Ontologia Formal

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Ontologia Formal Modelagem Conceitual
Giancarlo Guizzardi
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Conceptual Modeling
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Unified Modeling Language

• UML is a standard visual notation for the purpose
  of specifying descriptive and prescriptive models
  of software systems

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Formal Ontology and Conceptual Modeling

• Conceptual modeling should be founded on formal
  upper-level ontologies, i.e., it a conceptual
  modeling language should explicitly defined
  ontological semantics

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Formal Ontology and Conceptual Modeling

• Conceptual modeling should be founded on formal
  upper-level ontologies, i.e., it a conceptual
  modeling language should explicitly defined
  ontological semantics

OntoUML
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General Formal Ontology
Basic Ontological Relations Instantiation
,n Inherence i Holding h membership
? parthood lt,?,lte,ltu Framing f Containment
c Association a Location occ
Basic Ontological Categories Abstract Universals
Individuals Substance Moment Quality Relatio
nal Moments Situoid (process) Chronoid Topoid

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Individuals

• Individuals They belong to the realm of concrete
  entities, which means that they have necessarily
  temporal and spatial qualities.
• Individuals may be substances, moments,
  chronoids, topoids, situoids (processes).

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Substance

• A substance is that of which can exist by itself,
  i.e., they are not existentially constantly
  dependent on any other entity.
• Every substance is found on matter

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Moments

• It can only exist in another individual (e.g. a
  charge in a conductor, the color of a fruit, a
  purchase order, a flight connection)
• There are one-place moments which are
  existentially dependent on one substance
  (Quality)
• and relational moments which depend on a
  multitude of substances
• The inherence relation (i) glues moments to
  substances

ED(x,y) ? ??(x) ? ?(?(x)??(y))
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Relational Moments

• Distinction between formal and Material relations
• The relata Material relations are mediated by
  individuals called relators. Ex a
  flighconnection is a relator connecting airports

• h(c3427,Pisa,Paris)
• For every material relation, there is a relator
  universal whose instances connect individuals
  that share a relational moment

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Universals

• Universals entities that can be instantiated
  simultaneously by a multiplicity of different
  individuals that are similar in given respects.
  Time- and space-independent patterns of features
  
• The instantiation relation () is defined
  between individuals and universals and a
  higher-order instantiation relation (n) between
  universals of different orders

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Rigidity

• A Universal U is rigid (R) iff, every instance
  of U is necessarily so. A Universal T is
  anti-rigid (R) iff every instance of T is not
  necessarily so.
• Ex Person v.s. Student

RIGID(?) ? ?(??(x) ???(x)) ANTI-RIGID(?) ?
?(??(x) ????(x))
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External Dependence

• An individual x is externally dependent on an
  individual y iff, at any time that x exists, y
  also exists Ex Hole/Host
• A universal U is dependent (D) iff, for all its
  instances, there exists something they are
  externally dependent on.

DEP(?,?,R) ? ?(??(x) ??y?(y) ?R(x,y))
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-RD
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-R-D
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Part-whole relations

• Primary characteristics
• non-reflexive, asymmetric, transitive, weak
  supplementation
• Secondary characteristics
• shareable, essential, inseparable, mandatory

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Johns Brain
part-of
John
part-of
Knowledge Representation Group
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Contextual Part-Whole relations

• x ltU y means x is a part of y in the context of
  U
• For every universal U, there universals U1Un,
  such that xUi and yUi and every instance of
  Ui is part of an instance of U

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Person
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John
part-of
Johns Brain
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John
part-of
Johns Brain
?(?Person(x) ??!y Heart(y) ? partOf(y,x) ?(?Person
(x) ??!y Brain(y) ? ?partOf(y,x)
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Agradecimentos
Gerd Wagner, Eindhoven University of Technology,
The Netherlands

• Nicola Guarino,
• ISTC-CNR,
• Trento, Italy

Heinrich Herre, GOL, University of Leipzig,
Germany