On the logic of theory change: More maps between different kinds of contraction functions
Hans Rott · Cambridge University Press eBooks · 1992
INTRODUCTION There are many ways to change a theory. The tasks of adding a sentence to a theory and of retracting a sentence from a theory are non-trivial because they are usually constrained by at least three requirements. The result of a revision or contraction of a theory should again be a theory, i.e., closed under logical consequence, it should be consistent whenever possible, and it should not change the original theory beyond necessity. In the course of the Alchourrón-Gärdenfors-Makinson research programme, at least three different methods for constructing contractions of theories have been proposed. Among these the “safe contraction functions” of Alchourrón and Makinson (1985, 1986) have played as it were the role of an outsider. Gärdenfors and Makinson (1988, p. 88) for instance state that ‘another, quite different , way of doing this [contracting and revising theories] was described by Alchourrón and Makinson (1985).’ (Italics mine.) The aim of the present paper is to show that this is a miscasting. In any case, it seems that the intuitions behind safe contractions are fundamentally different from those behind its rivals, the partial meet contractions of Alchourrón, Gärdenfors and Makinson (1985) and the epistemic entrenchment contractions of Gärdenfors and Makinson (1988). Whereas the latter notions are tailored especially to handling theories (as opposed to sets of sentences which are not closed under a given consequence operation), safe contraction by its very idea focusses on minimal sets of premises sufficient to derive a certain sentence.