Journal of Logic, Language and Information

, Volume 4, Issue 2, pp 111–143 | Cite as

A rational reconstruction of the domain of feature structures

  • M. Andrew Moshier
Article

Abstract

Feature structures are employed in various forms in many areas of linguistics. Informally, one can picture a feature structure as a sort of tree decorated with information about constraints requiring that specific subtrees be identical (isomorphic). Here I show that this informal picture of feature structures can be used to characterize exactly the class of feature structures under their usual subsumption ordering. Furthermore, once a precise definition of tree is fixed, this characterization makes use only of standard domain-theoretic notions regarding the information borne by elements in a domain, thus removing (or better, explaining) all apparentlyad hoc choices in the original definition of feature structures. In addition, I show how this characterization can be parameterized in order to yield similar characterizations of various different notions of feature structure, including acyclic structures, structures with appropriateness conditions and structures with apartness conditions (used to model path inequations). The generalizations to other notions of feature structure also emphasize that the construction given here is in fact independent of the application to feature structures.

Key words

Feature structures domains constraints 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abramsky, Samson, 1991, “Domain theory in logical form,”Annals of Pure and Applied Logic 51, 1–77.Google Scholar
  2. Aït-Kaci, Hassan and Nasr, Roger, 1986, “LOGIN: A logig programming language with built-in inheritance,”Journal of Logic Programming 3, 185–215.Google Scholar
  3. Aït-Kaci, Hassan and Podelski, A., 1993, “Towards a meaning of LIFE,”Journal of Logic Programming, LNCS vol. 528, 255–274.Google Scholar
  4. Aït-Kaci, Hassan, Podelski, A. and Smolka, Gert, 1994, “A feature-based constraint system for logic programming with entailment,”Theoretical Computer Science 122(1–2), 263–283.Google Scholar
  5. Backofen, Rolf and Smolka, Gert, 1993, “A complete and recursive feature theory,” pp. 193–200 in31st Annual Meeting of the Association for Computational Linguistics, June 1993.Google Scholar
  6. Barwise, Jon, 1991, “Information links in domain theory,” Technical Report IULG-91-7, Indiana University Logic Group.Google Scholar
  7. Blackburn, Patrick, 1994, “Structures, language and translations: The structural approach to feature logics,” pp. 1–27 inConstraints, Language and Computation, M. A. Rosner, C.J. Rupp, and R. L. Johnson, eds., Academic Press.Google Scholar
  8. Carpenter, Robert, 1992,The Logic of Typed Feature Structures. Number 32 in Cambridge Tracts in Theoretical Computer Science, Cambridge University Press,Google Scholar
  9. Colmerauer, A., 1984 “Equations and inequations on finite and infinite trees,” pp. 85–99 inProceedings of the International Conference on Fifth Generation Computer Systems.Google Scholar
  10. Kaplan, Ronald and Bresnan, Joan, 1983 “Lexical Functional Grammar: A formal system for grammatical representation,” pp. 173–281 inThe Mental Representation of Grammatical Relations, Joan Bresnan, ed., MIT Press.Google Scholar
  11. Kay, Martin, 1979, “Functional grammar,” pp. 142–158 IiProceedings of the Fifth Annual Metting of the Berkeley Linguistics Society, February 1979.Google Scholar
  12. Mac Lane, Saunders, 1971,Categories for the Working Mathematician, Volume 5 ofGraduate Texts in Mathematics, Springer-Verlag.Google Scholar
  13. Moshier, Michael Andrew, 1988,Extensions to Unification Grammar for the Description of Programming Languages. PhD thesis, University of Michigan.Google Scholar
  14. Paterson, M.S. and Wegman, M.N., 1978, “Linear unification,”Journal of Computer and System Sciences 16, 158–167.Google Scholar
  15. Pereira, Fernando C.N. and Shieber, Stuart M., 1984, “The semantics of grammar formalisms seen as computer languages,” pp. 123–129 inProceedings of the 10th International Conference on Computational Linguistics: COLING 84, July 1984.Google Scholar
  16. Pierce, Benjamin C,1991, Basic Category Theory for Computer Scientists. MIT Press.Google Scholar
  17. Plotkin, Gordon, 1983, “Domains,” University of Edinburgh Lecture Notes.Google Scholar
  18. Pollard, Carl and Sag, Ivan A., 1987,Information-based Syntax and Semantics, Volume 1 ofCSLI Lecture Notes, CSLI.Google Scholar
  19. Smolka, Gert and Treinen, Ralf, 1994, “Records for logic programming,”Journal of Logic Programmingg 18(3), 229–258.Google Scholar
  20. Smyth, Michael, 1983, “The largest cartesian closed category of domains,”Theoretical Computer Science 27(1,2), 109–119.Google Scholar
  21. Vickers, Steven, 1989,Logic via Topology, Volume 5 ofCambridge Tracts in Theoretical Computer Science, Cambridge University Press.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • M. Andrew Moshier
    • 1
  1. 1.Chapman UniversityOrangeUSA

Personalised recommendations