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Multicontext Logic for Semigroups of Contexts

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Artificial Intelligence, Automated Reasoning, and Symbolic Computation (AISC 2002, Calculemus 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2385))

Abstract

A multicontext logic with algebraic structure is proposed, where contexts are either primitive or composed from other contexts. Composition of two contexts can support various intuitions: sequence concatenation, set union, multiset union, etc.

A local models semantics for algebraic context composition is defined, with a corresponding deductive calculus containing multilanguage bridge rules. Soundness and completeness results are proved for the case of semigroups of contexts, i.e. where context composition is an associative operation. Other properties of context composition, besides associativity, are defined by additional algebraic equations.

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References

  1. M. Benerecetti, P. Bouquet, and M. Bonifacio. Distributed context-aware applications. Human Computer Interaction, 16:213–228, 2001. Special issue on Context-aware computing.

    Article  Google Scholar 

  2. M. Benerecetti, P. Bouquet, and C. Ghidini. Contextual reasoning distilled. Journal of Theoretical and Experimental Artificial Intelligence, 2000.

    Google Scholar 

  3. Sačsa Buvačc, Vanja Buvačc, and Ian A. Mason. The semantics of propositional contexts. In Proceedings of the Eight International Symposium on Methodologies for Intelligent Systems, volume 869 of Lecture Notes in Artificial Intelligence. Springer Verlag, 1994.

    Google Scholar 

  4. Sačsa Buvačc, Vanja Buvačc, and Ian A. Mason. Metamathematics of context. Fundamenta Informaticae, 23(3), 1995.

    Google Scholar 

  5. T. Costello and A. Patterson. Quantifiers over contexts. In KR & R, 1998.

    Google Scholar 

  6. C. Dichev. Theory relations and context dependencies. In Proceedings of the 6th Australian Joint Conference on Artificial Intelligence (AI-93), pages 266–272, Melbourne, 1993.

    Google Scholar 

  7. Dov Gabbay and Rolf Nossum. Structured contexts with fibred semantics. In P. Bonzon, M. Cavalcanti, and R. Nossum, editors, Formal Aspects of Context. Applied Logic Series, Kluwer, 2000.

    Google Scholar 

  8. Chiara Ghidini. A Semantics for Contextual Reasoning: Theory and Two Relevant Applications. Ph.d. dissertation, Dipartimento di Informatica e Studî Aziendali, Università degli Studî di Roma “La Sapienza”, Roma, 1998.

    Google Scholar 

  9. Fausto Giunchiglia. Contextual reasoning. Epistemologia, special issue on I Lin-guaggi e le Macchine(XVI):345–364, 1993. IRST Technical Report 9211-20, IRST,Trento, Italy.

    Google Scholar 

  10. Fausto Giunchiglia and Luciano Serafini. Multilanguage hierarchical logics (or: how we can do without modal logics). Artificial Intelligence, 65:29–70, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  11. Ramanathan Guha and Douglas Lenat. Language, representation and contexts. Journal of Information Processing, 15(3):340–349, 1992.

    Google Scholar 

  12. Ramanathan V. Guha. Contexts: A Formalization and Some Applications. PhD thesis, Stanford University, 1991.

    Google Scholar 

  13. David Kaplan. Demonstratives: an essay on the semantics, logic, metaphysics, and epistemology of demonstratives and other indexicals. In Joseph Almog, John Perry, and Howard Wettstein, editors, Themes from Kaplan, pages 481–563. Oxford University Press, Oxford, 1989.

    Google Scholar 

  14. J. McCarthy and S. Buvačc. Formalising context, (expanded notes). In A. Aliseda, R. van Glabbeek, and D. Westerståhl, editors, Computing Natural Language, volume 81 of CSLI Lecture Notes, pages 13–50. Stanford University, Center for the Study of Language and Information, 1998.

    Google Scholar 

  15. Rolf Nossum. A uniform quantificational logic for algebraic notions of context. Skriftserien 82, Agder University College, N-4604 Kristiansand, Dec 2001. ISBN 82-7117-448-7.

    Google Scholar 

  16. John Perry. Indexicals, contexts, and unarticulated constituents. In Atocha Aliseda, Rob van Glabbeek, and Dag Westerståhl, editors, Computing Natural Language, pages 1–11. CSLI Publications, Stanford, California, 1998.

    Google Scholar 

  17. Luciano Serafini and Chiara Ghidini. Context-based semantics for information integration. In Pierre Bonzon, Marcos Cavalcanti, and Rolf Nossum, editors, Formal Aspects of Context, pages 175–192. Kluwer Academic Publishers, Dordrecht, 2000.

    Google Scholar 

  18. Luciano Serafini and Fausto Giunchiglia. ML systems: A proof theory for contexts. Journal of Logic, Language and Information, July 2001.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Agder University College, Gimlemoen, N-4604, Kristiansand, Norway

    Rolf Nossum

  2. ITC-IRST, Centro per la Ricerca Scientifica e Tecnologica, Via Sommarive 18, I-38050, Povo, Italy

    Luciano Serafini

Authors
  1. Rolf Nossum
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  2. Luciano Serafini
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Editor information

Editors and Affiliations

  1. University of Karlsruhe (TH), Am Fasanengarten 5, Postfach 6980, D-76128, Karlsruhe, Germany

    Jacques Calmet

  2. CMI, Université de Provence, 39 rue F. Juliot-Curie, 13453, Marseille Cedex 13, France

    Belaid Benhamou

  3. Research Institute for Symbolic Computation (RISC-Linz), Johannes Kepler University, A-4040, Linz, Austria

    Olga Caprotti

  4. ESIL, Université de la Méditerannée, 163 Avenue de Luminy, Marseille Cedex 09, France

    Laurent Henocque

  5. School of Computer Science, University of Birmingham, Birmingham, B15 2TT, UK

    Volker Sorge

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© 2002 Springer-Verlag Berlin Heidelberg

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Nossum, R., Serafini, L. (2002). Multicontext Logic for Semigroups of Contexts. In: Calmet, J., Benhamou, B., Caprotti, O., Henocque, L., Sorge, V. (eds) Artificial Intelligence, Automated Reasoning, and Symbolic Computation. AISC Calculemus 2002 2002. Lecture Notes in Computer Science(), vol 2385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45470-5_11

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  • DOI: https://doi.org/10.1007/3-540-45470-5_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43865-6

  • Online ISBN: 978-3-540-45470-0

  • eBook Packages: Springer Book Archive

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