Artificial Intelligence Description Logics - Background and Motivation for DL Relation between DL and FOPL (extensional Semantics) Example Definitions The horrible truth of DL T-Box, A-Box LOOM

Description Logics - Background Prevent flaws of Semantic Networks; provide clear semantics of nodes and links Derived from Inheritance Hierarchies (IS-A hierarchies; taxonomies; terminologies) and Frame Systems  Concepts, Roles, Features Series of KR Languages starting with KL-ONE, later KL-TWO, LOOM, CLASSIC,... Relate to FOPL via extensional semantics Applied e.g. in Semantic Web Languages (DAML+OIL)

Description Logics - Overview DL provide language constructs to define concepts. Concepts are interpreted as sets of individuals (extensional semantics). Concept definitions are linear expressions, combining concepts, roles, etc. to express constraints on the fillers of the concept. The IS-A hierarchy is reflected in the subsumption relation (super-class–sub-class relation), interpreted through set-inclusion.

Description Logics – Basic Elements Concepts Roles Features / Attributes Definition of concepts e.g. father  (AND (Parent Man)), Biped  (AND (Animal (exactly 2 has-legs Legs))) Primary / Atomic Concepts and Roles (not completely defined) Individual Concepts (define singletons) Instances (entities)

Description Logics – Principles Concepts correspond to unary predicates or sets Roles correspond to binary predicates / relations Features correspond to functions Concept-Definitions constrain filler-sets composed of concepts, roles, role restrictions using AND, OR, min-number, max-number etc. (Human (AND (Animal Biped Featherless))

Concept Definitions - Example (defconcept Person primary-concept) I (Person)  D (defrole gender atomic-role) I (gender)  D  D (defconcept Parent (AND Person (  has-child.Person)) I (Parent)  I (Person)  {x  D |  y: (x,y)  I (has-child)  y  I (Person) } (defconcept Man (AND Person (  gender.Male)) I (Man)  I (Person)  {x  D |  y: (x,y)  I( gender)  y  I (Male)}

Basic Architecture and Functions T-Box – terminological knowledge (definition of concepts) A-Box – assertional knowledge (statements about instances, concrete objects) Classification - insert concept into hierarchy based on it's description / definition TELL – insert knowledge into KB, e.g. define new concept or assert instance info ASK – querying KB,e.g. ask about existence of instance

LOOM - T-Box Example T-Box (Concept Definitions) (defconcept Person) (defrelation has-child :domain Person :range Person) (defconcept Male) (defconcept Person-with-Sons :is (:and Person (:at-least 1 has-child Male))) (defconcept Person-with-Two-Sons :is (and Person (:exactly 2 has-child Male)))

LOOM - A-Box Example A-Box (Assertions, Statements ) (tell (Person Fred)) (tell (has-child Fred Sandy)) (tell (Male Sandy))

LOOM - Example KB (defconcept Person) (defrelation has-child :domain Person :range Person) (defconcept Male) (defconcept Person-with-Sons :is (:and Person (:at-least 1 has-child Male))) (defconcept Person-with-Two-Sons :is (and Person (:exactly 2 has-child Male))) (tell (Person Fred)) (tell (has-child Fred Sandy)) (tell (Male Sandy))

LOOM - Example Reasoning (defconcept Person) (defrelation has-child :domain Person :range Person) (defconcept Male) (defconcept Person-with-Sons :is (:and Person (:at-least 1 has-child Male)))... (tell (Person Fred)) (tell (has-child Fred Sandy)) (tell (Male Sandy)) Conclude: (Person-with-Sons Fred)

LOOM - Program: definitions > (defconcept air-base :is-primitive (and Military-Installation (exactly 1 name) (at-least 1 runway-length) (exactly 1 service-branch))) |C|AIR-BASE > (defrelation name :range string) |R|NAME > (defrelation runway-length :domain air-base :range number) |R|RUNWAY-LENGTH

LOOM - Program: tell > (tellm (create ab-1 air-base) (name ab-1 "Atlanta NAS") (runway-length ab ))) Recognition changes at agent time 1: entry: AB-1 |C|MILITARY-INSTALLATION entry: AB-1 |C|AIR-BASE > (tellm (create ab-2 air-base) (name ab-2 "Mainland NAS") (runway-length ab )) Recognition changes at agent time 2: entry: AB-2 |C|MILITARY-INSTALLATION entry: AB-2 |C|AIR-BASE infered

LOOM - Program: retrieve > (retrieve ?p (air-base ?p)) ( |I| AB-1 |I| AB-2 ) > (retrieve ?p (and (air-base ?p) (for-some (?l) (and (runway-length ?p ?l) (> ?l 10000))))) ( |I| AB-1 ) Instances AB-1, AB-2 Instance AB-1

References Ian Horrocks and Ulrike Sattler: Description Logics - Basics, Applications, and More J. Heinsohn et al.: An Empirical Analysis of Terminological Representation Systems, Artificial Intelligence 68(2): , 1994 LOOM (Bob McGregor, USC) see course web page for links