## Identity and subsumption (2001)

Venue: | The Semantics of Relationships: an Interdisciplinary Perspective |

Citations: | 27 - 8 self |

### BibTeX

@INPROCEEDINGS{Guarino01identityand,

author = {Nicola Guarino and Christopher Welty},

title = {Identity and subsumption},

booktitle = {The Semantics of Relationships: an Interdisciplinary Perspective},

year = {2001},

publisher = {Kluwer}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. The intuitive simplicity of the so-called is-a (or subsumption) relationship has led to widespread ontological misuse. Where previous work has focused largely on the semantics of the relationship itself, we concentrate here on the ontological nature of its arguments, in order to tell whether a single is-a link is ontologically well-founded. For this purpose, we introduce some techniques based on the philosophical notions of identity, unity, and essence, which have been adapted to the needs of taxonomy design. We demonstrate the effectiveness of these techniques by taking real examples of poorly structured taxonomies, and revealing cases of invalid generalization. 1

### Citations

604 | Formal Ontology and Information Systems
- Guarino
(Show Context)
Citation Context ... condition that is both necessary and sufficient for identity. According to [Strawson, 1959], a property φ carries an IC iff the following formula holds for a suitable ρ: φ(x) ∧ φ(y) → (ρ(x,y) ↔ x=y) =-=(6)-=-sSince identity is an equivalence relation, it follows that ρ restricted to φ must also be an equivalence relation. For example, the property PERSON can be seen as carrying an IC if relations like hav... |

122 | C.: A formal ontology of properties
- Guarino, Welty
- 2000
(Show Context)
Citation Context ...xive. This means that, if χ denotes a suitable characteristic relation for φ, we can assume: The scheme (6) becomes therefore: ρ(x,y)=∀z(χ(x,z) ↔ χ(y,z)) (7) φ(x) ∧ φ(y) → (∀z(χ(x,z) ↔ χ(y,z)) ↔ x=y) =-=(8)-=- For instance, if we take φ as the property of being a set, and χ as the relation “hasmember”, this scheme tells us that two sets are identical iff they have the same members. An important advantage o... |

109 |
What IS-A is and isn’t: An analysis of taxonomic links in semantic networks
- Brachman
- 1983
(Show Context)
Citation Context ....e. ∀tφ( a, t) Examples of essential properties for a human being would be PERSON and HAVING A BRAIN. Definition 2 A property φ is rigid iff, necessarily, it is essential to all its instances, i.e. 3 =-=(2)-=-s∀xt ( φ ( x, t) → ∀t′φ( x, t′ )) For example, HAVING A BRAIN would be essential to human beings but not to all its instances, since it is not essential to -say- a dead corpse. On the other hand, PERS... |

68 | An Ontology of Meta-level Categories
- Guarino, Carrara, et al.
- 1994
(Show Context)
Citation Context ..., so a characteristic relation must be irreflexive. This means that, if χ denotes a suitable characteristic relation for φ, we can assume: The scheme (6) becomes therefore: ρ(x,y)=∀z(χ(x,z) ↔ χ(y,z)) =-=(7)-=- φ(x) ∧ φ(y) → (∀z(χ(x,z) ↔ χ(y,z)) ↔ x=y) (8) For instance, if we take φ as the property of being a set, and χ as the relation “hasmember”, this scheme tells us that two sets are identical iff they h... |

34 | Understanding top-level ontological distinctions
- Gangemi, Guarino
- 2001
(Show Context)
Citation Context ... φ is non-rigid iff it is not rigid, that is there is at least one instance such that φ is not essential to it: Non-rigidity can be further restricted as follows: 4 (3) ◆ ∃x (φ(x,t) ∧ ◆ ∃t’ ¬φ(x,t’)) =-=(4)-=- Definition 4 A property φ is anti-rigid iff all its instances are such that φ is not essential to them: ■ (∀xt φ(x,t) → ◆ ∃t’ ¬φ(x,t’)) (5) Consider for example the properties SPHERICAL and STUDENT: ... |

10 |
Individuation: Towards a Formal Toolkit for Ontological Analysis
- Guarino, Welty, et al.
(Show Context)
Citation Context ...have a brain). 5sallows us to take time into account more easily, clarifying the distinction between synchronic and diachronic identity: E(x,t) ∧ Ε(y,t’) ∧ φ(x,t)∧φ(y,t')→(∀z(χ(x,z,t)↔χ(y,z,t'))↔x=y) =-=(9)-=- Since we have now explicitly introduced time, it seemed safe to restrict our analysis to the case where the entities to be identified do actually exist, avoiding identity problems related to non-actu... |

5 |
Data abstractions: why and how
- Goldstein, Storey
- 1999
(Show Context)
Citation Context ...restricted as follows: 4 (3) ◆ ∃x (φ(x,t) ∧ ◆ ∃t’ ¬φ(x,t’)) (4) Definition 4 A property φ is anti-rigid iff all its instances are such that φ is not essential to them: ■ (∀xt φ(x,t) → ◆ ∃t’ ¬φ(x,t’)) =-=(5)-=- Consider for example the properties SPHERICAL and STUDENT: the former is nonrigid but not anti-rigid, since it may be the case that something (like a lump of clay) is spherical by accident, but it is... |

1 |
Identity is simple
- Akiba
- 2000
(Show Context)
Citation Context ...ological nature of its arguments. 1.LADSEB-CNR, Corso Stati Uniti 4, I-35127 Padova, Italy, email: Nicola.Guarino@ladseb.pd.cnr.it 2.Vassar College, Poughkeepsie, NY, USA, email: welty@cs.vassar.edu. =-=(1)-=-sThis chapter is organized as follows. First, we clarify some major issues lying behind the generic notion of identity, and the related notions of unity and essence. Then we show how these notions imp... |

1 |
Ontology driven conceptual analysis
- Guarino, Welty
(Show Context)
Citation Context ... even this requirement cannot easily be met, and we must regard ICs as simple constraints. For brevity, the formula (9) above can be rewritten as: E(x,t) ∧ Ε(y,t’) ∧ φ(x,t)∧φ(y,t')→(Σχ(x,y,t,t')↔x=y) =-=(10)-=- where Σχ is a sameness formula depending on χ, defined as Σχ(x,y,t,t')= def ∀z(χ(x,z,t)↔χ(y,z,t')) (11) We may conclude therefore that an IC for φ is a sameness formula Σχ that satisfies (10) and is ... |