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Collective entities and relations in concept languages

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Book cover Foundations of Knowledge Representation and Reasoning

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 810))

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Abstract

Collective entities and collective relations play an important role in natural language. In order to capture the full meaning of sentences like “The Beatles sing ‘Yesterday’ ”, a knowledge representation language should be able to express and reason about plural entities — like “the Beatles” — and their relationships — like “sing” — with any possible reading (cumulative, distributive or collective).

In this paper a way of including collections and collective relations within a concept language, chosen as the formalism for representing the semantics of sentences, is presented. A twofold extension of the ALC concept language is investigated: (1) special relations introduce collective entities either out of their components or out of other collective entities, (2) plural quantifiers on collective relations specify their possible reading. The formal syntax and semantics of the concept language is given, together with a sound and complete algorithm to compute satisfiability and subsumption of concepts, and to compute recognition of individuals. An advantage of this formalism is the possibility of reasoning and stepwise refining in the presence of scoping ambiguities. Moreover, many phenomena covered by the Generalized Quantifiers Theory are easily captured within this framework. In the final part a way to include a theory of parts (mereology) is suggested, allowing for a lattice-theoretical approach to the treatment of plurals.

This paper is a a reduced version of a paper to appear in Minds and Machines, special issue on Knowledge Representation for Natural Language Processing. This work has been partially supported by the Italian National Research Council (CNR), project “Sistemi Informatici e Calcolo Parallelo”, and by the IRST MAIA project. We would like to thank also Alessandro Artale, Werner Nutt and Achille Varzi for the helpful and incisive discussions we had with them.

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References

  1. J. Allgayer. LSB−ONE+ — dealing with sets efficiently. In Proc. of the 9 th ECAI, pages 13–18, Stockholm, Sweden, 1990.

    Google Scholar 

  2. J. Allgayer and E. Franconi. A semantic account of plural entities within a hybrid representation system. In Proc. of the 5 th International Symposium on Knowledge Engineering, pages 305–312, Seville, Spain, October 1992.

    Google Scholar 

  3. E. Bach. The algebra of events. Linguistics and Philosophy, 9:5–16, 1986.

    Google Scholar 

  4. J. Barwise and R. Cooper. Generalized quantifiers and natural language. Linguistics and Philosophy, 4:159–219, 1981.

    Google Scholar 

  5. F. M. Donini, B. Hollunder, M. Lenzerini, A. Marchetti Spaccamela, D. Nardi, and W. Nutt. The complexity of existential quantification in concept languages. Artificial Intelligence, 53:309–327, 1992.

    Google Scholar 

  6. F. M. Donini, M. Lenzerini, D. Nardi, and W. Nutt. The complexity of concept languages. In Proc. of the 2 nd International Conference on Principles of Knowledge Representation and Reasoning, pages 151–162, Cambridge, MA, 1991.

    Google Scholar 

  7. F. M. Donini, M. Lenzerini, D. Nardi, and W. Nutt. Tractable concept languages. In Proc. of the 12 th IJCAI, pages 458–465, Sidney, Australia, August 1991.

    Google Scholar 

  8. E. Franconi. Adding constraints inference to ABox reasoning. Abstract 9205-02, IRST, Povo TN, Italy, May 1992.

    Google Scholar 

  9. Enrico Franconi. A treatment of plurals and plural quantifications based on a theory of collections. Minds and Machines, special issue on Knowledge Representation for Natural Language Processing (to appear), 1993. A preliminary version appears in the Preprints of the International Workshop on Formal Ontology, N. Guarino and R. Poli (eds.), pages 219–249, Padova, Italy, 1993.

    Google Scholar 

  10. Enrico Franconi, Alessandra Giorgi, and Fabio Pianesi. A mereological approach to tense and aspect. In Proc. of the International Conference on Mathematical Linguistics, ICML-93, Barcelona, Spain, April 1993. (Abstract).

    Google Scholar 

  11. Enrico Franconi, Alessandra Giorgi, and Fabio Pianesi. Tense and aspect: a mereological approach. In Proc. of the 13 th IJCAI, Chambery, France, August 1993.

    Google Scholar 

  12. B. Hollunder. Hybrid inferences in KL-ONE-based knowledge representation systems. In Proc. of the 14 th German Workshop on Artificial Intelligence. Springer-Verlag, 1990.

    Google Scholar 

  13. B. Hollunder, W. Nutt, and M. Schmidt-Schauß. Subsumption algorithms for concept description languages. In Proc. of the 9 th ECAI, pages 348–353, Stockholm, Sweden, 1990.

    Google Scholar 

  14. Fred Landman. Groups, I. Linguistics and Philosophy, 12:559–605, 1989.

    Google Scholar 

  15. Fred Landman. Groups, II. Linguistics and Philosophy, 12:723–744, 1989.

    Google Scholar 

  16. L. Lesmo, M. Berti, and P. Terenziani. A network formalism for representing natural language quantifiers. In Proc. of the 8 th ECAI, pages 473–478, Munich, Germany, 1988.

    Google Scholar 

  17. Godehard Link. The logical analysis of plurals and mass terms: a lattice-theoretical approach. In R. Bauerle, C. Schwarze, and A. von Stechow, editors, Meaning, Use and Interpretation of Language, pages 302–323. Walter de Gruyter, 1983.

    Google Scholar 

  18. Godehard Link. Algebraic semantics for natural language: some philosophy, some applications. In Nicola Guarino and Roberto Poli, editors, Proc. of the International Workshop on Formal Ontology, pages 19–49, Padova, Italy, March 1993.

    Google Scholar 

  19. M. Poesio. Dialog-oriented ABoxing. In Proc. of the 5 th International Symposium on Methodologies for Intelligent Systems, pages 277–288, Knoxville, TN, 1990.

    Google Scholar 

  20. Massimo Poesio. Relational semantics and scope ambiguity. In J. Barwise, J. M. Gawron, G. Plotkin, and S. Tutiya, editors, Situation Semantics and its Applications, vol.2, chapter 20, pages 469–497. CSLI, Stanford, CA, 1991.

    Google Scholar 

  21. J. Quantz. How to fit generalized quantifiers into terminological logics. In Proc. of the 10 th ECAI, pages 543–547, Vienna, Austria, 1992.

    Google Scholar 

  22. M. Schmidt-Schauß and G. Smolka. Attributive concept descriptions with complements. Artificial Intelligence, 48(1):1–26, 1991.

    Google Scholar 

  23. S. C. Shapiro and W. J. Rapaport. The SNePS family. Computer and Mathematics with Applications, special issue: Semantic Networks in Artificial Intelligence, 23(2–5):243–275, March–May 1992.

    Google Scholar 

  24. P. Simons. Parts: A Study in Ontology. Clarendon Press, Oxford, 1987.

    Google Scholar 

  25. J. F. Sowa. Toward the expressive power of natural language. In J. F. Sowa, editor, Principles of Semantic Networks, pages 157–189. Morgan Kaufmann, 1991.

    Google Scholar 

  26. Bosco S. Tjan, David A. Gardiner, and James R. Slagle. Representing and reasoning with set referents and numerical quantifiers. In T. E. Nagle, J. A. Nagle, L. L. Gerholz, and P. W. Eklund, editors, Conceptual Structures, current reasearch and practice, chapter 2, pages 53–66. Ellis Horwood, 1992.

    Google Scholar 

  27. Michael P. Wellman and Reid G. Simmons. Mechanisms for reasoning about sets. In Proc. of AAAI-88, pages 398–402, St. Paul, MN, 1988.

    Google Scholar 

  28. Morton E. Winston, Roger Chaffin, and Douglas Herrmann. A taxonomy of part-whole relations. Cognitive Science, 11:417–444, 1987.

    Google Scholar 

  29. William A. Woods and James G. Schmolze. The KL-ONE family. Computer and Mathematics with Applications, special issue: Semantic Networks in Artificial Intelligence, 23(2–5):133–177, March–May 1992.

    Google Scholar 

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Authors and Affiliations

  1. Software Architectures and Technologies, IBM Germany, Schloß-Str. 70, D-7000, Stuttgart 1, Germany

    Jürgen Allgayer

  2. Istituto per la Ricerca Scientifica e Tecnologica (IRST), I-38050, Povo, TN, Italy

    Enrico Franconi

Authors
  1. Jürgen Allgayer
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  2. Enrico Franconi
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Gerhard Lakemeyer Bernhard Nebel

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© 1994 Springer-Verlag Berlin Heidelberg

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Allgayer, J., Franconi, E. (1994). Collective entities and relations in concept languages. In: Lakemeyer, G., Nebel, B. (eds) Foundations of Knowledge Representation and Reasoning. Lecture Notes in Computer Science, vol 810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58107-3_2

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  • DOI: https://doi.org/10.1007/3-540-58107-3_2

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  • Print ISBN: 978-3-540-58107-9

  • Online ISBN: 978-3-540-48453-0

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