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Multi-context Logics—A General Introduction

  • Chiara GhidiniEmail author
  • Luciano Serafini
Chapter

Abstract

Multi-context logics (MCLs) constitute a family of formalisms that allow one to integrate multiple logical theories (contexts) into an articulated structure, where different theories can affect one another via so-called bridge-rules. In the past 20 years multi-context logics has been developed, for contexts in propositional logics, first order logics, description logics and temporal logic. Each of these logics has been developed, in an independent manner, for representing and reasoning about contextual knowledge in a specific application domain instead of originating from a single general formal framework. The absence of such a general formal framework for Multi-Context Systems (MCS), from which to extract tailored versions for the different application domain, has led to the development of a rather heterogeneous family of formal systems, whose comparison is sometimes very difficult. Being able to represent all these systems as specifications of a general class would be very useful as, for instance, one could reuse results proven in one MCS in another one. In this chapter, the authors provide an a-posteriori, systematic, and homogeneous description of the various MCSs introduced in the past. The authors do this firstly by providing a general definition of the MCS framework with its main components, which is general enough to capture the various versions of MCSs. Then, an account of the main logical specialisations of the MCS framework is provided, with an explanation of the domain of application they have been developed for.

References

  1. Amir, E., Mcilraith, S.: Partition-based logical reasoning for first-order and propositional theories. Artif. Intell.162, 49–88 (2000)CrossRefMathSciNetGoogle Scholar
  2. Benerecetti, M., Bouquet, P., Ghidini, C.: Formalizing belief reports – The approach and a case study. In: Giunchiglia, F. (ed.) Proceedings AIMSA'98, 8th International Conference on Artificial Intelligence, Methodology, Systems, and Applications,LNAI, vol. 1480, pp. 62–75. Springer, Sozopol (1998a)Google Scholar
  3. Benerecetti, M., Giunchiglia, F., Serafini, L.: Model checking multiagent systems. J. Logic Comput.8(3), 401–423 (1998b)Google Scholar
  4. Borgida, A., Serafini, L.: Distributed description logics: Assimilating information from peer sources. J. Data Semantics1, 153–184 (2003)Google Scholar
  5. Bozzato, L., Serafini, L.: Materialization calculus for contexts in the semantic web. In: Proceedings of the 26th International Workshop on Description Logics, Ulm, Germany, 23–26 July 2013, pp. 552–572 (2013)Google Scholar
  6. Bozzato, L., Ghidini, C., Serafini, L.: Comparing contextual and flat representations of knowledge: a concrete case about football data. In: Proceedings of the 7th International Conference on Knowledge Capture, K-CAP 2013, Banff, Canada, 23–26 June 2013, pp. 9–16. ACM (2013)Google Scholar
  7. Brewka, G., Roelofsen, F., Serafini, L.: Contextual default reasoning. In: IJCAI 2007, Proceedings of the 20th International Joint Conference on Artificial Intelligence, Hyderabad, India, 6-12 January 2007, pp. 268–273 (2007)Google Scholar
  8. Brockmans, S., Haase, P., Serafini, L., Stuckenschmidt, H.: Formal and conceptual comparison of ontology mapping languages. In: Stuckenschmidt, H., Parent, C., Spaccapietra, S. (eds.) Modular Ontologies, Lecture Notes in Computer Science, vol. 5445, pp. 267–291. Springer, Heidelberg (2009)Google Scholar
  9. Buvac, S., Mason, I.A.: Propositional logic of context. In: Proceedings of the 11th National Conference on Artificial Intelligence. Washington, DC, USA, 11–15 July 1993, pp. 412–419. AAAI Press/MIT Press (1993)Google Scholar
  10. Cimatti, A., Serafini, L., Cimatti, R., Serafini, L.: Multi-agent reasoning with belief contexts: the approach and a case study. In: Wooldridge, M., Müller, J. P., Tambe, M. (eds.) Intelligent Agents: Proceedings of 1994 Workshop on Agent Theories, Architectures, and Languages, Lecture Notes in Computer Science, number 890, pp. 71–85. Springer, Heidelberg (1994)Google Scholar
  11. Fisher, M., Ghidini, C.: Executable specifications of resource-bounded agents. Autonom. Agents Multi-Agent Syst.21(3), 368–396 (2010)CrossRefGoogle Scholar
  12. Ghidini, C.: Modelling (un)bounded beliefs. In: Bouquet, P., Serafini, L., Brézillon , P., Benerecetti, M., Castellani, F. (eds.) Modelling and Using Context – Proceedings of the 2nd International and Interdisciplinary Conference, Context'99. Lecture Notes in Artificial Intelligence, vol.  1688, pp. 145–158. Springer, Heidelberg (1999)Google Scholar
  13. Ghidini, C., Giunchiglia, F.: Local models semantics, or contextual reasoning = locality + compatibility. Artif. Intell.127(2), 221–259 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  14. Ghidini, C., Serafini, L.: Distributed first order logics. In: Gabbay, D., de Rijke, M. (eds.) Frontiers of Combining Systems 2 (Papers presented at FroCoS’98), Studies in Logic and Computation, pp. 121 -140. Research Studies Press, Baldock (1998)Google Scholar
  15. Ghidini, C., Serafini, L., Tessaris, S.: On relating heterogeneous elements from different ontologies. In: Kokinov, B., Richardson, D., Roth-Berghofer, T., Vieu, L. (eds.) Proceedings of the Sixth International and Interdisciplinary Conference on Modeling and Using Context (CONTEXT'07), Lecture Notes in Artificial Intelligence, Roskilde University, Denmark, vol. 4635, pp. 234–247. Springer (2007)Google Scholar
  16. Giunchiglia, F., Serafini, L.: Multilanguage hierarchical logics, or: how we can do without modal logics. Artif. Intell.65(1), 29–70 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  17. Homola, M., Serafini, L.: Augmenting subsumption propagation in distributed description logics. Appl. Artif. Intell.24(1–2), 39–76 (2010)CrossRefGoogle Scholar
  18. Roelofsen, F., Serafini, L.: Complexity of contextual reasoning. In: McGuinness, D.L., Ferguson, G. (eds.) Proceedings of the Nineteenth National Conference on Artificial Intelligence, Sixteenth Conference on Innovative Applications of Artificial Intelligence, San Jose, California, USA, 25–29 July 2004, pp. 118–123. AAAI Press/MIT Press (2004)Google Scholar
  19. Serafini, L., Bouquet, P.: Comparing formal theories of context in ai. Artif. Intell.155(1–2), 41–67 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  20. Serafini, L., Ghidini, C.: Context based semantics for information integration. In: Bonzon, P., Cavalcanti, M., Nossum, R. (eds.) Formal Aspects of Context, Applied Logic Series, vol. 20, pp. 175-192. Springer Netherlands (2000)Google Scholar
  21. Serafini, L., Roelofsen, F.: Satisfiability for propositional contexts. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Ninth International Conference (KR2004), Whistler, Canada, 2–5 June 2004, pp. 369–376 (2004)Google Scholar
  22. Serafini, L., Tamilin, A.: Drago: Distributed reasoning architecture for the semantic web. In: Gómez-Pérez, A., Euzenat. J. (eds.) The Semantic Web: Research and Applications, Second European Semantic Web Conference, ESWC 2005, Heraklion, Crete, Greece, 29 May -1 June 2005, Proceedings. Lecture Notes in Computer Science, vol. 3532, pp. 361–376. Springer, Heidelberg (2005)Google Scholar
  23. Serafini, L., Tamilin, A.: Instance migration in heterogeneous ontology environments. In: The Semantic Web, 6th International Semantic Web Conference, 2nd Asian Semantic Web Conference, ISWC 2007 + ASWC 2007, Busan, Korea, 11–15 November 2007. Lecture Notes in Computer Science, vol. 4825, pp. 452–465. Springer (2007)Google Scholar
  24. Serafini, L., Borgida, A., Tamilin, A.: Aspects of distributed and modular ontology reasoning. In: IJCAI-05, Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence, Edinburgh, Scotland, UK, 30 July–5 August 2005, pp. 570–575 (2005a)Google Scholar
  25. Serafini, L., Stuckenschmidt, H., Wache, H.: A formal investigation of mapping language for terminological knowledge. In: 19th Joint Conference on Artificial Intelligence (IJCAI-05), pp. 576–581 (2005b)Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Fondazione Bruno KesslerTrentoItaly

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