## Heterogeneously Structured Ontologies Integration, Connection, and Refinement

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@MISC{Kutz_heterogeneouslystructured,

author = {Oliver Kutz and Dominik Lücke and Till Mossakowski},

title = {Heterogeneously Structured Ontologies Integration, Connection, and Refinement},

year = {}

}

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### Abstract

This paper systematically applies tools and techniques from the area of algebraic specification theory to corresponding ontology structuring and design tasks. We employ the heterogeneous structuring mechanisms of the heterogeneous algebraic specification language HetCasl for defining an abstract notion of structured heterogeneous ontology. This approach enables the designer to split up a heterogeneous ontology into semantically meaningful parts and employ dedicated reasoning tools to them. In particular, we distinguish three fundamentally different kinds of combining heterogeneous ontologies: integration, connection, and refinement.

### Citations

535 | Ontology Matching
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Citation Context ...or work on modularity in ontologies compare the workshop series (Haase et al. 2006, Cuenca Grau et al. 2007, Sattler & Tamilin 2008), and for work on ontology alignment/matching compare the textbook (=-=Euzenat & Shvaiko 2007-=-), as well as the workshops of the ‘Ontology Alignment Evaluation Initiative’ (see http://oaei.ontologymatching.org/). Bernstein 2002), (Madhavan et al. 2002), and in particular (Goguen 2005, 2006). I... |

477 |
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Citation Context ...ge extent independently of the details of the underlying logical system that is used. The notion of institutions was introduced by Goguen and Burstall in the late 1970s exactly for this purpose (see (=-=Goguen & Burstall 1992-=-)). They capture in a very abstract and flexible way the notion of a logical system by describing how, in any logical system, signatures, models, sentences (axioms) and satisfaction (of sentences in m... |

231 |
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Citation Context ...ts can be developed in a way that is completely independent of the specific nature of the underlying institution. 2 We assume some acquaintance with the basic notions of category theory and refer to (=-=Adámek et al. 1990-=-) or (Mac Lane 1998) for an introduction. If C is a category, C op is the dual category where all arrows 2 For an extensive treatment of model theory in this setting, see (Diaconescu 2008).are revers... |

215 | The even more irresistible SROIQ
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Citation Context ... are being designed in a broad spectrum of logics, with considerably varying expressivity and supporting quite different reasoning methods. Logics being used include description logics like SROIQ(D) (=-=Horrocks et al. 2006-=-), relational database schemes, as well as firstorder and modal logics. While modularity, aligning and re-using (parts of) ontologies has received considerable attention recently, 1 there is little wo... |

112 | L: Distributed Description Logics: Assimilating Information from Peer Sources
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(Show Context)
Citation Context ... be build from many-sorted vocabulary, and link relations are interpreted as relations connecting the sorts of the component logics. The main difference between distributed description logics (DDLs) (=-=Borgida & Serafini 2003-=-) and various E-connections now lies in the expressivity of the ‘link language’ L connecting the different ontologies. While the link language of DDL is a certain subBoolean fragment of many sorted AL... |

108 | S: Categories for the working mathematician. 2nd edition - Lane - 1998 |

101 | Representing and reasoning about mappings between domain models
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(Show Context)
Citation Context ...alignment/matching compare the textbook (Euzenat & Shvaiko 2007), as well as the workshops of the ‘Ontology Alignment Evaluation Initiative’ (see http://oaei.ontologymatching.org/). Bernstein 2002), (=-=Madhavan et al. 2002-=-), and in particular (Goguen 2005, 2006). In recent publications, we have discussed the problem of inheriting conservativity properties from parts (or modules) of an ontology to an overall integration... |

95 | E-connections of abstract description systems
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(Show Context)
Citation Context ...er of decidability: if the connected logics are decidable, then their connection will also be decidable. For lack of space, we can only roughly sketch the formal definitions, and refer the reader to (=-=Kutz et al. 2004-=-) for details. We assume that the languages L1 and L2 of two ontologies O1 and O2 are pairwise disjoint. To form a connection CE (O1, O2), fix a non-empty set E = {Ej | j ∈ J} of binary relation symbo... |

88 | Modular reuse of ontologies: Theory and practice - Grau, Horrocks, et al. - 2008 |

83 | A Framework for Handling Inconsistency in Changing Ontologies - Haase, Harmelen, et al. - 2005 |

41 |
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(Show Context)
Citation Context ...refer to (Adámek et al. 1990) or (Mac Lane 1998) for an introduction. If C is a category, C op is the dual category where all arrows 2 For an extensive treatment of model theory in this setting, see (=-=Diaconescu 2008-=-).are reversed. For a category C, we denote by |C| the class of its objects. Definition 1 (Institutions). An institution is a quadruple I = (Sign, Sen, Mod, |=) consisting of • a category Sign of sig... |

32 | Institution morphisms’, Formal aspects of computing - Goguen, Roşu |

31 | HeTS — the Heterogeneous Tool Set - Mossakowski - 2011 |

28 | Formalising ontologies and their relations
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Citation Context ...rovide a systematic account that parallels structuring techniques from algebraic specification with typical problems found in ontology design. Our work builds on and generalises and extends ideas of (=-=Bench-Capon & Malcolm 1999-=-), (Alagić & Copyright c○2008, Australian Computer Society, Inc. This paper appeared at the Knowledge Representation Ontology Workshop (KROW 2008), Sydney, Australia. Conferences in Research and Pract... |

25 | A model theory for generic schema management - Alagic, Bernstein - 2001 |

25 | Grothendieck institutions
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(Show Context)
Citation Context ...perhaps: reduction) of the Φ(Σ)model M ′ to a Σ-model. The so-called Grothendieck institution is a technical device for giving a semantics to heterogeneous theories involving several institution (see =-=Diaconescu 2002-=-, Mossakowski 2002). The Grothendieck institution is basically a flattening, or disjoint union, of the logic graph. A signature in the Grothendieck institution consists of a pair (L, Σ) where L is a l... |

20 | Comorphism-based grothendieck logics
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(Show Context)
Citation Context ...n) of the Φ(Σ)model M ′ to a Σ-model. The so-called Grothendieck institution is a technical device for giving a semantics to heterogeneous theories involving several institution (see Diaconescu 2002, =-=Mossakowski 2002-=-). The Grothendieck institution is basically a flattening, or disjoint union, of the logic graph. A signature in the Grothendieck institution consists of a pair (L, Σ) where L is a logic (institution)... |

18 | Connecting many-sorted theories - Baader, Ghilardi - 2005 |

12 | Institutionalising Ontology-Based Semantic Integration
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(Show Context)
Citation Context ...ossakowski et al. 2006). Moreover, the appendix contains additional details about the syntax of Casl (and HetCasl introduced below) as well as example specifications. 2.2 Heterogeneous Ontologies As (=-=Schorlemmer & Kalfoglou 2008-=-) argue convincingly, since ontologies are being written in many different formalisms, like relation schemata, description logics, first-order logic, and modal (first-order) logics, alignments of onto... |

11 | Formal properties of modularization - Konev, Lutz, et al. |

9 | Heterogeneous colimits - Codescu, Mossakowski |

9 | Conservativity in structured ontologies - Kutz, Mossakowski - 2008 |

9 |
Structured theories
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(Show Context)
Citation Context ...(Schorlemmer & Kalfoglou 2008) (using first-order logic), a predicate symbol p may be mapped to a formula ϕ. However, this is usually better captured by allowing for derived signature morphisms (see (=-=Sannella & Burstall 1983-=-)), which here are just signature morphisms into a conservative extension (e.g. an extension by the definition p(x) ⇔ ϕ). Secondly, and more importantly perhaps, there may simply be no suitable common... |

8 | Data, schema, ontology and logic integration - Goguen - 2005 |

7 |
Composition of Default Specifications
- Guerra
(Show Context)
Citation Context ...so-called quasicategory, which is a category that lives in a higher set-theoretic universe. 5 Note, however, that non-monotonic formalisms can only indirectly be covered this way, but compare, e.g., (=-=Guerra 2001-=-). Example 3. Description Logics. Signatures of the description logic ALC consist of a set of B of atomic concepts and a set R of roles, while signature morphisms provide respective mappings. Models a... |

6 | Information integration in institutions - Goguen |

5 | Qualitative constraint calculi: Heterogeneous verification of composition tables - Wölfl, Mossakowski, et al. - 2007 |

4 | Ontology Integration Using E-connections - Grau, Parsia, et al. - 2009 |

2 |
Development graphs—proof management for structured specifications’, Journal of Logic and Algebraic Programming 67(1–2
- Mossakowski, Autexier, et al.
- 2006
(Show Context)
Citation Context ... will generate a theorem link between the nodes representing sp1 and sp2 in the development graph. Details of the translation to development graphs, as well as a treatment of hiding, can be found in (=-=Mossakowski et al. 2006-=-). Moreover, the appendix contains additional details about the syntax of Casl (and HetCasl introduced below) as well as example specifications. 2.2 Heterogeneous Ontologies As (Schorlemmer & Kalfoglo... |

1 |
Finding all
- Kalyanpur, Parsia, et al.
- 2007
(Show Context)
Citation Context ...finition 6. We call an ontology O1 a (heterogeneous) sub-ontology of O2 iff O2 is a (heterogeneous) refinement of O1. The standard notion of sub-ontology as a subset of the axioms (Haase et al. 2005, =-=Kalyanpur et al. 2007-=-) is recovered in the homogeneous case if σ additionally is an injection. Moreover, our abstract definition of refinement entails the common definition in software engineering: consider O1 to be a spe... |

1 |
Shapes of Alignments: Construction
- Kutz, Mossakowski, et al.
- 2008
(Show Context)
Citation Context ...(or modules) of an ontology to an overall integration obtained through a colimit operation (Kutz & Mossakowski 2007, 2008), and analysed various alignment approaches from the institutional viewpoint (=-=Kutz et al. 2008-=-). This paper addresses the following: (1) we develop a rather abstract view of heterogeneously structured ontologies encompassing essentially all logics used in ontology design today and allowing to ... |