A Brief Comparison Of Pollock's Defeasible Reasoning And Ranking Functions

In this paper two theories of defeasible reasoning, Pollock's account and my theory of ranking functions, are compared, on a strategic level, since a strictly formal comparison would have been unfeasible. A brief summary of the accounts shows their basic difference: Pollock's is a strictly computational one, whereas ranking functions provide a regulative theory. Consequently, I argue that Pollock's theory is normatively defective, unable to provide a theoretical justification for its basic inference rules and thus an independent notion of admissible rules. Conversely, I explain how quite a number of achievements of Pollock's account can be adequately duplicated within ranking theory. The main purpose of the paper, though, is not to settle a dispute with formal epistemology, but rather to emphasize the importance of formal methods to the whole of epistemology.

[1]  Abhaya C. Nayak,et al.  Iterated belief change based on epistemic entrenchment , 1994 .

[2]  Satu Eloranta,et al.  On Iterated Belief Change , 1998, SCAI.

[3]  Moisés Goldszmidt,et al.  Rank-based Systems: A Simple Approach to Belief Revision, Belief Update, and Reasoning about Evidence and Actions , 1992, KR.

[4]  John L. Pollock,et al.  Belief Revision And Epistemology , 2000, Synthese.

[5]  H. Kyburg.  Iterated Belief Change Based on Epistemic Entrenchment* , 1994 .

[6]  Wolfgang Spohn,et al.  Concepts Are Beliefs About Essences , 2001 .

[7]  J. Armstrong.  Knowledge and Belief , 1953 .

[8]  Wolfgang Spohn,et al.  Ordinal Conditional Functions: A Dynamic Theory of Epistemic States , 1988 .

[9]  Wolfgang Spohn,et al.  Deterministic Causation , 2001 .

[10]  Hans Rott,et al.  Change, choice and inference , 2001 .

[11]  G. L. S. Shackle,et al.  Decision Order and Time in Human Affairs , 1962 .

[12]  H. Kyburg.  The Fixation of Belief and Its Undoing , 1994 .

[13]  Wolfgang Spohn,et al.  II—How to Understand the Foundations of Empirical Belief in a Coherentist Way , 1998 .

[14]  Wolfgang Spohn,et al.  Eine Theorie der Kausalität , 1983 .

[15]  Peter Gärdenfors,et al.  Knowledge in Flux , 1988 .

[16]  William Harper.  Rational Belief Change, Popper Functions and Counterfactuals , 1975 .

[17]  Kevin T. Kelly.  Iterated Belief Revision, Reliability, and Inductive Amnesia , 1999 .

[18]  Kevin T. Kelly.  The Logic of Reliable Inquiry , 1996 .

[19]  Wolfgang Spohn,et al.  On the Properties of Conditional Independence , 1994 .

[20]  Zoltan Domotor,et al.  Probability kinematics , 2004, Synthese.

[21]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[22]  J. Pollock.  Contemporary theories of knowledge , 1986 .

[23]  Finn Verner Jensen,et al.  Introduction to Bayesian Networks , 2008, Innovations in Bayesian Networks.

[24]  Rudolf Carnap,et al.  Logical foundations of probability , 1951 .

[25]  L. R. Harris.  Hypothetical reasoning , 1989 .

[26]  David Lindley,et al.  Logical foundations of probability , 1951 .

[27]  G. L. S. Shackle,et al.  Decision Order and Time in Human Affairs , 1962 .

[28]  H. Kyburg,et al.  Nomic probability and the foundations of induction , 1990 .

[29]  R. Jeffrey.  The Logic of Decision , 1984 .

[30]  Wolfgang Spohn,et al.  Ranking Functions, AGM Style , 1999 .