Ranking Functions, AGM Style

Ranking functions, having their first appearance under the name „ordinale Konditionalfunktionen“ in my Habilitationsschrift submitted in 1983, had several precursors of which I was only incompletely aware, among them Shackle’s functions of potential surprise (see Shackle 1969), Rescher’s plausibility indexing (see Rescher 1976), Adams’ e-semantics (see Adams 1975), Cohen’s inductive probabilities (see Cohen 1977), Shafer’s consonant belief functions (see Shafer 1976, ch. 10), and Ellis’ rational belief systems (see Ellis 1979). Concerning the actual genesis, however, their ancestor was Peter Gardenfors’ early work on belief revision (see Gardenfors 1979, 1981). This work inspired me enormously, perhaps because I found there the dynamical perspective to be most salient, and so I eventually came up with the ranking functions. To my surprise, however, belief revision theory and ranking theory went mainly separate ways. I am not sure about the reasons (I offer some speculations below), but in any case I believe that the separation is unnecessary. This paper intends to narrow the gap from the side of ranking functions. It tries to do so in four parts. Section 1 starts by resuming the mutual criticisms. Section 2 briefly introduces ranking theory and how it reflects belief revision theory. Section 3 tries to overcome the main reservation concerning ranking functions by discussing

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