vocational training provided by industry in 331.2592 For vocational education at secondary level , see 373.246 ; for adult vocational education , see 374.013 Topical neighborhood shaped by (among other things): Caption Class-here note Inclusion of topics Exclusion of topics Class-elsewhere note See reference ISKO-2010, Rome ©ZengPanzerSalaba

Summary: Our interests in Expressing Classification Schemes with OWL Class expression Built classes Classes to be built according to rules and instructions Class : Class Class + Auxiliary Table Class + Added Table Class + implied example Relationship expression Typical Class-to-class SubClassOf DisjointClasses EquivelantClasses More complicated Class-to-class Class-to-topic Index terms Class-here Class-elsewhere See reference … ISKO-2010, Rome ©ZengPanzerSalaba

Expressing Classification Schemes -- Part 3

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