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Concept Definitions & Inheritance in Knowledge Base: Description Logics & Data Management , Study notes of Computer Science

University of California - DavisComputer Science
Prof. Bertram T. Ludaescher

Description logics (dl), a logic language used for defining concepts and interrelating them to constrain meaning. The use of dl in scientific data management, specifically in 'gluing' sources and registering domain knowledge. The document also introduces the concepts of roots, structured inheritance networks, and knowledge bases in dl-style. Examples and exercises are provided to illustrate the concepts.

Typology: Study notes

Pre 2010

Uploaded on 07/31/2009

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B. Ludaescher, ECS289F-W05, Topics in Scientific D ata Management
Description Logic(s)
• Formerly known as “terminological logic(s)”
• Idea: logic language for
– defining concepts in terms of other concepts
– interrelating concepts
Îconstraining the meaning of concepts
• DL definition of “Happy Father”
(Example from Ian Horrocks, Ulrike Sattler)
B. Ludaescher, ECS289F-W05, Topics in Scientific D ata Management
formalized as an “ontology graph”
Purkinje cells and Pyramidal cells have dendrites
that have higher-order branches that contain spines.
Dendritic spines are ion (calcium) regulating components.
Spines have ion binding proteins. Neurotransmission
involves ionic activity (release). Ion-binding proteins
control ion activity (propagation) in a cell. Ion-regulating
components of cells affect ionic activity (release).
domain expert knowledge
Made usable for the system
using Description Logic
Example: Domain Knowledge
to “glue”
SYNAPSE
&
NCMIR
Data
B. Ludaescher, ECS289F-W05, Topics in Scientific D ata Management
Source Contextualization
through Ontology Refinement
In addition to registering
(“hanging off”) data relative to
existing concepts, a source
may also refine the mediator’s
domain map...
⇒
sources can register new
concepts at the mediator ...
⇒
increase your data usability
pf3
pf4

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B. Ludaescher, ECS289F-W05, Topics in Scientific Data Management

Description Logic(s)

  • Formerly known as “terminological logic(s)”
  • Idea: logic language for
    • defining concepts in terms of other concepts
    • interrelating concepts Î constraining the meaning of concepts
  • DL definition of “Happy Father” (Example from Ian Horrocks, Ulrike Sattler)

B. Ludaescher, ECS289F-W05, Topics in Scientific Data Management formalized as an “ontology graph”

Purkinje cells and Pyramidal cells have dendrites that have higher-order branches that contain spines. Dendritic spines are ion (calcium) regulating components. Spines have ion binding proteins. Neurotransmission involves ionic activity ( release ). Ion-binding proteins control ion activity (propagation) in a cell. Ion-regulating components of cells affect ionic activity ( release ).

domain expert knowledge

Made usable for the system using Description Logic

Example: Domain Knowledge

to “glue” SYNAPSE & NCMIR

Data

B. Ludaescher, ECS289F-W05, Topics in Scientific Data Management

Source Contextualization

through Ontology Refinement

In addition to registering (“hanging off”) data relative to existing concepts, a source may also refine the mediator’s domain map...

⇒ sources can register new concepts at the mediator ... ⇒ increase your data usability

B. Ludaescher, ECS289F-W05, Topics in Scientific Data Management

Roots

  • “Structured Inheritance Networks” [Brachman 1977]
  • KL-ONE [Brachman, Schmolze 1985]
  • Core ideas:
    • Building blocks: atomic concepts (unary predicates), atomic roles (binary predicates), individuals (constants)
    • Constructors for building complex concepts and roles from simpler ones
    • Automated inference for concept subsumption and instance classification (is-a/is-instance-of are not explicitly given by the user, but inferred from concept definitions/instance properties)

B. Ludaescher, ECS289F-W05, Topics in Scientific Data Management

Source: Description Logics Tutorial, Ian Horrocks and Ulrike Sattler, ECAI-2002, Lyon, France, July 23rd, 2002

(TBox)

(ABox)

B. Ludaescher, ECS289F-W05, Topics in Scientific Data Management

Knowledge Base (DL-Style)

  • Terminological Knowledge (TBox)
    • Concept Definition (naming of concepts):
    • Axiom (constraining of concepts):

=> a mediators “glue knowledge source”

  • Assertional Knowledge (ABox) about Individuals
    • n27_img118 : Neuron => the concrete instances/individuals of the concepts/classes that your sources export

B. Ludaescher, ECS289F-W05, Topics in Scientific Data Management

Back to Reasoning with the Family ...

  • concept definition: MyConcept ≡ DL-formula
  • concept inclusion: MyConcept ⊆ DL-formula
  • finite set of definitions is a terminology or TBox if

for every atomic concept A there is at most one

axiom whose lhs is A

B. Ludaescher, ECS289F-W05, Topics in Scientific Data Management

Definitorial Terminologies

  • In a Tbox T we distinguish: primitive concepts (occurring only on rhs) and defined concepts (occurring on lhs)
  • T is definitorial if every interpretation of primitive concepts yields exactly one model of T (and thus for the defined concepts) Î meaning of defined concepts is fixed once the primitive concepts are interpreted!
  • A directly uses B in T if B appears in the rhs of the definition of A
  • A uses B is the transitive closure of ‘ directly uses’
  • T is cyclic if A uses A for some A; else acyclic

One can show: If T is acyclic then T is definitorial

What about this one?

B. Ludaescher, ECS289F-W05, Topics in Scientific Data Management

Expansion of Terminologies

  • For acyclic T we can “unfold” concept

definitions until every defined concepts is

specified in terms of primitive concepts only

Î the expansion of a TBox T

  • Example: