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International Joint Conference on Knowledge Discovery, Knowledge Engineering, and Knowledge Management

IC3K 2016: Knowledge Discovery, Knowledge Engineering and Knowledge Management pp 191–212Cite as

The Mereologies of Upper Ontologies

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 914))

Abstract

Mereology, the formal theory of parts and wholes, has a played a prominent role within applied ontology. As a fundamental set of concepts for commonsense reasoning, it also appears in a number of upper level ontologies. Furthermore, such upper-level ontologies provide an account of the most basic, domain-independent, existing entities, such as time, space, objects, and processes. In this paper, we verify the core characterization of mereologies of the Suggested Upper Merged Ontology (SUMO), and the mereology of the Descriptive Ontology for Linguistic and Cognitive Engineering (DOLCE), while relating their axiomatizations via ontology mapping. We show that the existing axiomatization of SUMO omits some of the intended models of classical mereology, and we propose the correction and addition of axioms to address this issue. In addition, we show the formal relationship between the axiomatization of mereology in both upper-level ontologies.

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Change history

  • 05 February 2019

    In a previous version of this publication, the affiliation of the second editor was incomplete. This has now been corrected.

Notes

  1. 1.

    https://www.w3.org/2001/sw/wiki/OWL.

  2. 2.

    The expressive power of first-order logic makes its use necessary for the representation of mappings that characterize features that are not representable in lightweight languages, such as Description Logics. In addition, checking the correctness of those mappings results facilitated by the fact that first-order theorem proving in standard first-order logic is a mature field, and, although semi-decidable, first-order reasoning on small modules results in an acceptable trade-off among expressivity and efficiency.

  3. 3.

    This paper is an extended and expanded version of the paper “Verifying and Mapping the Mereotopology of Upper-Level Ontologies” that originally appeared in the Proceedings of Knowledge Engineering and Ontology Design (KEOD) 2016 [16].

  4. 4.

    We assume that an ontology is a set of sentences called axioms closed under logical entailment that state the properties that characterize the behaviour of a set of symbols representing constants, relations and functions, called the signature of the ontology.

  5. 5.

    A representation theorem is a theorem that formally classifies a given class of structures as equivalent to another class of structures whose properties are better understood. The stated equivalence makes possible the extrapolation of those properties to the classified structures, facilitating their understanding.

  6. 6.

    http://suo.ieee.org/SUO/KIF/suo-kif.html.

  7. 7.

    http://logic.stanford.edu/kif/kif.html.

  8. 8.

    A theory \({T'}\) is a conservative extension of a theory T if every theorem of T is a theorem of \({T'}\), and every theorem of \({T'}\) in the signature of T is also a theorem of T.

  9. 9.

    The proofs for all Propositions have been found using the Prover9 automated theorem prover, and models were constructed using Mace4. Results are available at: colore.oor.net/ontologies/sumo/mereotopology/proofs.

  10. 10.

    colore.oor.net/ontologies/lattices/join_semilattice.clif.

  11. 11.

    colore.oor.net/ontologies/mereology/strong_lub_mereology.clif.

  12. 12.

    colore.oor.net/ontologies/mereology/prod_mereology.clif.

  13. 13.

    colore.oor.net/ontologies/mereology/comp_mereology.clif.

  14. 14.

    http://wonderweb.semanticweb.org.

  15. 15.

    Axioms (48), (49), (53), and (54) are the instantiation of DOLCE higher-order axiom schemas for the subcategories of main categories Q and R which are relevant for our work. A complete version of DOLCE-CORE mereology represented in first-order logic is available at colore.oor.net/ontologies/dolce-core/mereology.in.

  16. 16.

    It can be proved that in an extensional mereology non-atomic entities whose proper parts are the same, are identical, i.e., every entity is exhaustively defined by its parts.

  17. 17.

    Available at colore.oor.net/ontologies/sumo/modules.

  18. 18.

    A n-ary function f from \(A^n\) to B is representable by a relation \(\varrho \) with arity (n+1), called the graph of f, such that:

    (a) Every tuple of \(\varrho \) is a tuple \(\langle \bar{x}, f(\bar{x})\rangle \) with \(\bar{x}\in A^n\) and \(f(\bar{x}) \in range(f)\).

    (b) If \(f(\bar{x})=b\) and \(f(\bar{z})=c\), then \(b=c\).

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Author information

Authors and Affiliations

  1. Computer Science, University of Toronto, 40 St. George Street, Toronto, ON, M5S 2E4, Canada

    Lydia Silva Muñoz

  2. Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, ON, M5S 3G8, Canada

    Michael Grüninger

Authors
  1. Lydia Silva Muñoz
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  2. Michael Grüninger
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Corresponding author

Correspondence to Michael Grüninger .

Editor information

Editors and Affiliations

  1. Instituto de Telecomunicações, Lisbon, Portugal

    Ana Fred

  2. Department of Software Technology, Delft University of Technology, Voorburg, Zuid-Holland, The Netherlands

    Jan Dietz

  3. Faculty of Exact Sciences and Engineering, University of Madeira, Funchal, Portugal

    David Aveiro

  4. Henley Business School, University of Reading, Reading, UK

    Kecheng Liu

  5. University of Coimbra, Coimbra, Portugal

    Jorge Bernardino

  6. Instituto Politecnico de Setúbal (IPS), Setúbal, Portugal

    Joaquim Filipe

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Silva Muñoz, L., Grüninger, M. (2019). The Mereologies of Upper Ontologies. In: Fred, A., Dietz, J., Aveiro, D., Liu, K., Bernardino, J., Filipe, J. (eds) Knowledge Discovery, Knowledge Engineering and Knowledge Management. IC3K 2016. Communications in Computer and Information Science, vol 914. Springer, Cham. https://doi.org/10.1007/978-3-319-99701-8_9

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  • DOI: https://doi.org/10.1007/978-3-319-99701-8_9

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