Principles of Core Ontologies and Levels of Reality

1
Principles of Core Ontologiesand Levels of
Reality

• Heinrich Herre
• Ontologies and
• Knowledge-Based Systems
• Research Group Onto-Med
• IMISE
• University Leipzig

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Contents

• GFO and Onto-Med
• Domains
• Conceptualizations
• Core Ontologies
• Levels of Reality
• Applications
• Conclusions

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Ontologies 1

• Category
• A category is presented by a linguistic
  expression F
• describing a system of conditions which can
  be
• predicated of entities
• satisfied by entities.
• instantiated by entities

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Ontologies 2

• Category
• Basic relations between categories C and
  entities e
• C is predicated of e, pred(C,e)
• E satisfies C, E C
• E is instance of C, e C
• Problem Are the relations , , pred(x,y)
  equivalent?

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Ontologies 3

• Classification of Categories

Category
Concept
Symbol
Transcendental Category
?
Universal
Multiple category approach J. E. Gracia
Metaphysics and its Tasks The Search for the
Categorial Foundation of Knowledge. SUNY
Series in Philosophy. Albany , 1999


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Ontologies 4

• Ontologies as knowledge bases
• An ontology is an axiomatization of a
  conceptualization represented in a formal
  language
• Formal systems for representation
• logic languages (FOL, DL, CL, OWL)
• graph-based systems (semantic nets, conceptual
• graphs, OBO-format)

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Ontologies 5

• Levels of generality of ontologies
• Top-Level Ontologies (TLO)
• Core domain ontologies (CO)
• Upper domain ontologies (UO)
• Domain ontologies (DO)

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Onto-Med

• Foundations of Formal Ontology
• Conceptual Tools for Development of Ontologies
• Domain-specific Ontologies, Core Ontologies
• Computer-based Applications
• Contact
• heinrich.herre_at_imise.uni-leipzig.de
• http//www.onto-med.de

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GFO 1

• GFO (General Formal Ontology)
• is a top level ontology being developed by the
  research
• group Onto-Med. Some features
• GFO integrates objects and processes
• Multi-categorial approach
• Levels of reality
• Categories of higher order

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GFO 2

Abstract top level Set / Item
Abstract Core Level
Basic Level
Material Stratum
Social Stratum
Psychological Stratum
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GFO 3 (Abstract Top Level)
Entity
Set
Item
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GFO 4 (Abstract Core Level)
Item
Category
Individual
Concept
Universal
Symbol Structure
Concrete
abstract
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GFO 5 (Selected Categories )
concrete individual
complex individual
space-time entity
role
function
relator
quality
time entity
spatial entity
occurrent
presential
Perpetuant
spatial boundary
space region
time region
time boundary
material structure
configur- ation
process
change
material boundary
material object
situation
situoid
topoid
chronoid
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Domains 1

• What is a domain?
• A primitive domain D is determined by
• a set Ind(D) of individuals
• a set V of views
• a set CP of classification principles
• D (Ind, V, CP)
• Note In a (general) domain D the set Ind(D) can
  be an
• arbitrary set of objects.

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Domains 2 (Subdomains)

Domain D
D(1)
D(2)
D(k)
..
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Domains 3 (Example)

• Biology
• Genetics
• Cytology
• Physiology
• Ethology
• Ecology

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Conceptualizations 1

• A conceptualization for a (primitive) domain
• D (Ind(D), V, CP) is determined by
• Ind(D) a set of individuals
• Cat(D) a set of categories associated to D
• (based on the classification principles and
  views in D)
• a set Rel(D) of relations on Ind and/or Cat(D)
• Denote Concept(D) (Ind(D), Cat(D), Rel(D))
  to be a conceptualization for D.

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Conceptualizations 2

• Let Concept(D) be a conceptualization of the
  domain D, and Cat(D) a set of categories
  associated with D.
• The categories Cat(D) of a conceptualization can
  be classified into
• principal categories
• elementary categories
• aspectual/facet categories

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Conceptualizations 3

• A set of principal categories of D (of first
  order)
• express what the domain is about
• is minimal and complete
• generate the system Cat(D) by classification and
  aspectual derivations (facet analysis)
• Furthermore
• principal categories of higher order are allowed.

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Conceptualizations 4

• Elementary categories of D
• based on classification principles of D
• define taxonomies
• determine a sub-concept relation

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Conceptualization 5

• aspectual derivatives of D
• basic facets
• linguistically defined categories
• There does not exist a complete system of
  principles to
• generate all aspectual derivatives (Conjecture).
• Claim
• There is a relation between aspectual derivatives
  and the
• semantics of natural language.

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Conceptualizations 6 (Examples)

• Classical Biology
• Principal categories (first order)
• organism (autopoietic systems)
• principal categories (second order) species (?)
• Elementary categories
• Kingdom, Order, Family, Genus, Species.

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Conceptualizations 7 (Examples)

• Aspectual derivatives
• African elephant (elementary).
• Open-ended set of aspectual derivatives
• African elephants in South Africa of a certain
  location
• during a certain time interval.
• African elephants living in Zoos of Germany.

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Conceptualizations 8

• African elephants used by Hannibal in invading
  the Roman empire.
• General principle take a natural language
  sentence F in which the term African elephant
  occurs, F(Ae). Consider the collection of all
  Afr. elephants which occur in all situations
  making the sentence F true.

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Conceptualizations 9

• Domain level categories.
• Let D be a domain and Cat(D) a set of categories
• associated to D.
• A domain level category M(D) of D is a higher
  order category satisfying the following
  conditions
• every category in Cat(D) is an instance of M(D)
• M(D) is transitively closed w.r.t. to
  instantiations
• M(D) does not belong to Cat(D)

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Core Ontologies 1

• What is a Core Ontology of a Domain D ?
• Core ontologies describe what a domain and its
  sub- domains are about and how they are related.
  Hence core ontologies of a domain D
• contain the principal categories of D and
• of its sub-domains (first and higher order)
• contain cross domain relations and domain
• level categories
• provide an integration of the sub-domains

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Core Ontologies 2

• Core domain ontologies are different from upper
  domain ontologies!
• An upper domain ontology of a domain ontology is
  only a selection of a more general part of a
  taxonomy.

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Core Ontologies 2

• D a domain and D(1),, D(n) sub-domains
• Princ(D) principal concepts of D
• Concept(D) (Cat(D), Rel(D))
• A conceptualization of a core ontology of D,
  denoted by ConcCoreOnt(D), is specified by
• (Princ(D),Princ(D(i))i?n , M(D(i)) i ?
  n, M(D), Rel(D),CoreRel(D))
• M(D) provides a level of description which
  allows to formally specify relations between the
  sub-domains, the set CoreRel(D) includes domain
  cross relations interrelating the domains
  D(1),,D(n). The components M(D(i)) i ? n, and
  M(D) can be empty.

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Core Ontologies 3

• A core ontology for (D,D(1),,D(n)) with respect
  to a core conceptualisation ConcCoreOnt(D) is
  specified
• by a set of axioms Ax(ConcCoreOnt(D)).
• Example of an axiom about the sub-domain of
  all species. Spec the level category of this
  sub-domain.
• ? X a b (X Spec ? a X ? b X ? female(a)
  ?
• male(b)? ? c pairing(x,y,c)))

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Core Ontologies 4

• Minimal core ontologies.
• The conceptualization of a minimal core
  ontology for
• (D,D(1),,D(n)) is specified by
• (PrincCat(D), ?iltnPrincCat(D(i)), Rel(D),
  CoreRel(D))
• A minimal core ontology does not contain
  domain level
• categories and meta-categories

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Core Ontologies 5

• Example GFO-Bio.
• Common project of IMISE, EVA and ME-Foundation.
• GFO-Bio is the first step in developing a core
  ontology in
• the sense set forth in this presentation.
• Principal concepts Organism, cell
• Open question characterization of relevant
  sub-domains and second
• order categories
• Details in R. Hoehndorf, F. Loebe, R. Poli, H.
  Herre J. Kelso GFO-Bio A new approach for
  integrating ontologies, Submitted.

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Core Ontologies 6

• Example Ontology of functions (FO)
• P. Burek PhD Thesis.
• FO is included in GFO and can be adapted to be a
  part of a core ontology of GO
• GO consists of three separated sub-ontologies
  (domains)
• cellular components
• biological functions
• biological processes

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Core ontologies 7

• A function F has three major aspects
• function structure represents the function
  independent from any realisation
• realization of a function describes the
  conditions
• on an entity for realizing the function
• has-function-relation ascribing a function to an
  entity

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Core Ontologies 8

• A functional item is a role universal having
  instances.
• Example
• function
• to transport oxygen
• functional item (role universal)
• oxygen transporter

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Core Ontologies 9

• Basic relation
• realizes (E, F, R) an instance of category E
  may play the role of a realizer of the function F
  by realizations of type R.
• Example E erythrocytes
• F oxygen transportation
• R oxygen transportation processes
  

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Core Ontologies 10

• x is a erythrocyte which is connected by a
  realizer with a process realizing the transport
  of oxygen. This realizer is an instance of the
  functional item F.
• realizes (E,F,R) impliziert zwei Relationen
• realizes(E,F,R) ? is-realization(R,F)
• realizes(E,F,R) ? has-function(E,F)
• is-realization(R,F) ? ? x realizes(x,F,R)
• has-function(E,F) ? ? z realizes(E,F, z)

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Core Ontologies 11

• Example of OBO Ontologies
• Links between processes and functions
• GO 0051119 (sugar transporter activity) F
• (can be interpreted as to transport sugar)
• Requirements sugar-molecule (CHEBI25407 or
• CHEBI25679) is located at some place.
• Goal location of the sugar molecule at a
  different
• location
• Functional Item role universal sugar
  transporter

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Core Ontologies 12

• Processes of type carbohydrate transport
  (GO0008643) are realizations of the function
• to transport sugar ( sugar transport
  activity)
• MAL21 (maltose permease) ist annoted with
• F sugar transport activity (GO 0051119)
• Representation by realizes(x,y,z)
• realizes(MAL21, GO0051119, GO0008643)

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Levels of reality 1

• Application of core ontologies to GFO.
• Ent class of all entities
• Entity anything that exists in the broadest
  sense
• We stipulate sub-domains Mat, Psy, Soc

Entity
Psychological Entity
Social Entitiy
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Levels of Reality 2

• GFO-Ent refers to three sub-domains whose
  top-level ontologies are denoted by
• GFO-Mat, GFO-Psy, GFO-Soc.
• What is a core ontology of the material stratum?
  Is there a
• difference between a top-level ontology and a
  core
• ontology of the material stratum ?

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Levels of Reality 3

• Claim
• The minimal core ontology of GFO-Mat equals the
  set of categories of concrete individuals
• CoreCat(GFO-Mat) CatConcreteInd(GFO)
• A full core ontology of GFO-Mat adds several
  meta-categories UnivCat, ConcCat, SymbCat.
• UnivCat meta-category of all universals
• ConcCat meta-category of all concepts
• SymbCat meta-category of all symbol
  structures

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Levels of Reality 4

• Principal categories of the psychological, and
  the social stratum.
• CoreCat(Psy) Cat(GFO-Psy) Meta(GFO-Psy)
• CoreCat(Mat) Cat(GFO-Mat) Meta(GFO-Mat)
• Problem. What are principal categories of the
  psychological and the social stratum?

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Levels of Reality 5

• What is a top-level ontology or a core
  ontology of the
• domain of all entities?
• Any solution depends on basic assumption in
  philosophy,
• hence there is no uniquely determined
  ontology of this
• kind.

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Levels of Reality 6

• Reflections on GFO(Ent)
• Basic categories Entity, Set, Item, Cat, Ind
• Relations existential dependency,
  instantiation,
• membership relation, part-of.
• GFO(Item), GFO(Set)
• GFO(Set) corresponds with one of the set
  theories
• (ZF, ZFC or a weaker system)

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Levels of Reality 7

• GFO(Item) is concerned with
• sub-domains of categories and individuals,
• relations between different kinds of categories
• (universals, concepts, symbols)
• relations between categories and individuals
• the categories MatStr, PsyStr, SocStr and their
  
• interrelations.

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Levels of Reality 8

• Open problems and tasks concerning GFO(Ent)
• Which relations exist between Concepts,
  Universals,
• and Symbols? Development of an ontological
  theory.
• Development of a theory for GFO-realism.
• What is the ontological status of sets and of
• mathematics?

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Applications 1

• Development of ontologies
• Integration of ontologies
• Representation of ontologies
• Applications of ontologies to sciences

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Applications 2

• Tools for Ontology Development and Integration
• Conceptual Tools
• Onto-Builder
• Supports the analysis of concepts and
  conceptual modelling.
• Onto-Integrator
• Supports the integration of ontologies
• CoreOntoBuilder,
• COnto-Builder, Ontogator, OntoGrator,
• Onto-Integrator, Onto-Builder
• Onto-Builder support the development of
  ontologies
• Onto-Integrator supports the integration of
  ontologies
• (includes the OntoMapper)
• Onto-Wiki supports the collaborative development
  of ontologies

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Applications 3

• Ontological-based Wikis as a framework for
  collaborative ontology development

GFOWiki
BOWiki
MedOWiki
EcOWiki

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Applications 4

• P. Burek, R. Hoehndorf , F. Loebe, J. Visagie,
  H. Herre, J. Kelso A Top-level Ontology of
  Functions and ist Application in the Open
  Biomedical Ontologies Bioinformatics, 2006
• R. Hoehndorf, F. Loebe, R. Poli, H. Herre J.
  Kelso GFO-Bio A new approach for integrating
  ontologies, Submitted.
• R. Hoehndorf, F. Loebe, J. Kelso, H. Herre
  Representing default knowledge to the interation
  of anatomy and phenotype ontologies
• BMC Bioinformatics, 2007
• R. Hoehndorf, K. Prüfer, M. Backhaus,
  H.Herre J. Kelso, F. Loebe, J. Visagie A
  Proposal for a Gene Function Wiki. OTM Workshops,
  2006 669 - 678

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Conclusion 1

• The development of core ontologies for domains is
• a central topic in ontology research.
• The results in this field of research have an
  impact on
• applications in different fields
• a) Practical applications
• Structuring of a domain and its sub domains,
• Developing integration ontologies
• Establishhing conceptual tools for ontology
  development

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Conclusion 2

• b) Application to sciences (life sciences,
  medicine, economy, psychology) (selected
  problems)
• Data analysis and generating database schemata
• New methods for modelling and simulation of
  processes
• (stem cells, IMISE)
• establishing the objective (real) value of a
  commodity (revival of the labour theory of value
  in economy)

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Acknowledgements

• Thanks to F. Loebe, R. Hoehndorf, J. Kelso, H.
  Michalek, R. Poli for stimulating discussions.

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End

• Thank you!

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