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

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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.

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References

  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. 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)

  3. Artale A., Franconi E.: A survey of temporal extensions of description logics. Ann. Math. Artif. Intell. 30(1–4), 171–210 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  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)

  5. Astesiano E., Kreowski H.-J., Krieg-Brückner B.: Algebraic Foundations of Systems Specification. Springer, Berlin (1999)

    Google Scholar 

  6. Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.F. (eds): The Description Logic Handbook. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  7. Baader F., Ghilardi S.: Connecting many-sorted theories. J. Symbol. Logic 72(2), 535–583 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  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)

  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)

  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)

    Article  Google Scholar 

  11. Bateman J., Tenbrink T., Farrar S.: The role of conceptual and linguistic ontologies in discourse. Discourse Processes 44(3), 175–213 (2007)

    Article  Google Scholar 

  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)

  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)

  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)

  15. Beall J.C., Restall G.: Logical Pluralism. Clarendon Press, Oxford (2006)

    Google Scholar 

  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)

  17. Belnap N.D.: Under Carnap’s lamp: flat pre-semantics. Stud. Log. 80(1), 1–28 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  18. Belnap N.D.: How a computer should think. In: Ryle, G. (eds) Contemporary Aspects of Philosophy, Oriel Press, Stocksfield (1977)

    Google Scholar 

  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. 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)

  21. Bennett B.: Modal logics for qualitative spatial reasoning. J. Interest Group Pure Appl. Log. 4, 23–45 (1996)

    MATH  Google Scholar 

  22. van Benthem: J. Logical dynamics meets logical pluralism?. Aust. J. Log. 6, 182–209 (2008)

    MATH  Google Scholar 

  23. Béziau, J.-Y. (ed.): Logica Universalis: Towards a General Theory of Logic. Birkhäuser, Basel (2005)

    MATH  Google Scholar 

  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)

  25. Bidoit, M., Mosses, P.D.: Casl User Manual. LNCS, vol. 2900 (IFIP Series). Springer, Berlin (2004)

  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)

  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)

  28. Borgida A.: On the relative expressiveness of description logics and predicate logics. Artif. Intell. 82(1–2), 353–367 (1996)

    Article  MathSciNet  Google Scholar 

  29. Borgida A., Serafini L.: Distributed description logics: assimilating information from peer sources. J. Data Semant. 1, 153–184 (2003)

    Google Scholar 

  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)

  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. 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. 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. 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)

  35. Carnap, R.: Logische Syntax der Sprache. Kegan Paul, 1934. English translation 1937, The Logical Syntax of Language

  36. Carnap R.: Empiricism, semantics, and ontology. Revue Internationale de Philosophie 4, 20–40 (1950)

    Google Scholar 

  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)

  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)

  39. Church A.: A formulation of the simple theory of types. J. Symbol. Log. 5(1), 56–69 (1940)

    Article  MATH  MathSciNet  Google Scholar 

  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)

  41. CoFI (The Common Framework Initiative).: Casl Reference Manual. LNCS, vol. 2960 (IFIP Series). Springer (2004). Available at http://www.cofi.info

  42. Cohn A., Hazarika S.: Qualitative spatial representation and reasoning: an overview. Fundam. Inform. 43, 2–32 (2001)

    MathSciNet  Google Scholar 

  43. Common Logic Working Group.: Common Logic: Abstract syntax and semantics. Tech. rep. (2003)

  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)

    Article  Google Scholar 

  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)

    MATH  MathSciNet  Google Scholar 

  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 2006/2007

    Article  Google Scholar 

  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)

  48. de Bouvère K.: Logical synonymity. Indagationes Mathematicae 27, 622–629 (1965)

    Google Scholar 

  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)

  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)

  51. Diaconescu R.: Grothendieck institutions. Appl. Categorical Struct. 10, 383–402 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  52. Diaconescu, R.: Institution-independent model theory. In: Studies in Universal Logic. Birkhäuser, Basel (2008)

  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. 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)

    Article  MATH  MathSciNet  Google Scholar 

  55. Dou, D., McDermot, D.: Towards theory translation. In: Declarative Agent Languages and Technologies IV. Springer, Berlin (2007)

  56. Enderton H.B.: A Mathematical Introduction to Logic. Academic Press, New York (1972)

    MATH  Google Scholar 

  57. Euzenat J., Shvaiko P.: Ontology Matching. Springer, Heidelberg (2007)

    MATH  Google Scholar 

  58. Evans, M.: Can there be vague objects? Analysis 38, 208 (1978) reprinted in his Collected Papers, Oxford, Clarendon Press (1985)

  59. Feferman S.: Hilbert’s program relativized: Proof-theoretical and foundational reductions. J. Symbol. Logic 53(2), 364–384 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  60. Fitting M., Mendelsohn R.L.: First–Order Modal Logic. Kluwer Academic Publishers, Dordrecht (1998)

    MATH  Google Scholar 

  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)

  62. Gabbay, D.: Fibring logics. Oxford Logic Guides, vol. 38. Clarendon Press, Oxford (1999)

  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)

  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)

  65. Gärdenfors P.: Conceptual Spaces—The Geometry of Thought. MIT Press, Bradford Books (2000)

    Google Scholar 

  66. Gardner M.: Logic Machines and Diagrams. McGraw-Hill, New York (1958)

    MATH  Google Scholar 

  67. Genesereth M.R., Nilsson N.J.: Logical Foundations of Artificial Intelligence. Morgan Kaufmann, Los Altos (1987)

    MATH  Google Scholar 

  68. Goguen J.A.: A Categorical Manifesto. Math. Struct. Comput. Sci. 1, 49–67 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  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)

  70. Goguen J.A.: Data, schema, ontology and logic integration. Log. J, IGPL 13(6), 685–715 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  71. Goguen, J.A.: Information integration in institutions. In: Moss, L. (ed.) Jon Barwise Memorial Volume. Indiana University Press, To appear (2006)

  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)

  73. Goguen J.A., Burstall R.M.: Institutions: abstract model theory for specification and programming. J. ACM 39, 95–146 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  74. Goguen J.A., Roşu G.: Institution morphisms. Form. Aspects Comput. 13, 274–307 (2002)

    Article  MATH  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

  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.

  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)

  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)

  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. Guarino N., Welty C.: Evaluating ontological decisions with OntoClean. Commun. ACM 45(2), 61–65 (2002)

    Article  Google Scholar 

  83. Guerra S.: Composition of default specifications. J. Log. Comput. 11(4), 559–578 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  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)

  85. Haack S.: Philosophy of Logics. Cambridge University Press, Cambridge (1978)

    Google Scholar 

  86. Haack S.: Deviant Logic, Fuzzy Logic: Beyond the Formalism. Cambridge University Press, Cambridge (1996)

    MATH  Google Scholar 

  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)

  88. Heller B., Herre H.: Ontological categories in GOL. Axiomathes 14(1–3), 57–76 (2004)

    Article  Google Scholar 

  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)

  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)

  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)

  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)

  93. Horridge, M., Drummond, N., Goodwin, J., Rector, A., Stevens, R., Wang, H.H.: The Manchester OWL Syntax. In: OWL: Experiences and Directions (2006)

  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)

  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. 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)

  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)

  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. 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)

  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)

  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. 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)

  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)

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

  106. Kutz, O.: \({\mathcal{E}}\) -connections and logics of distance. PhD thesis, The University of Liverpool (2004)

  107. Kutz O.: Notes on logics of metric spaces. Stud. Log. 85(1), 75–104 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  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)

  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)

  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)

  111. Kutz O., Lutz C., Wolter F., Zakharyaschev M.: \({\mathcal{E}}\) -connections of Abstract Description Systems. Artif. Intell. 156(1), 1–73 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  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)

  113. Kutz, O., Mossakowski, T.: Conservativity in Structured Ontologies. In: 18th European Conf. on Artificial Intelligence (ECAI-08), IOS Press, Patras, Greece (2008)

  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)

  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)

  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)

  117. Leibniz, G.W.: Sämtliche Schriften und Briefe—VI Sektion: Philosophische Schriften, Band IV, pp. 1680–1692. Akademie, Berlin (2001)

  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. Lewis, D.: Parts of Classes. Basil Blackwell, Oxford (1991) With an appendix by Burgess, J.P., Hazen, A.P., Lewis, D.

  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)

  121. Lukasiewicz T.: Expressive probabilistic description logics. Artif. Intell. 172(6–7), 852–883 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  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)

  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)

  124. Lutz, C., Wolter, F.: Modal logics of topological relations. Log. Methods Comput. Sci. 2(2) (2006)

  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)

  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)

  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)

  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)

  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)

  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)

  131. Mac Lane S.: Categories for the Working Mathematician, 2nd edn. Springer, Berlin (1998)

    MATH  Google Scholar 

  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)

  133. Marx M., Venema Y.: Multi-dimensional Modal Logic. Kluwer Academic Publishers, Dordrecht (1997)

    MATH  Google Scholar 

  134. Masolo, C., Borgo, S., Gangemi, A., Guarino, N., Oltramari, A.: Wonder Web Deliverable D18: Ontology Library. Tech. rep., ISTC-CNR (2003)

  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)

  136. McCorduck, P.: Machines Who Think: A Personal Inquiry into the History and Prospects of Artificial Intelligence. Peters, Wellesley, 2nd rev edn. (2004)

  137. Meseguer, J.: General logics. In: Logic Colloquium 87, pp. 275–329. North Holland (1989)

  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)

  139. Minsky, M.; A framework for representing knowledge. In: Winston, P. (ed.) The Psychology of Computer Vision. McGraw-Hill (1975)

  140. Mossakowski, T.: Comorphism-based Grothendieck logics. In: Mathematical Foundations of Computer Science. LNCS, vol. 2420, pp. 593–604. Springer (2002)

  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)

  142. Mossakowski T., Autexier S., Hutter D.: Development graphs—proof management for structured specifications. J. Log. Algebraic Program. 67(1–2), 114–145 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  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)

  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)

  145. Mossakowski, T., Maeder, C., Lüttich, K.: The heterogeneous tool set. In: Beckert, B. (ed.) VERIFY 2007, vol. 259. CEUR-WS (2007)

  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)

  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 Contest

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

  150. Newell A., Simon H.A.: Computer science as empirical inquiry: symbols and search. Commun. ACM 19(3), 113–126 (1976)

    Article  MathSciNet  Google Scholar 

  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)

  152. Nipkow, T., Paulson, L.C., Wenzel, M.L.: Isabelle/HOL—a proof assistant for higher-order logic. LNCS, vol. 2283. Springer (2002)

  153. Normann, I.: Automated theory interpretation. PhD thesis, Department of Computer Science, Jacobs University, Bremen (2009)

  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)

  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)

    Article  MathSciNet  Google Scholar 

  156. Parsons T.: Nonexistent Objects. Yale University Press, New Haven and London (1980)

    Google Scholar 

  157. Patel-Schneider P.F.: A four-valued semantics for terminological logics. Artif. Intell. 38(3), 319–351 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  158. Pieczkowski A.: Über Theorien im erweiterten Sinne. Stud. Log. 33(4), 317–331 (1974)

    Article  MathSciNet  Google Scholar 

  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)

  160. Priest, G.: In contradiction: a study of the transconsistent, Nijhoff International Philosophy Series, vol. 39. Dordrecht, Martinus Nijhoff, The Hague (1987)

  161. Priest, G.: Logic: One or many? In: Brown, B., Woods, J. (eds.) Logical Consequences. Hermes (2001)

  162. Priest G.: Logical pluralism hollandaise. Aust. J. Log. 6, 210–214 (2008)

    MATH  MathSciNet  Google Scholar 

  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)

  164. Restall G.: Carnap’s tolerance, language change and logical pluralism. J. Philos. 99, 426–443 (2002)

    Article  MathSciNet  Google Scholar 

  165. Ridder, L.: Mereologie—Ein Beitrag zur Ontologie und Erkenntnistheorie. Philosophische Abhandlungen, vol. 83. Vittorio Klostermann, Frankfurt am Main (2002)

  166. Rodrigues, O., Russo, A.: A Translation Method for Belnap Logic. Research Report Doc 98/7, Imperial College London, September 1998

  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)

  168. Schorlemmer, M., Kalfoglou, Y.: Institutionalising ontology-based semantic integration. J. Appl. Ontol. 3(3) (2008)

  169. Schröder L., Mossakowski T.: HasCASL: Integrated higher-order specification and program development. Theor. Comput. Sci. 410(12–13), 1217–1260 (2009)

    Article  MATH  Google Scholar 

  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)

  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)

  172. Shehtman V.: “Everywhere” and “Here”. J. Appl. Non-Classical Log. 9 (1999)

  173. Sheremet M., Tishkovsky D., Wolter F., Zakharyaschev M.: A logic for concepts and similarity. J. Log. Comput. 17(3), 415–452 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  175. Simons P.: Parts: A Study in Ontology. Clarendon Press, Oxford (1987)

    Google Scholar 

  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. Dordrecht

  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)

    Article  Google Scholar 

  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)

  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)

  180. Tarski A.: Der Aussagenkalkül und die Topologie. Fundamenta Mathematicae 31, 103–134 (1938)

    Google Scholar 

  181. Venn J.: Symbolic Logic. The MacMillan Company, London (1881)

    Google Scholar 

  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)

  183. Voronkov, A.: Inconsistencies in ontologies. In: JELIA-06, p. 19. (2006)

  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)

  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)

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  1. SFB/TR 8 Spatial Cognition, University of Bremen, Cartesium, Enrique-Schmidt Strasse, 28359, Bremen, Germany

    Oliver Kutz & Dominik Lücke

  2. DFKI GmbH and SFB/TR 8 Spatial Cognition, University of Bremen, Cartesium, Enrique-Schmidt Strasse, 28359, Bremen, Germany

    Till Mossakowski

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To Joseph Goguen

This paper is an expanded version of [108], with material drawn from [109, 110, 112, 114].

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Kutz, O., Mossakowski, T. & Lücke, D. Carnap, Goguen, and the Hyperontologies: Logical Pluralism and Heterogeneous Structuring in Ontology Design. Log. Univers. 4, 255–333 (2010). https://doi.org/10.1007/s11787-010-0020-3

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