Representation of Concept Representation of Concept Specialization - - PowerPoint PPT Presentation

Representation of Concept Representation of Concept Specialization Distance through Specialization Distance through Resemblance Resemblance R Relations elations

Miguel-Ángel Sicilia, Elena García*, Paloma Díaz, Ignacio Aedo

DEI Laboratory, Carlos III University {msicilia, pdp}@inf.uc3m.es, aedo@ia.uc3m.es

*Computer Science Dept, Alcalá University

elena.garciab@uah.es

Contents Contents

1. 1. The The gen gen/spec /spec relation relation 2. 2. The notion of The notion of Spec Distance Spec Distance 3. 3. Discriminators Discriminators and and subclassing subclassing 4. 4. Resemblance Relations as Resemblance Relations as measures of measures of Spec Spec Distance Distance 5. 5. Assessing resemblance relations Assessing resemblance relations 6. 6. Case Study Case Study 7. 7. Conclusions and future directions Conclusions and future directions

The The gen gen-

• spec

spec relation relation

• The

The gen gen-

• spec

spec relation describes relation describes hierarchies of concepts hierarchies of concepts ( (classifiers classifiers) organized around the ) organized around the notion of notion of strictly additive strictly additive extension. extension.

– – Essentially ( Essentially (Liskov’s Liskov’s subtype requirement): subtype requirement):

if a property if a property Φ Φ Φ Φ Φ Φ Φ Φ(x) (x) applies to instances applies to instances x x∈ ∈ ∈ ∈ ∈ ∈ ∈ ∈T T then if then if S S is a subclass of is a subclass of T T, , Φ Φ Φ Φ Φ Φ Φ Φ(y) (y)∀ ∀ ∀ ∀ ∀ ∀ ∀ ∀y y∈ ∈ ∈ ∈ ∈ ∈ ∈ ∈S S must must be true. be true.

– – Used under different names (terms, Used under different names (terms, concepts, types) in knowledge concepts, types) in knowledge representation (including representation (including ontologies

• ntologies),

), databases and OO programming. databases and OO programming.

The notion of specialization distance The notion of specialization distance

• The

The gen gen-

• spec

spec relation is usually relation is usually considered as considered as equally strong equally strong between any pair of classifiers. between any pair of classifiers.

• But humans are capable of

But humans are capable of assessing (at least, in assessing (at least, in relative relative terms) terms) how much how much a subclass a subclass differs from one of its super differs from one of its super-

• classes (and

classes (and vice vice-

• versa

versa). ).

– – A modeling notion of A modeling notion of specialization specialization distance distance is needed. is needed.

Example of specialization distance Example of specialization distance

Musical-Instruments Keyboard-Instruments Pianos Musical-Organs Accordions Musical-Instruments, Recreational Equipment, Supplies and Accesories Fitness-Equipment Toys

“shortest” “intermediate” “longest”

UNSPSC UNSPSC example example... ...

Discriminators Discriminators

• From a specific class

From a specific class A A, , a number a number

• f specialization hierarchies may be
• f specialization hierarchies may be

defined by different defined by different discriminators. discriminators.

– – In their most simple definition, discriminators In their most simple definition, discriminators can be defined as subsets of subclasses from can be defined as subsets of subclasses from a specific class. a specific class. – – Example (from class Example (from class Cyc Cyc’s ’s RoadVehicle RoadVehicle): ):

dmotor= {RoadVehicle-Electric, RoadVehicle-InternalCombustion} droom = {Bus, Automobile, Motorcycle}

Resemblance Relations as Resemblance Relations as spec spec-

• distance

distance

• A resemblance relation

A resemblance relation

R:D R:D× × × × × × × ×D D→ → → → → → → →[0..1] [0..1] is a reflexive and

is a reflexive and symmetric relation that expresses a symmetric relation that expresses a form of partial ( form of partial (di di-

• )similarity.

)similarity.

– – We use them as an We use them as an operationalization

• perationalization
• f the intuitive notion of
• f the intuitive notion of spec distance

spec distance. . – – They are defined locally to a class in They are defined locally to a class in the form the form: :

R RX

X:{c}

:{c} × × × × × × × × p p(d,c)

(d,c)→

→ → → → → → →[0..1] [0..1]

given that given that p p(d,c)

(d,c) represent the set of

represent the set of subclasses of subclasses of c c discriminated by discriminated by d d. .

Assessing Assessing spec distances spec distances

• Two levels:

Two levels:

– – A A micro micro-

• level

level, in which the distance between , in which the distance between a class and its subclasses for a class and its subclasses for a specific a specific discriminator is assessed. discriminator is assessed. – – At a At a sub sub-

• tree

tree level, in which distances level, in which distances (obtained at the micro (obtained at the micro-

• level) inside a

level) inside a hierarchy tree including descendants of a hierarchy tree including descendants of a given classifier are somehow ’harmonized’. given classifier are somehow ’harmonized’.

• In both cases, human assessments (like

In both cases, human assessments (like “subclass “subclass B B is closer to is closer to superclass superclass A A then subclass then subclass C C”) need to be converted ”) need to be converted to numerical values to numerical values heuristically heuristically (i.e. (i.e. comparing the assessments). comparing the assessments).

Case Study (I) Case Study (I)

• We have extended DAML+OIL Web

We have extended DAML+OIL Web

• ntology description language to
• ntology description language to

represent the just described represent the just described resemblance relations resemblance relations

Sample RDF markup Sample RDF markup < <daml daml:Class :Class rdf rdf:ID="A"> :ID="A"> < <rdfs rdfs: :subClassOf rdf subClassOf rdf:resource="#B"> :resource="#B"> <ext: <ext:withDiscriminator rdf withDiscriminator rdf:ID= :ID=” ”d1 d1” ”/> /> <ext: <ext:withResemblance withResemblance grade= grade=” ”0.8 0.8” ”/> /> </ </rdfs rdfs: :subClassOf subClassOf> > </ </daml daml:Class> :Class>

Case Study (I Case Study (II I) )

• A recommender agent posses a set of

A recommender agent posses a set of beliefs beliefs C CU

U about the “interest” of user

about the “interest” of user U U in some subjects. in some subjects.

– – If If piano

piano ∈ ∈ ∈ ∈ ∈ ∈ ∈ ∈ C CU

U then the agent has two options:

then the agent has two options:

• going up to

going up to Keyboard Keyboard-

• instruments

instruments, or , or

• down to specializations of

down to specializations of piano piano (like spinet, (like spinet, console or grand pianos). console or grand pianos).

– – The agent would choose the shorter distance The agent would choose the shorter distance (the larger resemblance) (the larger resemblance)

• in this case, down, since the way up represents a

in this case, down, since the way up represents a bigger step. bigger step.

– – This behavior may prevent the agent to jump to This behavior may prevent the agent to jump to “excessively” abstract categories. “excessively” abstract categories.

Conclusions Conclusions

• We have introduced the notion of

We have introduced the notion of spec spec distance distance as a measure of the as a measure of the differentiation differentiation grade grade of a classifier

• f a classifier

from its sub from its sub-

• classifiers.

classifiers.

• Spec distance

Spec distance can be represented as a can be represented as a set of (partial) set of (partial) resemblance relations resemblance relations. .

– – The elicitation of that relations from The elicitation of that relations from humans can be carried out locally to a humans can be carried out locally to a class, or along a hierarchy path. class, or along a hierarchy path. – – The presented approach can be The presented approach can be represented in DAML+OIL and used to represented in DAML+OIL and used to build adaptation behaviors. build adaptation behaviors.

Future Directions Future Directions

• Empirical studies

Empirical studies are required to come are required to come up with a up with a reliable reliable and and valid valid approach approach to the construction of this kind of to the construction of this kind of resemblance relations. resemblance relations.

• Related topics on the structure of the

Related topics on the structure of the gen gen-

• spec

spec relation, e.g.: relation, e.g.:

– – Distance between ‘ Distance between ‘siblings siblings’ ’ – – Semantic relatedness between Semantic relatedness between discriminators. discriminators.