Skip to main content
SpringerLink
Log in

A treatment of plurals and plural quantifications based on a theory of collections

  • General Articles
  • Published:
Minds and Machines Aims and scope Submit manuscript

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 theA−C 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 is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Allgayer, J. and Franconi, E. (1992a), ‘Collective Entities and Relations in Concept Languages’, inWorkshop Notes of the ECAI Workshop on Theoretical Foundations of Knowledge Representation and Reasoning, Vienna, Austria. 1–5. Appears also in the Working Notes of the AAAI Fall Symposium ‘Issues in Description Logics: Users Meet Developer”, Cambridge MA, October 1992.

  • Allgayer, J. and Franconi, E. (1992b), ‘A Semantic Account of Plural Entities Within a Hybrid Representation System’, inProc. of the 5 th International Symposium on Knowledge Engineering, Seville, Spain, pp. 305–312.

  • Allgayer, J., Jansen-Winkeln, R., Reddig, C., and Reithinger, N. (1989), ‘Bidirectional Use of Knowledge in the Multi-Modal NL Access System XTRA’, inProc. of the 11 th IJCAI, Detroit, MI.

  • Allgayer, J. (1990). ‘L SE−ONE+ — Dealing with Sets Efficiently’, inProc of the 9 th ECAI, Stockholm, Sweden, pp. 13–18.

  • Baader, F. and Hollunder, B. (1991), ‘A Terminological Knowledge Representation System with Complete Inference Algorithm’, inProc. of the Workshop on Processing Declarative Knowledge, Kaiserslautern, Germany, pp. 67–86.

  • Bach, E. (1986), ‘The Algebra of Events’,Linguistics and Philosophy 9, 5–16.

    Google Scholar 

  • Barwise, J. and Cooper, R. (1981), ‘Generalized Quantifiers and Natural Language’,Linguistics and Philosophy 4, 159–219.

    Google Scholar 

  • Bateman, John A., Kasper, Robert T., Moore, Johanna D., and Whitney, Richard A. (1990), ‘A General Organization of Knowledge for Natural Language Processing: The PENMAN Upper Model’, Technical report, USC/Information Science Institute, Marina del Rey CA.

  • Cattoni, R. and Franconi, E. (1990), ‘Walking Through the Semantics of Frame-Based Description Languages: A Case Study’, inProc. of the 5 th International Symposium on Methodologies for Intelligent Systems, Knoxville, TN, pp. 234–241.

  • Donini, F.M., Lenzerini, M., Nardi, D., and Nutt, W. (1991a), ‘The Complexity of Concept Languages’, inProc. of the 2 nd International Conference on Principles of Knowledge Representation and Reasoning, Cambridge, MA, pp. 151–162.

  • Donini, F.M., Lenzerini, M., Nardi, D., and Nutt, W. (1991b), ‘Tractable Concept Languages’, inProc. of the 12 th IJCAI, Sidney, Australia, pp. 458–465.

  • Donini, F.M., Hollunder, B., Lenzerini, M., Spaccamela, A. Marchetti, Nardi, D., and Nutt, W. (1992), ‘The Complexity of Existential Quantification in Concept Languages’,Artificial Intelligence 53, 309–327.

    Google Scholar 

  • Franconi, Enrico, Giorgi, Alessandra, and Pianesi, Fabio (1993a), ‘A Mereological Approach to Tense and Aspect’, inProc. of the International Conference on Mathematical Linguistics, ICML-93, Barcelona, Spain. (Abstract).

  • Franconi, Enrico, Giorgi, Alessandra, and Pianesi, Fabio (1993b). ‘Tense and Aspect: A Mereological Approach’, inProc. of the 13 th IJCAI, Chambery, France pp. 1222–1228.

  • Franconi, E. (1991), ‘A Short Presentation of YAK, a Hybrid Knowledge Representation System’, in Peltason, C., Luck, K.von; and Kindermann, C. (eds.),Proc. of the Terminological Logic Users Workshop, Berlin, Germany, Department of Computer Science, Technische Universität Berlin, pp. 174–177.

  • Franconi, E. (1992), ‘Adding Constraints Inference to ABox Reasoning’, Abstract 9205-02, IRST, Povo TN, Italy.

    Google Scholar 

  • Hollunder, B. and Baader, F. (1991), ‘Qualifying Number Restriction in Concept Languages’, inProc. of the 2 nd International Conference on Principles of Knowledge Representation and Reasoning, Cambridge, MA, pp. 335–346.

  • Hollunder, B., Nutt, W., and Schmidt-Schau§, M. (1990), ‘Subsumption Algorithms for Concept Description Languages’, InProc. of the 9 th ECAI, Stockholm, Sweden, pp. 348–353.

  • Hollunder, B. (1990), Hybrid Inferences in KL-ONE-Based Knowledge Representation Systems’, inProc. of the 14 th German Workshop on Artificial Intelligence, Springer-Verlag.

  • Kempson, R. and Cormack, A. (1981). ‘Ambiguity and Quantification’,Linguistics and Philosophy 4(2): 259–310.

    Google Scholar 

  • Landman, Fred (1989a), ‘Groups, I’,Linguistics and Philosophy 12, 559–605.

    Google Scholar 

  • Landman, Fred (1989b), ‘Groups, II’,Linguistics and Philosophy 12, 723–744.

    Google Scholar 

  • Lavelli, Alberto, Magnini, Bernardo, and Strapparava, Carlo (1992), ‘An Approach to Multilevel Semantics for Applied Systems’, inProc. of the 3rd ACL Conference on Applied Natural Language Processing, Trento, Italy, pp. 17–24.

  • Lesmo, L., Berti, M., and Terenziani, P. (1988), ‘A Network Formalism for Representing Natural Language Quantifiers’, inProc. of the 8 th ECAI, Munich, Germany, pp. 473–478.

  • Link, Godehard (1983), ‘The Logical Analysis of Plurals and Mass Terms: A Lattice-Theoretical Approach’, in Bauerle, R., Schwarze, C., and Stechow, Avon (eds.),Meaning, Use and Interpretation of Language. Walter de Gruyter, pp. 307–323.

  • Link, Godehard (1993), ‘Algebraic Semantics for Natural Language: Some Philosophy, Some Applications’, in Guarino, Nicola and Poli, Roberto, (eds.),Proc. of the International Workshop on Formal Ontology, Padova, Italy, pp. 19–49.

  • Poesio, M. (1990), ‘Dialog-Oriented ABoxing’, inProc. of the 5 th International Symposium on Methodologies for Intelligent Systems, Knoxville, TN, pp. 277–288.

  • Poesio, Massimo (1991). ‘Relational Semantics and Scope Ambiguity’, in Barwise, J., Gawron, J.M., Plotkin, G., and Tutiya, S. (eds.),Situation Semantics and its Applications, Vol. 2. CSLI, Stanford, CA, Chapter 20, pp. 469–497.

  • Quantz, J. (1992), ‘How to Fit Generalized Quantifiers into Terminological Logics’, inProc. of the 10 th ECAI, Vienna, Austria, pp. 543–547.

  • Samek, Vieri Lodovici and Strapparava, Carlo (1990), ‘Identifying Noun Phrase References: The Topic Module of the AlFresco System’, inProc. of the 9 th ECAI, Stockholm, Sweden, pp. 573–578.

  • Schmidt-Schau§, M. and Smolka, G. (1991). ‘Attributive Concept Descriptions with Complements’,Artificial Intelligence 48(1), 1–26.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • Sowa, J.F. (1991), ‘Toward the Expressive Power of Natural Language’, in Sowa, J.F. (ed.),Principles of Semantic Networks, Morgan Kaufmann, pp. 157–189.

  • Stock, Oliviero (1991), ‘Natural Language and Exploration of an Information Space: The AlFresco Interactive System’, inProc. of the 12 th IJCAI, Sidney, Australia, pp. 972–978.

  • Tjan, Bosco S., Gardiner, David A., and Slagle, James R. (1992), ‘Representing and Reasoning with Set Referents and Numerical Quantifiers’, in Nagle, T.E., Nagle, J.A., Gerholz, L.L., and Eklund, P.W., (eds.),Conceptual Structures, Current Research and Practice, Ellis Horwood, Chapter 2, pp. 53–66.

  • van Benthem, J. (1986),Essays in Logical Semantics, Studies in Linguistics and Philosophy. D. Reidel Publ. Co., Dordrecht, Holland.

    Google Scholar 

  • Weischedel, R.M. (1989), ‘A Hybrid Approach to Representation in the Janus Natural Language Processor’, inProc. of ACL-89, Vancouver, British Columbia.

  • Wellman, Michael P. and Simmons, Reid G. (1988), ‘Mechanisms for Reasoning About Sets’, inProc. of AAAI-88, St. Paul, MN, pp. 398–402.

  • Winston, Morton E., Chaffin, Roger, and Hermann, Douglas (1987), ‘A Taxonomy of Part-Whole Relations’,Cognitive Science 11, 417–444.

    Google Scholar 

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

    Google Scholar 

  • Zancanaro, Massimo, Stock, Olivero, and Strapparava, Carlo (1993). ‘Dialogue Cohesion Sharing and Adjusting in an Enhanced Multimodal Environment’, inProc. of the 13 th IJCAI, Chambery, France.

Download references

Author information

Authors and Affiliations

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

    Enrico Franconi

Authors
  1. Enrico Franconi
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Franconi, E. A treatment of plurals and plural quantifications based on a theory of collections. Mind Mach 3, 453–474 (1993). https://doi.org/10.1007/BF00974106

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00974106

Key words

Search

Navigation