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An Introduction toDescription Logics

(chapter 2 of DLHB)

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What Are Description Logics?

•  A family of logic based Knowledge Representation formalisms

 – Descendants of semantic networks and KL-ONE

 – Describe domain in terms of concepts (classes), roles

(relationships) and individuals

• Distinguished by: – Formal semantics (typically model theoretic)

• Decidable fragments of !"

• #losely related to $ropositional %odal & Dynamic "ogics

 – $ro'ision of inference services

• ound and complete decision procedures for ey problems

• *mplemented systems (highly optimised)

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Origions of DLs

• Knowledge connecting persons, parents, etc.• Described as semantic network 

• Semantic networks whitout a semantics

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DL Architecture

Knowledge Base

Tbox (schema)

Abox (data)

Man ´ Human u Male

Happy-Father ´ Man u 9 has-childFemale u 

!ohn " Happy-Father

h!ohn# Maryi " has-child  I

  n   f  e

  r  e  n  c  e   $  y  s

   t  e  m

   I  n   t  e  r   f  a  c  e

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Short History of Description Logics

Phase 1:

 – *ncomplete systems (+ac, #lassic, "oom, )

 – +ased on structural algorithms

Phase :

 – De'elopment of ta!leau algorithms and comple"it# results

 – -ableau.based systems for Pspace logics (eg, Kris, #rac)

 – *n'estigation of optimisation techni/ues

Phase $:

 – -ableau algorithms for ver# e"pressive D"s – %ighl# optimised tableau systems for E"p&ime logics (eg, a#-,

D"$, Racer)

 – Relationship to modal logic and decidable fragments of !"

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Latest Developments

Phase ':

 – %ature implementations

 – %ainstream applications and -ools

• (ata!ases

 – #onsistency of conceptual schemata (00R, 1%" etc)

 – chema integration

 – 2uery subsumption (wrt a conceptual schema)

• !ntologies and )emantic *e! (and +rid)

 – !ntology engineering (design, maintenance, integration)

 – Reasoning with ontology.based marup (meta.data)

 – er'ice description and disco'ery

 – ,ommercial implementations

• #erebra system from 3etwor *nference "td

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Description Logic Family

• (Ls are a famil# of logic !ased K formalisms

• Particular languages mainl# characterised !#: – )et of constructors for !uilding comple" concepts and roles

from simpler ones

 – )et of a"ioms for asserting facts a!out concepts. roles andindividuals

• )implest logic in this famil# is named AL

• Others are specified !# adding some suffi"es like U ε N C:

 – ALC

 – ALCU

 – etc/

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Description logic AL 

• Example constructs:

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More AL family members

• (is0unction U2

• Full e"istential 3uantification ε 2

• Num!er restrictions N2

• Full negation C2

• E"ample:

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Other DL Concept an !ole

Constructors• ange of other constructors found in (Ls. including: – 4ualified num!er restrictions. e/g/. ≤ has,hild/Female.

≥1 hasParent/5ale

 – Nominals singleton concepts2. e/g/. 67tal#8

 – 7nverse roles. e/g/. has,hild 9  hasParent2 – &ransitive roles. e/g/. has,hild descendant2

 – ole composition. e/g/. hasParent o has;rother uncle2

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DL as fragments of "reicate Logic

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Lisp li#e style for DL

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DL $no%lege &ase

• (L Knowledge ;ase K;2 normall# separated into parts:

 – &;o" is a set of a"ioms descri!ing structure of domain i/e/. a

conceptual schema2. e/g/:

• %app#Father ≡ 5an ⊆  has,hild/Female Π <

• Elephant ⊆ =nimal ΠLarge Π +re#

• transitiveancestor2

 – =;o" is a set of a"ioms descri!ing a concrete situation data2.

e/g/:

• >ohn:%app#Father 

• ?>ohn.5ar#@:has,hild

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'erminologies or '&o(es

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'erminologies or 'bo(es )cont*+

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,nference services

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,nference service- concept satisfiability

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,nference services base on satisfiability

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,nference service- concept subsumption

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Concept e(amples

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.(ample ta(onomy

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Worl escription- A&o(

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A&o( inference services

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Abo( inference services )cont*+

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A&o( e(ample

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'&o( ta(onomy plus iniviuals

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Open %orl assumption