74.419 Artificial Intelligence 2004 - 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 setsRoles• correspond to binary predicates / relationsFeatures• correspond to functionsConcept-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) DD

(defconcept Parent (AND Person (has-child.Person))I (Parent) I (Person) {xD | y: (x,y)

I (has-child) y I (Person) }

(defconcept Man (AND Person (gender.Male)) I (Man) I (Person) {xD | 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-1 12050)))

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-2 9000))

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):367-397, 1994

• LOOM (Bob McGregor, USC)

http://www.isi.edu/isd/LOOM/LOOM-HOME.html

see course web page for links