Representation of Concept Representation of Concept Specialization - PowerPoint PPT Presentation

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

The gen gen- -spec spec relation relation The • The gen gen- -spec spec relation describes relation describes • The hierarchies of concepts hierarchies of concepts ( classifiers classifiers ) organized around the ) organized around the ( notion of strictly additive strictly additive notion of extension. extension. – Essentially (Liskov’s Liskov’s subtype requirement): subtype requirement): – Essentially ( if a property Φ Φ Φ Φ (x) Φ ∈ ∈ ∈ T ∈ Φ Φ Φ x ∈ ∈ ∈ ∈ (x) applies to instances applies to instances x if a property T , Φ Φ (y) Φ Φ Φ ∀ y ∀ ∀ ∀ ∈ ∈ ∈ S ∈ Φ Φ Φ (y) ∀ ∀ ∀ ∀ y ∈ ∈ ∈ ∈ then if S then if S is a subclass of is a subclass of T T , 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 ontologies ontologies), ), representation (including databases and OO programming. databases and OO programming.

The notion of specialization distance The notion of specialization distance • The gen gen- -spec spec relation is usually relation is usually • The considered as equally strong equally strong considered as between any pair of classifiers. between any pair of classifiers. • But humans are capable of • But humans are capable of assessing (at least, in relative relative assessing (at least, in terms) how much how much a subclass a subclass terms) differs from one of its super- - differs from one of its super classes (and vice vice- -versa versa ). ). classes (and A modeling notion of specialization specialization – – A modeling notion of distance distance is needed. is needed.

Example of specialization distance Example of specialization distance UNSPSC example UNSPSC example... ... Musical-Instruments, Recreational Equipment, Supplies and Accesories “longest” Musical-Instruments Fitness-Equipment Toys “intermediate” Keyboard-Instruments “shortest” Pianos Musical-Organs Accordions

Discriminators Discriminators • From a specific class A , a number a number • From a specific class A , of specialization hierarchies may be of specialization hierarchies may be defined by different discriminators. discriminators. defined by different – 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 Cyc Cyc ’s ’s RoadVehicle ): – Example (from class RoadVehicle ): d motor = {RoadVehicle-Electric, RoadVehicle-InternalCombustion} d room = {Bus, Automobile, Motorcycle}

Resemblance Relations as spec spec- -distance distance Resemblance Relations as • A resemblance relation A resemblance relation • × × D × × → [0..1] → → → R:D × × × × D → → → → [0..1] is a reflexive and is a reflexive and R:D symmetric relation that expresses a symmetric relation that expresses a form of partial (di di- -)similarity. )similarity. form of partial ( – We use them as an We use them as an operationalization operationalization – of the intuitive notion of spec distance spec distance . . of the intuitive notion of – They are defined locally to a class in They are defined locally to a class in – the form: : the form :{c} × × × p × × × × × (d,c) → → → → → [0..1] → → → R X p (d,c) [0..1] R X :{c} given that p represent the set of given that p (d,c) (d,c) represent the set of subclasses of c c discriminated by discriminated by d . subclasses of d .

Assessing spec distances spec distances Assessing • 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 sub sub- -tree tree level, in which distances level, in which distances – At a (obtained at the micro- -level) inside a level) inside a (obtained at the micro 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 B B is closer to is closer to superclass superclass A “subclass A then subclass C ”) need to be converted then subclass C ”) need to be converted to numerical values heuristically heuristically (i.e. (i.e. to numerical values comparing the assessments). comparing the assessments).

Case Study (I) Case Study (I) • We have extended DAML+OIL Web We have extended DAML+OIL Web • ontology description language to ontology description language to represent the just described represent the just described resemblance relations resemblance relations <daml < daml:Class :Class rdf rdf:ID="A"> :ID="A"> < <rdfs rdfs: :subClassOf rdf subClassOf rdf:resource="#B"> :resource="#B"> <ext:withDiscriminator rdf <ext: withDiscriminator rdf:ID= :ID=” ”d1 d1” ”/> /> <ext:withResemblance <ext: withResemblance grade= grade=” ”0.8 0.8” ”/> /> </ </rdfs rdfs: :subClassOf subClassOf> > </daml </ daml:Class> :Class> Sample RDF markup Sample RDF markup

Case Study (II I) ) Case Study (I • A recommender agent posses a set of A recommender agent posses a set of • beliefs C about the “interest” of user U beliefs U about the “interest” of user C U U in some subjects. in some subjects. piano ∈ ∈ ∈ C ∈ ∈ ∈ ∈ ∈ – If – If piano U then the agent has two options: then the agent has two options: C U • going up to going up to Keyboard , or • Keyboard- -instruments instruments , 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 as a measure of the as a measure of the distance differentiation grade grade of a classifier differentiation of a classifier from its sub- -classifiers. classifiers. from its sub • Spec distance Spec distance can be represented as a can be represented as a • set of (partial) resemblance relations resemblance relations . . set of (partial) – 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 reliable reliable and and valid valid approach approach up with a 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- -spec spec relation, e.g.: relation, e.g.: gen – Distance between ‘ Distance between ‘ siblings siblings ’ ’ – – Semantic relatedness between Semantic relatedness between – discriminators. discriminators.