Logica Universalis

, Volume 4, Issue 2, pp 255–333 | Cite as

Carnap, Goguen, and the Hyperontologies: Logical Pluralism and Heterogeneous Structuring in Ontology Design

Article

Abstract

This paper addresses questions of universality related to ontological engineering, namely aims at substantiating (negative) answers to the following three basic questions: (i) Is there a ‘universal ontology’?, (ii) Is there a ‘universal formal ontology language’?, and (iii) Is there a universally applicable ‘mode of reasoning’ for formal ontologies? To support our answers in a principled way, we present a general framework for the design of formal ontologies resting on two main principles: firstly, we endorse Rudolf Carnap’s principle of logical tolerance by giving central stage to the concept of logical heterogeneity, i.e. the use of a plurality of logical languages within one ontology design. Secondly, to structure and combine heterogeneous ontologies in a semantically well-founded way, we base our work on abstract model theory in the form of institutional semantics, as forcefully put forward by Joseph Goguen and Rod Burstall. In particular, we employ the structuring mechanisms of the heterogeneous algebraic specification language HetCasl for defining a general concept of heterogeneous, distributed, highly modular and structured ontologies, called hyperontologies. Moreover, we distinguish, on a structural and semantic level, several different kinds of combining and aligning heterogeneous ontologies, namely integration, connection, and refinement. We show how the notion of heterogeneous refinement can be used to provide both a general notion of sub-ontology as well as a notion of heterogeneous equivalence of ontologies, and finally sketch how different modes of reasoning over ontologies are related to these different structuring aspects.

Mathematics Subject Classification (2010)

Primary 68T30 Secondary 03C95 

Keywords

Ontologies reasoning modularity logical pluralism combination techniques algebraic specification institution theory 

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References

  1. 1.
    Adámek, J., Herrlich, H., Strecker, G.: Abstract and Concrete Categories. Wiley, New York (1990). Available at http://www.math.uni-bremen.de/dmb/acc.pdf
  2. 2.
    Alagić, S., Bernstein, P.A.: A Model Theory for Generic Schema Management. In: Proc. of DBPL-01, LNCS, vol. 2397, pp. 228–246. Springer, Berlin (2002)Google Scholar
  3. 3.
    Artale A., Franconi E.: A survey of temporal extensions of description logics. Ann. Math. Artif. Intell. 30(1–4), 171–210 (2000)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Artale, A., Kontchakov, R., Lutz, C., Wolter, F., Zakharyaschev, M.: Temporalising tractable description logics. In: Proc. of the 14th Int. Symposium on Temporal Representation and Reasoning (TIME) Washington, DC, USA, IEEE, pp. 11–22 (2007)Google Scholar
  5. 5.
    Astesiano E., Kreowski H.-J., Krieg-Brückner B.: Algebraic Foundations of Systems Specification. Springer, Berlin (1999)Google Scholar
  6. 6.
    Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.F. (eds): The Description Logic Handbook. Cambridge University Press, Cambridge (2003)MATHGoogle Scholar
  7. 7.
    Baader F., Ghilardi S.: Connecting many-sorted theories. J. Symbol. Logic 72(2), 535–583 (2007)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Baader, F., Lutz, C., Milicic, M., Sattler, U., Wolter, F.: Integrating description logics and action formalisms: first results. In: Proceedings of the Twentieth National Conference on Artificial Intelligence (AAAI-05) Pittsburgh (2005)Google Scholar
  9. 9.
    Bateman, J., Castro, A., Normann, I., Pera, O., Garcia, L., Villaveces, J.-M.: OASIS common hyper-ontological framework (COF). Deliverable D1.2.1, EU Project OASIS (2010)Google Scholar
  10. 10.
    Bateman J., Hois J., Ross R., Tenbrink T.: A linguistic ontology of space for natural language processing. Artif. Intell. 174(14), 1027–1071 (2010)CrossRefGoogle Scholar
  11. 11.
    Bateman J., Tenbrink T., Farrar S.: The role of conceptual and linguistic ontologies in discourse. Discourse Processes 44(3), 175–213 (2007)CrossRefGoogle Scholar
  12. 12.
    Bateman, J.: Ontological diversity: the case from space. In: Galton, A., Mizoguchi, R. (eds.) Formal Ontology in Information Systems - Proceedings of the Sixth International Conference (FOIS 2010), vol. 209. IOS Press (2010)Google Scholar
  13. 13.
    Baumgartner, P., Suchanek, F.M.: Automated reasoning support for first-order ontologies. In: Alferes, J., Bailey, J., May, W., Schwertel, U. (eds.) Principles and Practice of Semantic Web Reasoning 4th International Workshop (PPSWR 2006), Revised Selected Papers. LNAI, vol. 4187. Springer, Berlin (2006)Google Scholar
  14. 14.
    Beall, J.C., Restall, G.: Defending Logical Pluralism. In: Brown, B., Woods, J. (eds.) Logical Consequences: Rival Approaches. Proceedings of the 1999 Conference of the Society of Exact Philosophy. Stanmore, Hermes (2001)Google Scholar
  15. 15.
    Beall J.C., Restall G.: Logical Pluralism. Clarendon Press, Oxford (2006)Google Scholar
  16. 16.
    Bekiaris, E., Bonfiglio, S.: The OASIS Concept. In: Stephanidis, C. (ed.) Universal Access in Human-Computer Interaction. Addressing Diversity. Lecture Notes in Computer Science, vol. 5614, pp. 202–209. Springer, Berlin (2009)Google Scholar
  17. 17.
    Belnap N.D.: Under Carnap’s lamp: flat pre-semantics. Stud. Log. 80(1), 1–28 (2005)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Belnap N.D.: How a computer should think. In: Ryle, G. (eds) Contemporary Aspects of Philosophy, Oriel Press, Stocksfield (1977)Google Scholar
  19. 19.
    Belnap N.D.: A useful four-valued logic. In: Dunn, J., Epstein, G. (eds) Modern Uses of Multiple-Valued Logics, pp. 8–37. Reidel, Dordrecht (1977)Google Scholar
  20. 20.
    Bench-Capon, T.J.M., Malcolm, G.: Formalising Ontologies and Their Relations. In: Proc. of DEXA-99. LNCS, vol. 1677, pp. 250–259. Springer, Berlin (1999)Google Scholar
  21. 21.
    Bennett B.: Modal logics for qualitative spatial reasoning. J. Interest Group Pure Appl. Log. 4, 23–45 (1996)MATHGoogle Scholar
  22. 22.
    van Benthem: J. Logical dynamics meets logical pluralism?. Aust. J. Log. 6, 182–209 (2008)MATHGoogle Scholar
  23. 23.
    Béziau, J.-Y. (ed.): Logica Universalis: Towards a General Theory of Logic. Birkhäuser, Basel (2005)MATHGoogle Scholar
  24. 24.
    Bhatt, M., Dylla, F., Hois, J.: Spatio-terminological inference for the design of ambient environments. In: Hornsby, K.S., Claramunt, C., Denis, M., Ligozat, G. (eds.) Conference on Spatial Information Theory (COSIT’09), pp. 371–391. Springer (2009)Google Scholar
  25. 25.
    Bidoit, M., Mosses, P.D.: Casl User Manual. LNCS, vol. 2900 (IFIP Series). Springer, Berlin (2004)Google Scholar
  26. 26.
    Birnbaum, L., Forbus, K.D., Wagner, E., Baker, J., Witbrock, M.: Analogy, intelligent ir, and knowledge integration for intelligence analysis: situation tracking and the whodunit problem. In: Proceedings of the International Conference on Intelligence Analysis (2005)Google Scholar
  27. 27.
    Bittner, T., Donnelly, M.: Computational ontologies of parthood, componenthood, and containment. In: Kaelbling, L.P., Saffiotti, A. (eds.) IJCAI. Professional Book Center, pp. 382–387 (2005)Google Scholar
  28. 28.
    Borgida A.: On the relative expressiveness of description logics and predicate logics. Artif. Intell. 82(1–2), 353–367 (1996)CrossRefMathSciNetGoogle Scholar
  29. 29.
    Borgida A., Serafini L.: Distributed description logics: assimilating information from peer sources. J. Data Semant. 1, 153–184 (2003)Google Scholar
  30. 30.
    Borzyszkowski, T.: Higher-order logic and theorem proving for structured specifications. In: Bert, D., Choppy, C., Mosses, P.D. (eds.) WADT. Lecture Notes in Computer Science, vol. 1827, pp. 401–418. Springer (1999)Google Scholar
  31. 31.
    Brachman R.J.: On the epistemological status of semantic networks. In: Findler, N.V. (eds) Associative Networks: Representation and Use of Knowledge by Computers, Academic Press, London (1979)Google Scholar
  32. 32.
    Braüner T., Ghilardi S.: First-order modal logic. In: Benthem, J.v., Blackburn, P., Wolter, F. (eds) Handbook of Modal Logic, Elsevier, Amsterdam (2006)Google Scholar
  33. 33.
    Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Epistemic first-order queries over description logic knowledge bases. In: Proc. of the 2006 Description Logic Workshop (DL 2006), CEUR Electronic Workshop Proceedings, vol. 189 (2006). http://ceur-ws.org/Vol-189/
  34. 34.
    Calvanese, D., Giacomo, G.D., Lembo, D., Lenzerini, M., Poggi, A., Rosati, R.: Ontology-based database access. In: Proc. of SEBD, pp. 324–331 (2007)Google Scholar
  35. 35.
    Carnap, R.: Logische Syntax der Sprache. Kegan Paul, 1934. English translation 1937, The Logical Syntax of LanguageGoogle Scholar
  36. 36.
    Carnap R.: Empiricism, semantics, and ontology. Revue Internationale de Philosophie 4, 20–40 (1950)Google Scholar
  37. 37.
    Carnap, R.: Intellectual autobiography. In: Schilpp, P.A. (ed.) The philosophy of Rudolf Carnap. The Library of Living Philosophers, vol. 11. Open Court, La Salle (1963)Google Scholar
  38. 38.
    ten Cate, B., Conradie, W., Marx, M., Venema, Y.: Definitorially complete description logics. In: Doherty, P., Mylopoulos, J., Welty, C. (eds.) Proceedings of KR 2006, pp. 79–89. AAAI Press, Menlo Park (2006)Google Scholar
  39. 39.
    Church A.: A formulation of the simple theory of types. J. Symbol. Log. 5(1), 56–69 (1940)MATHCrossRefMathSciNetGoogle Scholar
  40. 40.
    Codescu, M., Mossakowski, T.: Heterogeneous colimits. In: Boulanger, F., Gaston, C., Schobbens, P.-Y. (eds.) MoVaH’08 Workshop on Modeling, Validation and Heterogeneity (2008)Google Scholar
  41. 41.
    CoFI (The Common Framework Initiative).: Casl Reference Manual. LNCS, vol. 2960 (IFIP Series). Springer (2004). Available at http://www.cofi.info
  42. 42.
    Cohn A., Hazarika S.: Qualitative spatial representation and reasoning: an overview. Fundam. Inform. 43, 2–32 (2001)MathSciNetGoogle Scholar
  43. 43.
    Common Logic Working Group.: Common Logic: Abstract syntax and semantics. Tech. rep. (2003)Google Scholar
  44. 44.
    Conesa J., Storey V.C., Sugumaran V.: Usability of upper level ontologies: the case of ResearchCyc. Data Knowl. Eng. 69(4), 343–356 (2010)CrossRefGoogle Scholar
  45. 45.
    Cuenca Grau B., Horrocks I., Kazakov Y., Sattler U.: Modular Reuse of Ontologies: Theory and Practice. J. Artif. Intell. Res. (JAIR) 31, 273–318 (2008)MATHMathSciNetGoogle Scholar
  46. 46.
    Cuenca Grau B., Horrocks I., Motik B., Parsia B., Patel-Schneider P., Sattler U.: OWL 2: The next step for OWL. Web Semantics: Science, Services and Agents on the World Wide Web 6(4), 309–322 (2008) Semantic Web Challenge 2006/2007CrossRefGoogle Scholar
  47. 47.
    Cuenca Grau, B., Parsia, B., Sirin, E.: Ontology integration using \({\mathcal{E}}\) -connections. In: Stuckenschmidt, H., Parent, C., Spaccapietra, S. (eds.) Modular Ontologies—Concepts, Theories and Techniques for Knowledge Modularization. LNCS, vol. 5445. Springer (2009)Google Scholar
  48. 48.
    de Bouvère K.: Logical synonymity. Indagationes Mathematicae 27, 622–629 (1965)Google Scholar
  49. 49.
    Del Vescovo, C., Parsia, B., Sattler, U., Schneider, T.: The modular structure of an ontology: an empirical study. In: Kutz, O., Hois, J., Bao, J., Cuenca Grau, B. (eds.) Modular Ontologies—Proceedings of the Fourth International Workshop (WoMO 2010) (Toronto, Canada). Frontiers in Artificial Intelligence and Applications, vol. 210, pp. 11–24. IOS Press (2010)Google Scholar
  50. 50.
    Delugach, H.S.: Towards conceptual structures interoperability using common logic. In: Croitoru, M., Jäschke, R., Rudolph, S. (eds.) Proc. of the Third Conceptual Structures Tool Interoperability Workshop, held at the 16th International Conference on Conceptual Structures (ICCS 2008), July 7, 2008, UTM (Université Toulouse Le Mirail), Toulouse, France (2008)Google Scholar
  51. 51.
    Diaconescu R.: Grothendieck institutions. Appl. Categorical Struct. 10, 383–402 (2002)MATHCrossRefMathSciNetGoogle Scholar
  52. 52.
    Diaconescu, R.: Institution-independent model theory. In: Studies in Universal Logic. Birkhäuser, Basel (2008)Google Scholar
  53. 53.
    Diaconescu R., Goguen J., Stefaneas P.: Logical Support for Modularisation. In: Huet, G., Plotkin, G. (eds) Papers presented at the second annual Workshop on Logical environments, Edinburgh, Scotland, pp. 83–130. Cambridge University Press, New York (1993)Google Scholar
  54. 54.
    Donini F.M., Lenzerini M., Nardi D., Nutt W., Schaerf A.L: An epistemic operator for description logics. Artif. Intell. 100(1–2), 225–274 (1998)MATHCrossRefMathSciNetGoogle Scholar
  55. 55.
    Dou, D., McDermot, D.: Towards theory translation. In: Declarative Agent Languages and Technologies IV. Springer, Berlin (2007)Google Scholar
  56. 56.
    Enderton H.B.: A Mathematical Introduction to Logic. Academic Press, New York (1972)MATHGoogle Scholar
  57. 57.
    Euzenat J., Shvaiko P.: Ontology Matching. Springer, Heidelberg (2007)MATHGoogle Scholar
  58. 58.
    Evans, M.: Can there be vague objects? Analysis 38, 208 (1978) reprinted in his Collected Papers, Oxford, Clarendon Press (1985)Google Scholar
  59. 59.
    Feferman S.: Hilbert’s program relativized: Proof-theoretical and foundational reductions. J. Symbol. Logic 53(2), 364–384 (1988)MATHCrossRefMathSciNetGoogle Scholar
  60. 60.
    Fitting M., Mendelsohn R.L.: First–Order Modal Logic. Kluwer Academic Publishers, Dordrecht (1998)MATHGoogle Scholar
  61. 61.
    Freksa, C.: Using orientation information for qualitative spatial reasoning. In: Theories and methods of spatio-temporal reasoning in geographic space. LNCS, vol. 639, pp. 162–178. Springer, Berlin (1992)Google Scholar
  62. 62.
    Gabbay, D.: Fibring logics. Oxford Logic Guides, vol. 38. Clarendon Press, Oxford (1999)Google Scholar
  63. 63.
    Gabbay, D., Kurucz, A., Wolter, F., Zakharyaschev, M.: Many-Dimensional Modal Logics: Theory and Applications. No. 148 in Studies in Logic and the Foundations of Mathematics. Elsevier Science Publishers, Amsterdam (2003)Google Scholar
  64. 64.
    Gangemi, A., Guarino, N., Masolo, C., Oltramari, A., Schneider, L.: Sweetening Ontologies with dolce. In: Proc. of EKAW 2002. LNCS, vol. 2473, pp. 166–181. Springer, Berlin (2002)Google Scholar
  65. 65.
    Gärdenfors P.: Conceptual Spaces—The Geometry of Thought. MIT Press, Bradford Books (2000)Google Scholar
  66. 66.
    Gardner M.: Logic Machines and Diagrams. McGraw-Hill, New York (1958)MATHGoogle Scholar
  67. 67.
    Genesereth M.R., Nilsson N.J.: Logical Foundations of Artificial Intelligence. Morgan Kaufmann, Los Altos (1987)MATHGoogle Scholar
  68. 68.
    Goguen J.A.: A Categorical Manifesto. Math. Struct. Comput. Sci. 1, 49–67 (1991)MATHCrossRefMathSciNetGoogle Scholar
  69. 69.
    Goguen, J.A.: Ontology, society, and ontotheology. In: Varzi, A.C., Vieu, L. (eds.) Formal Ontology in Information Systems: Proceedings of the Third International Conference (FOIS-2004). Frontiers in Artificial Intelligence and Applications, IOS Press, pp. 95–105 (2004)Google Scholar
  70. 70.
    Goguen J.A.: Data, schema, ontology and logic integration. Log. J, IGPL 13(6), 685–715 (2005)MATHCrossRefMathSciNetGoogle Scholar
  71. 71.
    Goguen, J.A.: Information integration in institutions. In: Moss, L. (ed.) Jon Barwise Memorial Volume. Indiana University Press, To appear (2006)Google Scholar
  72. 72.
    Goguen, J.A., Burstall, R.M.: Introducing institutions. In: Clarke, E., Kozen, D. (eds.) Proc. Logics of Programming Workshop. LNCS, vol. 164, pp. 221–256. Springer (1984)Google Scholar
  73. 73.
    Goguen J.A., Burstall R.M.: Institutions: abstract model theory for specification and programming. J. ACM 39, 95–146 (1992)MATHCrossRefMathSciNetGoogle Scholar
  74. 74.
    Goguen J.A., Roşu G.: Institution morphisms. Form. Aspects Comput. 13, 274–307 (2002)MATHCrossRefGoogle Scholar
  75. 75.
    Grenon P., Smith B., Goldberg L.: Biodynamic ontology: applying BFO in the biomedical domain. In: Pisanelli, D.M. (eds) Ontologies in Medicine, pp. 20–38. IOS Press, Amsterdam (2004)Google Scholar
  76. 76.
    Gruber T.R.: Toward principles for the design of ontologies used for knowledge sharing. Int. J. Hum.-Comput. Stud. 43(4–5), 907–928 (1995)CrossRefGoogle Scholar
  77. 77.
    Grüninger, M., Hahmann, T., Hashemi, A., Ong, D.: Ontology verification with repositories. In: Galton, A., Mizoguchi, R. (eds.) Formal Ontology in Information Systems—Proceedings of the Sixth International Conference (FOIS-2010). Frontiers in Artificial Intelligence and Applications, vol. 209, pp. 317–330. IOS Press (2010)Google Scholar
  78. 78.
    Guarino, N.: The ontological level. In: Casati, R., Smith, B., White, G. (eds.) Philosophy and the Cognitive Sciences (1994). Hölder-Pichler-Tempsky, pp. 443–456. Proc. of the 16th Wittgenstein Symposium, Kirchberg, Austria, Vienna, August 1993.Google Scholar
  79. 79.
    Guarino, N.: Formal ontology and information systems. In: Guarino, N. (ed.) Formal Ontology in Information Systems, Proc. of FOIS-98, Trento, Italy, June 6–8, pp. 3–15. IOS Press, Amsterdam (1998)Google Scholar
  80. 80.
    Guarino, N.: The ontological level: revisiting 30 years of knowledge representation. In: Borgida, A., Chaudhri, V., Giorgini, P., Yu, E. (eds.) Conceptual Modelling: Foundations and Applications. Essays in Honor of John Mylopoulos, pp. 52–67. Springer (2009)Google Scholar
  81. 81.
    Guarino N., Giaretta P.: Ontologies and knowledge bases: towards a terminological clarification. In: Mars, N. (eds) Towards Very Large Knowledge Bases: Knowledge Building And Knowledge Sharing, pp. 25–32. IOS Press, Amsterdam (1995)Google Scholar
  82. 82.
    Guarino N., Welty C.: Evaluating ontological decisions with OntoClean. Commun. ACM 45(2), 61–65 (2002)CrossRefGoogle Scholar
  83. 83.
    Guerra S.: Composition of default specifications. J. Log. Comput. 11(4), 559–578 (2001)MATHCrossRefMathSciNetGoogle Scholar
  84. 84.
    Guizzardi, G.: Modal Aspects of object types and part-whole relations and the de re/de dicto distinction. In: Krogstie, J., Opdahl, A.L., Sindre, G. (eds.) Advanced Information Systems Engineering, 19th International Conference (CAiSE-07). Lecture Notes in Computer Science, vol. 4495, pp. 5–20. Springer (2007)Google Scholar
  85. 85.
    Haack S.: Philosophy of Logics. Cambridge University Press, Cambridge (1978)Google Scholar
  86. 86.
    Haack S.: Deviant Logic, Fuzzy Logic: Beyond the Formalism. Cambridge University Press, Cambridge (1996)MATHGoogle Scholar
  87. 87.
    Haase, P., van Harmelen, F., Huang, Z., Stuckenschmidt, H., Sure, Y.: A framework for handling inconsistency in changing ontologies. In: Proc. of the 4th International Semantic Web Conference (ISWC-05). LNCS, vol. 3729, pp. 353–367. Springer (2005)Google Scholar
  88. 88.
    Heller B., Herre H.: Ontological categories in GOL. Axiomathes 14(1–3), 57–76 (2004)CrossRefGoogle Scholar
  89. 89.
    Herre, H.: The ontology of mereological systems. In: Poli, R., Seibt, J., Healy, M., Kameas, A. (eds.) Theory and Applications of Ontology - volume 1: Philosophical Perspectives. Springer (2010)Google Scholar
  90. 90.
    Hois, J., Bhatt, M., Kutz, O.: Modular ontologies for architectural design. In: Proc. of the 4th Workshop on Formal Ontologies Meet Industry, FOMI-09, Vicenza, Italy. Frontiers in Artificial Intelligence and Applications, vol. 198. IOS Press (2009)Google Scholar
  91. 91.
    Hois, J., Kutz, O.: Counterparts in language and space—similarity and \({\mathcal{S}}\) -Connection. In: Eschenbach, C., Grüninger, M. (eds.) Formal Ontology in Information Systems (FOIS 2008), pp. 266–279. IOS Press (2008)Google Scholar
  92. 92.
    Hois, J., Kutz, O.: Natural language meets spatial calculi. In: Freksa, C., Newcombe, N.S., Gärdenfors, P., Wölfl, S. (eds.) Spatial Cognition VI. Learning, Reasoning, and Talking about. Space. 6th International Conference on Spatial Cognition. LNCS, pp. 266–282. Springer (2008)Google Scholar
  93. 93.
    Horridge, M., Drummond, N., Goodwin, J., Rector, A., Stevens, R., Wang, H.H.: The Manchester OWL Syntax. In: OWL: Experiences and Directions (2006)Google Scholar
  94. 94.
    Horrocks, I., Kutz, O., Sattler, U.: The Even More Irresistible \({\mathcal{SROIQ}}\) . In: Proc. of the 10th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR2006), pp. 57–67. AAAI Press (June 2006)Google Scholar
  95. 95.
    Kalfoglou Y., Schorlemmer M.: The information flow approach to ontology-based semantic alignment. In: Poli, R., Healy, M., Kameas, A. (eds) Theory and Applications of Ontology: Computer Applications, Springer, Berlin (2010)Google Scholar
  96. 96.
    Kalyanpur, A., Parsia, B., Horridge, M., Sirin, E.: Finding all Justifications of OWL DL Entailments. In: Proc. of ISWC/ASWC2007. LNCS, vol. 4825, pp. 267–280. Springer, Berlin (2007)Google Scholar
  97. 97.
    Kazakov, Y.: An extension of regularity conditions for complex role inclusion axioms. In: Grau, B.C., Horrocks, I., Motik, B., Sattler, U. (eds.) Proc. of DL-09., vol. 477 of CEUR Workshop Proceedings, CEUR-WS.org (2009)Google Scholar
  98. 98.
    Keet C.M., Artale A.: Representing and reasoning over a taxonomy of part-whole relations. Appl. Ontol. 3(1–2), 91–110 (2008)Google Scholar
  99. 99.
    Klinov, P., Mazlack, L.J.: On possible applications of rough mereology to handling granularity in ontological knowledge. In: Proceedings of the 22nd National Conference on Artificial Intelligence (AAAI-07), pp. 1876–1877. AAAI Press, Menlo Park (2007)Google Scholar
  100. 100.
    Knauff, M., Rauh, R., Schlieder, C.: Preferred mental models in qualitative spatial reasoning: a cognitive assessment of Allen’s calculus. In: Proc. of the 17th Annual Conference of the Cognitive Science Society (1995)Google Scholar
  101. 101.
    Konev B., Lutz C., Walther D., Wolter F.: Formal properties of modularization. In: Stuckenschmidt, H., Spaccapietra, S. (eds) Ontology Modularization, Springer, Berlin (2008)Google Scholar
  102. 102.
    Konev, B., Lutz, C., Walther, D., Wolter, F.: Semantic modularity and module extraction in description logics. In: 18th European Conf. on Artificial Intelligence (ECAI-08) (2008)Google Scholar
  103. 103.
    Kontchakov, R., Lutz, C., Toman, D., Wolter, F., Zakharyaschev, M.: The combined approach to query answering in DL-lite. In: Lin, F., Sattler, U. (eds.) Proceedings of the 12th International Conference on Principles of Knowledge Representation and Reasoning (KR2010). AAAI Press, Menlo Park (2010)Google Scholar
  104. 104.
    Kotas J., Pieczkowski A.: Allgemeine logische und mathematische Theorien. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik (now ‘Mathematical Logic Quarterly’) 16(6), 353–376 (1970)MATHCrossRefMathSciNetGoogle Scholar
  105. 105.
    Kracht, M., Kutz, O.: Logically possible worlds and counterpart semantics for modal logic. In: Jacquette, D. (ed.) Philosophy of Logic, Handbook of the Philosophy of Science, vol. 5, pp. 943–996. Elsevier, Amsterdam (2007)Google Scholar
  106. 106.
    Kutz, O.: \({\mathcal{E}}\) -connections and logics of distance. PhD thesis, The University of Liverpool (2004)Google Scholar
  107. 107.
    Kutz O.: Notes on logics of metric spaces. Stud. Log. 85(1), 75–104 (2007)MATHCrossRefMathSciNetGoogle Scholar
  108. 108.
    Kutz, O., Lücke, D., Mossakowski, T.: Heterogeneously structured ontologies—integration, connection, and refinement. In: Meyer, T., Orgun, M.A. (eds.) Advances in Ontologies. Proceedings of the Knowledge Representation Ontology Workshop (KROW 2008). CRPIT, ACS, vol. 90, pp. 41–50. Sydney, Australia (2008)Google Scholar
  109. 109.
    Kutz, O., Lücke, D., Mossakowski, T.: Modular construction of models—towards a consistency proof for the foundational ontology Dolce. In: 1st Int. Workshop on Computer Science as Logic-Related. ICTAC 2008, Istanbul, Turkey (2008)Google Scholar
  110. 110.
    Kutz, O., Lücke, D., Mossakowski, T., Normann, I.: The OWL in the Casl—designing ontologies across logics. In: Dolbear, C., Ruttenberg, A., Sattler, U. (eds.) OWL: Experiences and Directions, 5th International Workshop (OWLED-08) (co-located with ISWC-08, Karlsruhe, Germany, October 26–27), CEUR-WS, vol. 432 (2008)Google Scholar
  111. 111.
    Kutz O., Lutz C., Wolter F., Zakharyaschev M.: \({\mathcal{E}}\) -connections of Abstract Description Systems. Artif. Intell. 156(1), 1–73 (2004)MATHCrossRefMathSciNetGoogle Scholar
  112. 112.
    Kutz, O., Mossakowski, T.: Modules in transition: conservativity, composition, and colimits. In: 2nd Int. Workshop on Modular Ontologies (WoMO-07). K-CAP, Whistler BC, Canada (2007)Google Scholar
  113. 113.
    Kutz, O., Mossakowski, T.: Conservativity in Structured Ontologies. In: 18th European Conf. on Artificial Intelligence (ECAI-08), IOS Press, Patras, Greece (2008)Google Scholar
  114. 114.
    Kutz, O., Mossakowski, T., Codescu, M.: Shapes of alignments: construction, combination, and computation. In: Sattler, U., Tamilin, A. (eds.) Proc. of the 1st Workshop on Ontologies: Reasoning and Modularity (WORM-08) CEUR-WS, vol. 348. ESWC, Tenerife (2008)Google Scholar
  115. 115.
    Kutz, O., Normann, I.: Context discovery via theory interpretation. In: Proc. of the IJCAI Workshop on Automated Reasoning about Context and Ontology Evolution, ARCOE-09, Pasadena, California (2009)Google Scholar
  116. 116.
    Kutz, O., Wolter, F., Zakharyaschev, M.: Connecting abstract description systems. In: Proc. of the 8th Conference on Principles of Knowledge Representation and Reasoning (KR-02), pp. 215–226. Morgan Kaufmann (2002)Google Scholar
  117. 117.
    Leibniz, G.W.: Sämtliche Schriften und Briefe—VI Sektion: Philosophische Schriften, Band IV, pp. 1680–1692. Akademie, Berlin (2001)Google Scholar
  118. 118.
    Lenat D.B., Guha R.V.: Building large knowledge-based systems: representation and inference in the Cyc project. Addison-Wesley, Reading (1990)Google Scholar
  119. 119.
    Lewis, D.: Parts of Classes. Basil Blackwell, Oxford (1991) With an appendix by Burgess, J.P., Hazen, A.P., Lewis, D.Google Scholar
  120. 120.
    Lucanu, D., Li, Y.-F., Dong, J.S.: Semantic web languages—towards an institutional perspective. In: Futatsugi, K., Jouannaud, J.-P., Meseguer, J. (eds.) Algebra, Meaning, and Computation, Essays Dedicated to Joseph A. Goguen on the Occasion of His 65th Birthday. Lecture Notes in Computer Science, vol. 4060, pp. 99–123. Springer (2006)Google Scholar
  121. 121.
    Lukasiewicz T.: Expressive probabilistic description logics. Artif. Intell. 172(6–7), 852–883 (2008)MATHCrossRefMathSciNetGoogle Scholar
  122. 122.
    Lutz, C., Schröder, L.: Probabilistic description logics for subjective uncertainty. In: Lin, F., Sattler, U. (eds.) Proceedings of the 12th International Conference on Principles of Knowledge Representation and Reasoning (KR2010). AAAI Press, Menlo Park (2010)Google Scholar
  123. 123.
    Lutz, C., Walther, D., Wolter, F.: Conservative extensions in expressive description logics. In: Proceedings of IJCAI-07, pp. 453–458. AAAI Press, Menlo Park (2007)Google Scholar
  124. 124.
    Lutz, C., Wolter, F.: Modal logics of topological relations. Log. Methods Comput. Sci. 2(2) (2006)Google Scholar
  125. 125.
    Lutz, C., Wolter, F.: Mathematical logic for life science ontologies. In: Ono, H., Kanazawa, M., de Queiroz, R.J.G.B. (eds.) WoLLIC. Lecture Notes in Computer Science, vol. 5514, pp. 37–47. Springer (2009)Google Scholar
  126. 126.
    Lutz, C., Wolter, F., Zakharyaschev, M.: Temporal description logics: a survey. In: Proceedings of the Fourteenth International Symposium on Temporal Representation and Reasoning. IEEE Computer Society Press (2008)Google Scholar
  127. 127.
    Ma, Y., Hitzler, P.: Paraconsistent reasoning for OWL 2. In: RR ’09: Proceedings of the 3rd International Conference on Web Reasoning and Rule Systems, pp. 197–211. Springer, Berlin (2009)Google Scholar
  128. 128.
    Ma, Y., Hitzler, P.: Distance-based measures of inconsistency and incoherency for description logics. In: Haarslev, V., Toman, D., Weddell, G. (eds.) Proceedings of the 23rd International Workshop on Description Logics (DL-2010), vol. 573. CEUR Workshop Proceedings, pp. 475–485. Waterloo, Canada (2010)Google Scholar
  129. 129.
    Ma, Y., Hitzler, P., Lin, Z.: Algorithms for paraconsistent Reasoning with OWL. In: Franconi, E., Kifer, M., May, W. (eds.) ESWC. Lecture Notes in Computer Science, vol. 4519. pp. 399–413. Springer (2007)Google Scholar
  130. 130.
    Ma, Y., Hitzler, P., Lin, Z.: Paraconsistent resolution for four-valued description logics. In: Proceedings of the 2007 International Workshop on Description Logics (DL-2007), Brixen-Bressanone, Italy, June 2007. CEUR Workshop Proceedings, vol. 250, pp. 395–402 (June 2007)Google Scholar
  131. 131.
    Mac Lane S.: Categories for the Working Mathematician, 2nd edn. Springer, Berlin (1998)MATHGoogle Scholar
  132. 132.
    Madhavan, J., Bernstein, P., Domingos, P., Halevy, A.: Representing and reasoning about mappings between domain models. In: Proc. of AAAI 2002. Edmonton, Canada (2002)Google Scholar
  133. 133.
    Marx M., Venema Y.: Multi-dimensional Modal Logic. Kluwer Academic Publishers, Dordrecht (1997)MATHGoogle Scholar
  134. 134.
    Masolo, C., Borgo, S., Gangemi, A., Guarino, N., Oltramari, A.: Wonder Web Deliverable D18: Ontology Library. Tech. rep., ISTC-CNR (2003)Google Scholar
  135. 135.
    Masters, J.: Structured knowledge source integration and its applications to information fusion. In: Proceedings of the Fifth International Conference on Information Fusion (FUSION 2002). Annapolis, MD, IEEE (2002)Google Scholar
  136. 136.
    McCorduck, P.: Machines Who Think: A Personal Inquiry into the History and Prospects of Artificial Intelligence. Peters, Wellesley, 2nd rev edn. (2004)Google Scholar
  137. 137.
    Meseguer, J.: General logics. In: Logic Colloquium 87, pp. 275–329. North Holland (1989)Google Scholar
  138. 138.
    Meseguer, J., Martí-Oliet, N.: From abstract data types to logical frameworks. In: Selected papers from the 10th Workshop on Specification of Abstract Data Types Joint with the 5th COMPASS Workshop on Recent Trends in Data Type Specification, pp. 48–80. Springer, London (1995)Google Scholar
  139. 139.
    Minsky, M.; A framework for representing knowledge. In: Winston, P. (ed.) The Psychology of Computer Vision. McGraw-Hill (1975)Google Scholar
  140. 140.
    Mossakowski, T.: Comorphism-based Grothendieck logics. In: Mathematical Foundations of Computer Science. LNCS, vol. 2420, pp. 593–604. Springer (2002)Google Scholar
  141. 141.
    Mossakowski, T.: Institutional 2-cells and Grothendieck institutions. In: Futatsugi, K., Jouannaud, J.-P., Meseguer, J. (eds.) Algebra, Meaning and Computation. Essays Dedicated to Joseph A. Goguen. LNCS 4060, pp. 124–149. Springer (2006)Google Scholar
  142. 142.
    Mossakowski T., Autexier S., Hutter D.: Development graphs—proof management for structured specifications. J. Log. Algebraic Program. 67(1–2), 114–145 (2006)MATHCrossRefMathSciNetGoogle Scholar
  143. 143.
    Mossakowski, T., Haxthausen, A., Sannella, D., Tarlecki, A.: CASL: The Common Algebraic Specification Language. In: Bjorner, M.H.D. (ed.) Logics of Formal Specification Languages. Monographs in Theoretical Computer Science. Springer, Heidelberg, ch. 3, pp. 241–298 (2008)Google Scholar
  144. 144.
    Mossakowski, T., Maeder, C., Lüttich, K.: The heterogeneous tool set. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424. Springer, pp. 519–522 (2007)Google Scholar
  145. 145.
    Mossakowski, T., Maeder, C., Lüttich, K.: The heterogeneous tool set. In: Beckert, B. (ed.) VERIFY 2007, vol. 259. CEUR-WS (2007)Google Scholar
  146. 146.
    Mossakowski, T., Tarlecki, A.: Heterogeneous logical environments for distributed specifications. In: Corradini, A., Montanari, U. (eds.) WADT 2008. Lecture Notes in Computer Science, vol. 5486, pp. 266–289. Springer (2009)Google Scholar
  147. 147.
    Mossakowski T., Tarlecki A., Diaconescu R.: What is a logic translation?. Logica Universalis 3(1), 95–124 (2009) Winner of the Universal Logic 2007 ContestCrossRefMathSciNetGoogle Scholar
  148. 148.
    Motik B., Horrocks I., Sattler U.: Bridging the Gap Between OWL and Relational Databases. J. Web Semant. Sci. Serv. Agents World Wide Web 7(2), 74–89 (2009)CrossRefGoogle Scholar
  149. 149.
    Newell, A., Shaw, J.C., Simon, H.A.: Report on a general problem-solving program. In: Proceedings of the International Conference on Information Processing (IFIP), pp. 256–264 (1959)Google Scholar
  150. 150.
    Newell A., Simon H.A.: Computer science as empirical inquiry: symbols and search. Commun. ACM 19(3), 113–126 (1976)CrossRefMathSciNetGoogle Scholar
  151. 151.
    Niles, I., Pease, A.: Towards a standard upper ontology. In: FOIS-01: Proc. of the International Conference on Formal Ontology in Information Systems, pp. 2–9. ACM, New York (2001)Google Scholar
  152. 152.
    Nipkow, T., Paulson, L.C., Wenzel, M.L.: Isabelle/HOL—a proof assistant for higher-order logic. LNCS, vol. 2283. Springer (2002)Google Scholar
  153. 153.
    Normann, I.: Automated theory interpretation. PhD thesis, Department of Computer Science, Jacobs University, Bremen (2009)Google Scholar
  154. 154.
    Odintsov, S.P., Wansing, H.: Inconsistency-tolerant description logic. Motivation and Basic Systems. In: Hendricks, V., Malinowski, J. (eds.) Trends in Logic. 50 Years of Studia Logica, no. 21 in Trends in Logic, pp. 301–335. Kluwer Academic Publishers, Dordrecht (2003)Google Scholar
  155. 155.
    Odintsov S.P., Wansing H.: Inconsistency-tolerant description logic. Part II: A tableau algorithm for \({\mathcal{C}\mathcal{ALC}^{C}}\). J. Appl. Log. 6(3), 343–360 (2008)CrossRefMathSciNetGoogle Scholar
  156. 156.
    Parsons T.: Nonexistent Objects. Yale University Press, New Haven and London (1980)Google Scholar
  157. 157.
    Patel-Schneider P.F.: A four-valued semantics for terminological logics. Artif. Intell. 38(3), 319–351 (1989)MATHCrossRefMathSciNetGoogle Scholar
  158. 158.
    Pieczkowski A.: Über Theorien im erweiterten Sinne. Stud. Log. 33(4), 317–331 (1974)CrossRefMathSciNetGoogle Scholar
  159. 159.
    Pokrywczyński, D., Malcolm, G.: Towards a functional approach to modular ontologies using institutions. In: Kutz, O., Hois, J., Bao, J., Cuenca Grau, B. (eds.) Modular Ontologies—Proceedings of the Fourth International Workshop (WoMO 2010). Frontiers in Artificial Intelligence and Applications, vol. 210, pp. 53–66. IOS Press, Toronto (2010)Google Scholar
  160. 160.
    Priest, G.: In contradiction: a study of the transconsistent, Nijhoff International Philosophy Series, vol. 39. Dordrecht, Martinus Nijhoff, The Hague (1987)Google Scholar
  161. 161.
    Priest, G.: Logic: One or many? In: Brown, B., Woods, J. (eds.) Logical Consequences. Hermes (2001)Google Scholar
  162. 162.
    Priest G.: Logical pluralism hollandaise. Aust. J. Log. 6, 210–214 (2008)MATHMathSciNetGoogle Scholar
  163. 163.
    Randell, D.A., Cui, Z., Cohn, A.G.: A spatial logic based on regions and connection. In: Proceedings of the 3rd International Conference on the Principles of Knowledge Representation and Reasoning (KR’92), pp. 165–176. Morgan Kaufmann, Los Altos (1992)Google Scholar
  164. 164.
    Restall G.: Carnap’s tolerance, language change and logical pluralism. J. Philos. 99, 426–443 (2002)CrossRefMathSciNetGoogle Scholar
  165. 165.
    Ridder, L.: Mereologie—Ein Beitrag zur Ontologie und Erkenntnistheorie. Philosophische Abhandlungen, vol. 83. Vittorio Klostermann, Frankfurt am Main (2002)Google Scholar
  166. 166.
    Rodrigues, O., Russo, A.: A Translation Method for Belnap Logic. Research Report Doc 98/7, Imperial College London, September 1998Google Scholar
  167. 167.
    Sannella, D., Burstall, R.: Structured theories in LCF. In: Proc. 8th Colloq. on Trees in Algebra and Programming. Lecture Notes in Computer Science, vol. 159, pp. 377–391. Springer (1983)Google Scholar
  168. 168.
    Schorlemmer, M., Kalfoglou, Y.: Institutionalising ontology-based semantic integration. J. Appl. Ontol. 3(3) (2008)Google Scholar
  169. 169.
    Schröder L., Mossakowski T.: HasCASL: Integrated higher-order specification and program development. Theor. Comput. Sci. 410(12–13), 1217–1260 (2009)MATHCrossRefGoogle Scholar
  170. 170.
    Schulz, S., Romacker, M., Hahn, U.: Part-whole reasoning in medical ontologies revisited—introducing SEP triplets into classification-based description logics. In: Proc. AMIA Symposium, pp. 830–834 (1998)Google Scholar
  171. 171.
    Seidenberg, J., Rector, A.L.: Representing transitive propagation in OWL. In: Embley, D.W., Olivé, A., Ram, S. (eds.) Proc. of ER 2006, 25th International Conference on Conceptual Modeling, Tucson, AZ, USA, November 6–9. LNCS, vol. 4215, pp. 255–266. Springer (2006)Google Scholar
  172. 172.
    Shehtman V.: “Everywhere” and “Here”. J. Appl. Non-Classical Log. 9 (1999)Google Scholar
  173. 173.
    Sheremet M., Tishkovsky D., Wolter F., Zakharyaschev M.: A logic for concepts and similarity. J. Log. Comput. 17(3), 415–452 (2007)MATHCrossRefMathSciNetGoogle Scholar
  174. 174.
    Sheremet M., Wolter F., Zakharyaschev M.: A modal logic framework for reasoning about comparative distances and topology. Ann. Pure Appl. Log. 161(4), 534–559 (2010)CrossRefMathSciNetGoogle Scholar
  175. 175.
    Simons P.: Parts: A Study in Ontology. Clarendon Press, Oxford (1987)Google Scholar
  176. 176.
    Simons P. (1991) On being spread out in time: temporal parts and the problem of change. In: Spohn W. et al. (eds) Existence and Explanation. Kluwer Academic Publishers. DordrechtGoogle Scholar
  177. 177.
    Sioutos N., de Coronado S., Haber M.W., Hartel F.W., Shaiu W.-L., Wright L.W.: NCI Thesaurus: a semantic model integrating cancer-related clinical and molecular information. J. Biomed. Inform. 40(1), 30–43 (2007)CrossRefGoogle Scholar
  178. 178.
    Straccia, U.: A sequent calculus for reasoning in four-valued description logics. In: Galmiche, D. (ed.) Proc. of TABLEAUX-97: Int. Conference on Automated Reasoning with Analytic Tableaux and Related Methods, Pont-à-Mousson, France, May 13–16. LNCS, vol. 1227, pp. 343–357. Springer (1997)Google Scholar
  179. 179.
    Suntisrivaraporn, B., Baader, F., Schulz, S., Spackman, K.: Replacing SEP-triplets in SNOMED CT using tractable description logic operators. In: AIME ’07: Proceedings of the 11th conference on Artificial Intelligence in Medicine, pp. 287–291. Springer, Berlin (2007)Google Scholar
  180. 180.
    Tarski A.: Der Aussagenkalkül und die Topologie. Fundamenta Mathematicae 31, 103–134 (1938)Google Scholar
  181. 181.
    Venn J.: Symbolic Logic. The MacMillan Company, London (1881)Google Scholar
  182. 182.
    Villadsen, J.: Paraconsistent query answering systems. In: FQAS ’02: Proceedings of the 5th International Conference on Flexible Query Answering Systems, pp. 370–384. Springer, London (2002)Google Scholar
  183. 183.
    Voronkov, A.: Inconsistencies in ontologies. In: JELIA-06, p. 19. (2006)Google Scholar
  184. 184.
    Zhou, L., Huang, H., Qi, G., Ma, Y., Huang, Z., Qu, Y.: Paraconsistent query answering over DL-lite ontologies. In: Proceedings of the Third Chinese Semantic Web Symposium (CSWS-09) (2009)Google Scholar
  185. 185.
    Zimmermann, A., Krötzsch, M., Euzenat, J., Hitzler, P.: Formalizing ontology alignment and its operations with category theory. In: Proc. of FOIS-06, pp. 277–288 (2006)Google Scholar

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Authors and Affiliations

  1. 1.SFB/TR 8 Spatial CognitionUniversity of BremenBremenGermany
  2. 2.DFKI GmbH and SFB/TR 8 Spatial CognitionUniversity of BremenBremenGermany

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