The Journal of Symbolic Logic

Research Article

On the logic of theory change: Partial meet contraction and revision functions

Carlos E. Alchourróna1, Peter Gärdenforsa2 and David Makinsona31

a1 Universidad de Buenos Aires, Buenos Aires, Argentina

a2 Lunds Universitet, Lund, Sweden

a3 American University of Beirut, Beirut, Lebanon

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, Gärdenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourrón 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 Gärdenfors 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 Gàrdenfors investigated, with a further representation theorem established.

(Received October 18 1983)

(Revised May 01 1984)

Footnotes

1   This paper was written while the third author was on leave from UNESCO. The contents are the responsibility of the authors and not of the institutions.