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Part-Whole Reasoning in Object-Centered Frameworks. Patrick Lambrix Linköpings universitet. Outline. Databases Knowledge representation - early approaches - description logics. Databases.

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Part whole reasoning in object centered frameworks l.jpg

Part-Whole Reasoning in Object-Centered Frameworks

Patrick Lambrix

Linköpings universitet


Outline l.jpg
Outline

  • Databases

  • Knowledge representation

    - early approaches

    - description logics


Databases l.jpg
Databases

  • Support for complex/composite objects one of the important requirements for object-oriented databases.

    - object-oriented database system manifesto, 1989

    - third-generation database system manifesto, 1990.


Requirements for databases supporting composite objects l.jpg
Requirements for DatabasesSupporting Composite Objects

  • Object identity to which parts can be assigned.

  • Modeling of part-whole relations.

  • Derived values in wholes and parts.

  • Wholes can be manipulated as a whole.

  • Constraints on part-whole relations.

  • View composite objects at different levels.

  • Flexible transaction management.


Orion l.jpg
ORION

  • Composite objects are classified with respect to:

    - dependent parts

    - exclusive / shared parts

  • Query facilities for traversing part-of hierarchy.

  • Clustering, authorization, locking.


Change propagation l.jpg
Change propagation

  • Issue in several other OODBMSs

    Should changes in parts (always) be propagated to the whole?

    Should new versions of parts give rise to new versions of the whole?


Early approaches in knowledge representation l.jpg
Early approaches in knowledge representation

  • CSAW (1977)

  • Represent part-of

  • Dependence

  • NETL (1979)

  • Represent part-of, transitive

  • Transitive closure

  • Part-of hierarchy is integrated in semantic network


Early approaches in knowledge representation8 l.jpg
Early approaches in knowledge representation

  • Schubert (1979, 1981)

  • Represent part-of, partial ordering, object level

  • Extensionality

  • Unique empty part

  • Overlap, merging, difference operators

  • Parts graph based on partitions


Slide9 l.jpg

lamp

P

P

electrical

system

support

structure

stand

top

P

P

lamp

shade

socket

bulb

cord

switch

P

cable

plug



Part whole reasoning in description logics11 l.jpg
Part-whole reasoning in description logics

  • Conceptual modeling issues

  • P: A language for an engineering application (Sattler)

  • ALCS: quantifying over collections and parts (Franconi)

  • ’inheritance’ via part-of (Bernauer)

  • Reasoning services

    (Lambrix, Padgham & Shahmehri)


Conceptual modeling issues l.jpg
Conceptual modeling issues

  • Explicit introduction of wholes in the model

  • Clear distinction between parts and other attributes of a whole

  • Transitivity issues

  • Names of parts

  • Vertical and horizontal relationships


Explicit introduction of wholes in the model l.jpg

Implicit

John:

age: 35

sex: male

wife: Mary

Mary:

age: 33

sex: female

husband: John

Explicit

John:

age: 35

sex: male

Mary:

age: 33

sex: female

Mary-john-family:

wife: Mary

husband: John

Explicit introduction of wholes in the model


Explicit introduction of wholes in the model14 l.jpg
Explicit introduction of wholes in the model

  • Reusability

  • Understandability

  • Extendibility


Clear distinction between parts and other attributes of a whole l.jpg
Clear distinction between parts and other attributes of a whole

  • Distinguish part attributes from other attributes

  • Needed for first-class status of part attributes (particular semantics, reasoning services)


Transitivity issues l.jpg
Transitivity issues whole

  • PART-OF, transitive

  • Basic PART-OF, transitive

    Non-transitive sub-relations possible

  • Kinds of part-whole relations


Names of parts l.jpg

Car(car1), whole

wheel1 < car1

Wheel(wheel1)

Car(car1)

Has-wheel(car1,wheel1)

Wheel(wheel1)

Implicit assumption

Has-wheel is a kind of part attribute

Names of parts


Names of parts18 l.jpg
Names of parts whole

  • Part attributes need to be tagged

  • Formal properties of PART-OF may not hold for sub-relations (e.g. transitivity)

  • Easy to specify particular characteristics (e.g. domain and cardinality restrictions)


Vertical and horizontal relationships l.jpg
Vertical and horizontal relationships whole

  • Vertical relationships

  • Dependence between the existence of the whole and the existence of parts (and vice versa)

  • Dependence between the properties of the whole and of the parts (and vice versa)


Vertical and horizontal relationships20 l.jpg
Vertical and horizontal relationships whole

  • Horizontal relationships

  • Constraints among parts that characterize the integrity of the whole



Main ideas l.jpg
Main ideas whole

  • Different kinds of part-whole relations

  • Inverses (whole-part relations)

  • Composition table of part relations

  • Specific interactions between parts and whole


Direct part whole relations l.jpg
Direct part-whole relations whole

  • Is-direct-component

  • Is-direct-member

  • Is-direct-segment

  • Is-direct-quantity

  • Is-direct-stuff

  • Is-direct-ingredient


Part whole and whole part relations l.jpg
Part-whole and whole-part relations whole

  • Part-whole relations:

    transitive closures of direct relations

  • Whole-part relations:

    Inverses of part-whole relations


Composition tables l.jpg
Composition tables whole

CC

MC

SE

SO

IO

CC

MC

SE

QM

SO

IO


Interactions between parts and whole l.jpg
Interactions between parts and whole whole

  • Exclusive parts: one of the direct part roles has at most one filler.

    Brain =

    (and (atmost 1 Is-direct-component Human) …)

  • Essential parts: existence of part is essential.

    Human =

    (and (exists (inv Is-direct-component) Brain) …)


Language l.jpg
Language whole

  • ALC +

    Inverse roles

    Role disjunction

    Role composition

    Transitive closure of roles

    Qualified number restrictions

    Role conjunction



Main ideas29 l.jpg
Main ideas whole

  • Give semantics to plurals and plural quantifiers

  • Quantifiers for different plural readings

    The Beatles sing ’yesterday’.


Examples l.jpg
Examples whole

Location of connected parts of a stereo-system is the same as the location of the stereo-system.

Stereo-system = (and

(exists has-part remote-control)

(exists (DR connected location) room) …)

Remote-control = (and (not connected) … )


Language31 l.jpg
Language whole

  • ALC + PART-OF

    Satisfiability is a PSPACE-complete problem



Main ideas33 l.jpg
Main ideas whole

  • Part-sensitive subsumption

    Based on taxonomy and partonomy

  • Part-of, transitive


Assumptions l.jpg
Assumptions whole

  • Focus on medical domain

  • Mainly component/integral object and place/area

  • Transitivity across these types often acceptable


Approach l.jpg
Approach whole

  • Explicit taxonomy for is-a and

    explicit partonomy for part-whole relations

  • PART-OF, transitive

  • 2 kinds of subsumption

    - ’ordinary’ subsumption

    - part-sensitive subsumption

  • Restricted language

    Concept: base concept + role restrictions


Reasoning services lambrix padgham shahmehri l.jpg
Reasoning services whole(Lambrix, Padgham & Shahmehri)


Main ideas37 l.jpg
Main ideas whole

  • Named parts

  • Specialized constructs for parts

  • Horizontal (and vertical) constraints

  • Specialized reasoning services for part-of


Underlying model l.jpg
Underlying model whole

Underlying assumptions

  • Named direct parts: x is n-part of y

  • x is part of y iff there is a chain of named part relations between x and y

  • Axiom 1: object x is not part of x

  • Axiom 2: composite object has at least two parts

  • Axiom 3: if y is a direct part of x, then there is no other object z such that y is part of z and z is part of x


Underlying model39 l.jpg
Underlying model whole

Module:

x is a module of y

iff all parts of x are parts of y and y has also other parts

Compositional inclusion:

partial order based on part and module


Underlying model40 l.jpg
Underlying model whole

  • No extensionialty

  • No principle of sum

  • Axiom 2 not checked for individuals


Terminological knowledge l.jpg
Terminological knowledge whole

  • Similar constructs for part relations as for roles

  • Specialized constructs

  • Horizontal and vertical constraints

    - relationships between parts

    - relationships between parts and whole

  • Modules


Terminological knowledge42 l.jpg
Terminological knowledge whole

document = (and

(atleast 1 supervisor) (atmost 1 supervisor)

(atleastp 1 title-part) (atmostp 1 title-part)

(allp title-part string)

(atleastp 3 section-part)

(allp section-part section)

(allp reference-part reference)

(order-constraint title-part section-part)

(order-constraint section-part reference-part))


Slide43 l.jpg

Supervisor (1,1) whole

document

reference-part

(0,-)

title-part

(1,1)

section-part

(3,-)

<

<

string

section

reference


Terminological knowledge44 l.jpg
Terminological knowledge whole

standard-document = (and

document

(atleast 1 author)

(atmost 1 author)

(atmostp 3 section-part) )


Terminological knowledge45 l.jpg
Terminological knowledge whole

  • Horizontal constraints

    (pp-constraint married husband-part wife-part)

    (order-constraint title-part section-part)

  • Vertical constraints

    (same-filler item-part.item-number item-number)

    (aggregate location-part location-supervisor pick-space-supervisor)


Assertional knowledge l.jpg
Assertional knowledge whole

  • Similar constructs for part-relations as for roles

  • Part hierarchy (compositional inclusion)


Assertional knowledge47 l.jpg
Assertional knowledge whole

d : (and document

(part-fills title-part t)

(part-fills section-part s1 s2 s3)

(fills project-name dl-project)

(fills supervisor John))

t: (and string (before s1 in d))

s1: (and section (before s2 in d))

s2: (and section (before s3 in d))

s3: section


Slide48 l.jpg

dl-project whole

project-name

d

john

supervisor

title-part

section-part

section-part

section-part

t

s1

s2

s3

<(d)

<(d)

<(d)


Slide49 l.jpg

Part hierarchy whole

dl-project

d

john

t

s1

s2

s3


Reasoning service composes l.jpg
Reasoning service: wholecomposes

Idea: when can a number of parts be used to compose a composite object of a given type

  • Parts need to belong to right concept

  • Order constraints are satisfied

  • Number of parts conforms to the given concept

  • No unnecessary parts

  • Explicitly required parts are present


Slide51 l.jpg

{ <t,title-part>, <s1,section-part>, <s2, section-part>, <s3, section-part>}

t before s1, t before s2, t before s3

composes document

document

title-part

section-part

section-part

section-part

t

s1

s2

s3

string

section


Reasoning service completion l.jpg
Reasoning service: <s3, section-part>}completion

Idea: given a number of parts and their properties, what extra information is needed for building a composite object of a given type

  • A completion of a set of parts w.r.t. a concept and a knowledge base KB is a pair

    1. KB’ (KB included in KB’)

    2. other parts

    such that the old + other parts compose the concept in KB’


Slide53 l.jpg

Complete {t, s1} to a standard-document <s3, section-part>}

Standard-document

title-part

section-part

section-part

section-part

t

s1

s3

s2

<

<

string

section

<


Reasoning service completion54 l.jpg
Reasoning service: <s3, section-part>}completion

Variants:

  • Only use new parts

  • Only use parts from a given set of parts

  • Use already partially completed objects

  • Preference relations between completions


Example application l.jpg
Example application <s3, section-part>}

TRIFU: knowledge-based information retrieval system for search on content, properties and structure of documents

  • Document representation

  • Query representation

  • Query answering


Example application56 l.jpg
Example application <s3, section-part>}

Document representation

- Description logic individual

* concept description

* part-of hierarchy

- Indexed in glimpse


Example application57 l.jpg
Example application <s3, section-part>}

Query language (extension of document representation language):

  • Queries on types and values

  • Queries on contents (full-text search)

  • Queries involving structure of documents

    * query and retrieval restricted to parts

    * access to documents based on structure

  • Combinations using and, or, and-not


Example application58 l.jpg
Example application <s3, section-part>}

Retrieve only parts

select from section

where ’logic’ occurs

and within-some document


Example application59 l.jpg
Example application <s3, section-part>}

access to documents based on structure

select from document

where includes-some

(select from paragraph

where (’retrieval’ occurs

and includes-some

(select from figure

where ’model’ occurs in caption)


Example application60 l.jpg
Example application <s3, section-part>}

access to documents based on structure

select from section

where within-some

(select from document

whereincludes-object paper121-abstract

and includes-object paper121-title))


Example application61 l.jpg
Example application <s3, section-part>}

Query answering is a combination of

  • Description logic services

  • Information retrieval services


Literature l.jpg
Literature <s3, section-part>}

  • Artale, A., Franconi, E., Guarino, N., Pazzi, L.,Part-whole relations in object-centered systems: an overview, Data & Knowledge Engineering, 20(3):347-383, 1996.

  • Lambrix, P., Part-Whole Reasoning in an Object-Centered Framework, Lecture Notes in Artificial Intelligence 1771, Springer, 2000.


Literature63 l.jpg
Literature <s3, section-part>}

  • Bernauer, J., Analysis of part-whole realtion and subsumption in the medical domain, Data & Knowledge Engineering, 20(3):405-415, 1996.

  • Franconi, E., A treatment of plurals and plural quantification based on a theory of collections, Minds and Machines, 3(4):453-474, 1993.


Literature64 l.jpg
Literature <s3, section-part>}

  • Sattler, U., A concept language for an engineering application with part-whole relations, Proceedings of the international workshop on description logics, 119-123, 1995.

  • Data & Knowledge Engineering, 20(3), 1996. Special Issue on Modeling Parts and Wholes.


Literature65 l.jpg
Literature <s3, section-part>}

  • Lambrix, P., Padgham, L., Conceptual modeling in a document management environment using part-of reasoning in description logics, Data & Knowledge Engineering, 32(1):51-68, 2000.

  • Lambrix, P., Shahmehri, N., Querying Documents using Content, Structure and Properties, Journal of Intelligent Information Systems, 15(3):287-307, 2000.


Exercise sattler l.jpg
Exercise: Sattler <s3, section-part>}

  • Dependent parts: parts depend on the existence of a whole.

    Define the concept ceiling as dependent on the concept room.

  • Multi-possessed parts: parts that are shared by different wholes.

    Define the concept reactor-system as composed of reactors that all have the same tank as part.


Exercise franconi l.jpg
Exercise: Franconi <s3, section-part>}

  • Define the concept car such that the location (a city) of the engine is the same as the location of the car.


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