Notre Dame Journal of Formal Logic

An Algebraic Theory of Structured Objects

Chrysafis Hartonas

Abstract

We present an algebraic theory of structured objects based on and generalizing Aczel's theory of form systems. Notions of identity of structured objects and of transformations of systems of such objects are discussed. A generalization of Aczel's representation theorem is proven.

Article information

Source
Notre Dame J. Formal Logic, Volume 38, Number 1 (1997), 65-80.

Dates
First available in Project Euclid: 12 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1039700697

Digital Object Identifier
doi:10.1305/ndjfl/1039700697

Mathematical Reviews number (MathSciNet)
MR1479369

Zentralblatt MATH identifier
0889.03044

Subjects
Primary: 03B70: Logic in computer science [See also 68-XX]
Secondary: 03E70: Nonclassical and second-order set theories

Citation

Hartonas, Chrysafis. An Algebraic Theory of Structured Objects. Notre Dame J. Formal Logic 38 (1997), no. 1, 65--80. doi:10.1305/ndjfl/1039700697. https://projecteuclid.org/euclid.ndjfl/1039700697


Export citation

References

  • Aczel, P., Non-Well-Founded Sets, CSLI Lecture Notes, vol. 14, Stanford University, Stanford, 1988. Zbl 0668.04001 MR 89j:03039
  • Aczel, P., “Replacement systems and the axiomatization of situation theory,” pp. 3–33 in Situation Theory and its Applications, CSLI Lecture Notes, vol. 1, Stanford University, Stanford, 1990.
  • Aczel, P., and N. Mendler, “A final coalgebra theorem,” pp. 357–65 in Lecture Notes in Computer Science, vol. 389, Springer-Verlag, Berlin, 1994. MR 91f:18001
  • Aczel, P., and R. Lunnon, “Universes and parameters,” pp. 1–22 in Situation Theory and its Applications, CSLI Lecture Notes, vol. 2, Stanford University, Stanford, 1991. MR 1167607
  • Barwise, J., “Notes on a model for situation theory,” preprint, 1989.
  • Barwise, J., Admissible Sets and Structures, Springer-Verlag, Berlin, 1975. Zbl 0316.02047 MR 54:12519
  • Barwise, J., and J. Etchemendy, The Liar, Oxford University Press, Oxford, 1987. Zbl 0678.03001 MR 88k:03009
  • Lunnon, R., Generalized Universes, Ph.D. Disssertation, University of Manchester, Manchester, 1991.
  • Tzouvaras, A., “Significant parts and identity of artifacts,” Notre Dame Journal of Formal Logic, vol. 34 (1993), pp. 445–52. Zbl 0795.03006 MR 94f:03037
  • Westersthal, D., “Parametric types and propositions in first-order situation theory,” pp. 98–117 in Situation Theory and its Applications, CSLI Lecture Notes, vol. 1, Stanford University, Palo Alto, 1990.
  • Williams, J. G., Instantiation Theory, Lecture Notes in Artificial Intelligence, vol. 518, Springer-Verlag, Berlin, 1991. Zbl 0785.68084 MR 94d:68093