## Formalising Ontologies and Their Relations (1999)

Venue: | In Proceedings of DEXA’99 |

Citations: | 29 - 1 self |

### BibTeX

@INPROCEEDINGS{Bench-capon99formalisingontologies,

author = {Trevor Bench-capon and Grant Malcolm},

title = {Formalising Ontologies and Their Relations},

booktitle = {In Proceedings of DEXA’99},

year = {1999},

pages = {250--259},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

. Ontologies allow the abstract conceptualisation of domains, but a given domain can be conceptualised through many different ontologies, which can be problematic when ontologies are used to support knowledge sharing. We present a formal account of ontologies that is intended to support knowledge sharing through precise characterisations of relationships such as compatibility and refinement. We take an algebraic approach, in which ontologies are presented as logical theories. This allows us to characterise relations between ontologies as relations between their classes of models. A major result is cocompleteness of specifications, which supports merging of ontologies across shared sub-ontologies. 1 Introduction Over the last decade ontologies --- best characterised as explicit specifications of a conceptualisation of a domain [17] --- have become increasingly important in the design and development of knowledge based systems, and for knowledge representations generally. They...

### Citations

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Citation Context ... which supports merging of ontologies across shared sub-ontologies. 1 Introduction Over the last decade ontologies --- best characterised as explicit specifications of a conceptualisation of a domain =-=[17]-=- --- have become increasingly important in the design and development of knowledge based systems, and for knowledge representations generally. They have been shown to be useful in -- knowledge acquisi... |

489 |
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Citation Context ... CafeOBJ [8]. This provides support for prototyping and theorem proving. A theory morphism 1 OE : T ! T 0 between order-sorted theories induces a functor from models of T 0 to models of T (see, e.g., =-=[10]-=-, though Proposition 7 presents the essential ideas). This means that any model D 0 of T 0 gives rise to a model OED 0 of T ; this allows us to define morphisms of data domains as follows: Definition ... |

408 |
Category Theory for Computing Science
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Citation Context ... an ad hoc syntax. For reasons of space, the presentation below assumes some familiarity with algebraic specifications (introductions can be found in [22, 9]) and also with basic category theory (see =-=[20, 1]-=- for introductions). A more detailed presentation, including proofs absent from the present paper, can be found in [2]. Our ontologies specify classes of entities with attributes. These attributes tak... |

275 |
An initial algebra approach to the specification, correctness and implementation of abstract data types
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Citation Context ...Sigma is the collection of typed operation symbols, and E is the set of equations, and where D is a model of T . We often write D instead of (T ; D). We do not require that D be an initial model of T =-=[15]-=-, although in many cases that would be an obvious choice. Any computable algebra can be specified equationally [4]; even uncomputable algebras, such as the reals, can be used in ontological specificat... |

223 |
Categories for the working mathematician, volume 5 of Graduate Texts in Mathematics
- Lane
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Citation Context ... an ad hoc syntax. For reasons of space, the presentation below assumes some familiarity with algebraic specifications (introductions can be found in [22, 9]) and also with basic category theory (see =-=[20, 1]-=- for introductions). A more detailed presentation, including proofs absent from the present paper, can be found in [2]. Our ontologies specify classes of entities with attributes. These attributes tak... |

208 | Order-sorted algebra I: Equational deduction for multiple inheritance, overloading, exceptions and partial operations
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Citation Context ...he types of some of its attributes, so we consider these types to be a part of ontological specifications. We formalise this part of specifications using the notion of order-sorted algebraic theory ; =-=[14, 11]-=- give details of order-sorted algebra, the following is an example of a theory for the natural numbers, in the notation of the language OBJ [16, 11]. th NAT is sorts Nat NonZeroNat . subsort NonZeroNa... |

162 |
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Citation Context ...' way (a colimit) of combining related ontologies that share some subcomponents. A proof is given in [2]; an example is given below. Colimits are standard in combining algebraic theories (for example =-=[5]-=-; see also [18], whose cocompleteness results for order-sorted theories are used in the proof of Theorem 11). Example 12. The following is a common subcomponent for the ontologies of Examples 4 and 9.... |

145 |
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Citation Context ...syntax; the motivating examples given below are in an ad hoc syntax. For reasons of space, the presentation below assumes some familiarity with algebraic specifications (introductions can be found in =-=[22, 9]-=-) and also with basic category theory (see [20, 1] for introductions). A more detailed presentation, including proofs absent from the present paper, can be found in [2]. Our ontologies specify classes... |

114 | A hidden agenda
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Citation Context ... theories at the level of institutions [10] shows that many other logics, such as Horn clause logic, are possible, while still retaining cocompleteness. Our ontologies are similar to `hidden algebra' =-=[13, 12]-=- in having a fixed data universe (hidden algebra also has a notion of behavioural equivalence that is not relevant to our present purposes). This allows us to reuse some results from hidden algebra. F... |

107 |
Algebraic Semantics of Imperative Programs
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Citation Context ...he types of some of its attributes, so we consider these types to be a part of ontological specifications. We formalise this part of specifications using the notion of order-sorted algebraic theory ; =-=[14, 11]-=- give details of order-sorted algebra, the following is an example of a theory for the natural numbers, in the notation of the language OBJ [16, 11]. th NAT is sorts Nat NonZeroNat . subsort NonZeroNa... |

103 |
Universal Algebra
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Citation Context ...syntax; the motivating examples given below are in an ad hoc syntax. For reasons of space, the presentation below assumes some familiarity with algebraic specifications (introductions can be found in =-=[22, 9]-=-) and also with basic category theory (see [20, 1] for introductions). A more detailed presentation, including proofs absent from the present paper, can be found in [2]. Our ontologies specify classes... |

100 |
Using explicit ontologies in kbs development
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Citation Context ...the design and development of knowledge based systems, and for knowledge representations generally. They have been shown to be useful in -- knowledge acquisition (e.g. [23]); -- knowledge reuse (e.g. =-=[19]-=-) and sharing (e.g. [17]); and -- verification and validation of knowledge based systems (e.g. [3]). It has become recognised that even in a given domain multiple conceptualisations, and hence ontolog... |

44 |
Jos'e Meseguer, Kokichi Futatsugi, and Jean-Pierre Jouannaud. Introducing OBJ
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Citation Context ...using the notion of order-sorted algebraic theory ; [14, 11] give details of order-sorted algebra, the following is an example of a theory for the natural numbers, in the notation of the language OBJ =-=[16, 11]-=-. th NAT is sorts Nat NonZeroNat . subsort NonZeroNat ! Nat . op 0 : -? Nat . op s : Nat -? NonZeroNat . op p : NonZeroNat -? Nat . var N : Nat . eq p(s(N)) = N . endth The details of this notation ar... |

43 |
Automated Generation of Model-Based Knowledge-Acquisition Tools
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Citation Context ...ecome increasingly important in the design and development of knowledge based systems, and for knowledge representations generally. They have been shown to be useful in -- knowledge acquisition (e.g. =-=[23]-=-); -- knowledge reuse (e.g. [19]) and sharing (e.g. [17]); and -- verification and validation of knowledge based systems (e.g. [3]). It has become recognised that even in a given domain multiple conce... |

39 |
and Andrzej Tarlecki. Toward formal development of programs from algebraic specifications
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Citation Context ... 0 is a refinement of the ontology O. This is because any model of O 0 gives rise to, by Proposition 7 and Definition 8, a model of O. This approach is standard in algebraic specification (see, e.g., =-=[24]-=-). A more general way of relating ontologies is through pairs of morphisms: Definition 10. A relation between ontologies O 1 and O 2 consists of an ontologysO and a pair of morphismssi : O ! O i for i... |

36 |
Algebraic specifications of computable and semicomputable data types, Theoretical Computer Science 50
- Bergstra, Tucker
- 1987
(Show Context)
Citation Context ... often write D instead of (T ; D). We do not require that D be an initial model of T [15], although in many cases that would be an obvious choice. Any computable algebra can be specified equationally =-=[4]-=-; even uncomputable algebras, such as the reals, can be used in ontological specifications by fixing an appropriate model D (for example, the reals provide a model of the theory NAT). An important adv... |

33 | The Logic of Typed Feature Structures, volume 32 of Cambridge Tracts in Theoretical - Carpenter - 1992 |

25 | Hidden Coinduction: behavioral correctness proofs for objects
- Goguen, Malcolm
- 1999
(Show Context)
Citation Context ... theories at the level of institutions [10] shows that many other logics, such as Horn clause logic, are possible, while still retaining cocompleteness. Our ontologies are similar to `hidden algebra' =-=[13, 12]-=- in having a fixed data universe (hidden algebra also has a notion of behavioural equivalence that is not relevant to our present purposes). This allows us to reuse some results from hidden algebra. F... |

8 | Interconnection of object specifications
- Malcolm
- 1996
(Show Context)
Citation Context ...odels of O 1 and O 2 agree on their shared parts (i.e., on O), then those models can be `merged' to provide a model of the colimiting ontology. Similar results in an algebraic setting can be found in =-=[21, 7]-=-. 4 Conclusions We have presented an algebraic approach to formalising ontologies, and used this to capture various relationships between ontologies. Ontologies are specified as classes partially orde... |

7 |
A semantical study of the object paradigm
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- 1996
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Citation Context ...odels of O 1 and O 2 agree on their shared parts (i.e., on O), then those models can be `merged' to provide a model of the colimiting ontology. Similar results in an algebraic setting can be found in =-=[21, 7]-=-. 4 Conclusions We have presented an algebraic approach to formalising ontologies, and used this to capture various relationships between ontologies. Ontologies are specified as classes partially orde... |

4 |
The role of Ontologies in the Verification and Validation of Knowledge Based Systems
- Bench-Capon
- 1998
(Show Context)
Citation Context ... They have been shown to be useful in -- knowledge acquisition (e.g. [23]); -- knowledge reuse (e.g. [19]) and sharing (e.g. [17]); and -- verification and validation of knowledge based systems (e.g. =-=[3]-=-). It has become recognised that even in a given domain multiple conceptualisations, and hence ontologies, are possible. The conceptualisations will inevitably be oriented to the tasks to be carried o... |

1 |
Relating ontologies. Draft available at http://www.csc.liv.ac.uk/~grant/ps
- Bench-Capon, Malcolm
- 1999
(Show Context)
Citation Context ...troductions can be found in [22, 9]) and also with basic category theory (see [20, 1] for introductions). A more detailed presentation, including proofs absent from the present paper, can be found in =-=[2]-=-. Our ontologies specify classes of entities with attributes. These attributes take values in data types such as numbers, booleans, lists and so on. Sometimes it is convenient to make changes in the t... |

1 |
Haxthausen and Friederike Nickl. Pushouts of order-sorted algebraic specifications
- Anne
- 1996
(Show Context)
Citation Context ...it) of combining related ontologies that share some subcomponents. A proof is given in [2]; an example is given below. Colimits are standard in combining algebraic theories (for example [5]; see also =-=[18]-=-, whose cocompleteness results for order-sorted theories are used in the proof of Theorem 11). Example 12. The following is a common subcomponent for the ontologies of Examples 4 and 9. Car Model colo... |