Advertisement

On the Logic of Theory Change: Partial Meet Contraction and Revision Functions

  • Carlos E. Alchourrón
  • Peter Gärdenfors
  • David Makinson
Part of the Springer Graduate Texts in Philosophy book series (SGTP, volume 1)

Abstract

This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of its axiomatic bases), that fails to imply the proposition being eliminated. In the present paper, the authors study a broader class, including contraction functions that may be less than maximal. Specifically, they investigate “partial meet contraction functions”, which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated. Basic properties of these functions are established: it is shown in particular that they satisfy the Gardenfors postulates, and moreover that they are sufficiently general to provide a representation theorem for those postulates. Some special classes of partial meet contraction functions, notably those that are “relational” and “transitively relational”, are studied in detail, and their connections with certain “supplementary postulates” of Gardenfors investigated, with a further representation theorem established.

References

  1. Alchourron, C. E., & Makinson, D. (1982a). Hierarchies of regulations and their logic, new studies in deontic logic (pp. 125–148), R. Hilpinen (Ed.), Dordrecht: Reidel.Google Scholar
  2. Alchourron, C. E., & Makinson, D. (1982b). On the logic of theory change: Contraction functions and their associated revision functions. Theoria, 48, 14–37.CrossRefGoogle Scholar
  3. Gärdenfors, P. (1978). Conditionals and changes of belief The logic and epistemology of scientific change. In I. Niiniluoto & R. Tuomela (Eds.), Acta Philosophica Fennica (Vol. 30, pp. 381–404).Google Scholar
  4. Gärdenfors, P. (1982). Rules for rational changes of belief 320311: Philosophical essays dedicated to Lennart Åqvist on his fiftieth birthday (pp. 88–101), (T. Pauli, Ed., Philosophical studies no. 34). Uppsala: Department of Philosophy, University of Uppsala.Google Scholar
  5. Gärdenfors, P. (1984). Epistemic importance and minimal changes of belief. Australasian Journal of Philosophy, 62, 136–157.CrossRefGoogle Scholar
  6. Makinson, D. (1985). How to give it up: A survey of some formal aspects of the logic of theory change. Synthese, 62, 347–363.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Carlos E. Alchourrón
    • 1
  • Peter Gärdenfors
    • 2
  • David Makinson
    • 3
  1. 1.Universidad de Buenos AiresBuenos AiresArgentina
  2. 2.Lund UniversityLundSweden
  3. 3.London School of EconomicsLondonUK

Personalised recommendations