We show in this paper that the AGM postulates are too weak to ensure the rational preservation of conditional beliefs during belief revision, thus permitting improper responses to sequences of observations. We remedy this weakness by proposing four additional postulates, which are sound relative to a qualitative version of probabilistic conditioning. Contrary to the AGM framework, the proposed postulates characterize belief revision as a process which may depend on elements of an epistemic state that are not necessarily captured by a (...) belief set. We also show that a simple modification to the AGM framework can allow belief revision to be a function of epistemic states. We establish a model-based representation theorem which characterizes the proposed postulates and constrains, in turn, the way in which entrenchment orderings may be transformed under iterated belief revision. (shrink)

Frank Ramsey was the greatest of the remarkable generation of Cambridge philosophers and logicians which included G. E. Moore, Bertrand Russell, Ludwig Wittgenstein and Maynard Keynes. Before his tragically early death in 1930 at the age of twenty-six, he had done seminal work in mathematics and economics as well as in logic and philosophy. This volume, with a new and extensive introduction by D. H. Mellor, contains all Ramsey's previously published writings on philosophy and the foundations of mathematics. The latter (...) gives the definitive form and defence of the reduction of mathematics to logic undertaken in Russell and Whitehead's Principia Mathematica; the former includes the most profound and original studies of universals, truth, meaning, probability, knowledge, law and causation, all of which are still constantly referred to, and still essential reading for all serious students of these subjects. (shrink)

The dissertation gives an account of the principles guiding the rational revision of belief. I develop a non-probabilistic account of belief revision. My central thesis is the claim that there are two quite different kinds of rational belief change; two methods suited to two different sorts of situation. I call these methods updating and supposing. This claim, presented in Chapter Two, is argued on the basis of results proved in Chapter One. Chapters Three and Four are applications of the distinction (...) between updating and supposing to two areas of current philosophical debate: the semantics of conditionals; and the theory of deliberation dynamics. The discussion of conditionals appeals to the temporal asymmetry in knowledge. Why is it that we know more about the past than about the future? Chapter Five offers a new answer to that old question, based on an account of recording devices as physical systems stable under perturbation. ;I hope to have shown that many of these philosophical questions--questions about belief revision, decision theory, and conditionals, that have traditionally been framed in probabilistic terms--can be most fruitfully discussed without ever mentioning probability. (shrink)

How to accept a conditional? F. P. Ramsey proposed the following test in (Ramsey 1990).(RT) If A, then B must be accepted with respect to the current epistemic state iff the minimal hypothetical change of it needed to accept A also requires accepting B.

Philosophical logicians proposing theories of rational belief revision have had little to say about whether their proposals assist or impede the agent's ability to reliably arrive at the truth as his beliefs change through time. On the other hand, reliability is the central concern of formal learning theory. In this paper we investigate the belief revision theory of Alchourron, Gardenfors and Makinson from a learning theoretic point of view.

How to accept a conditional? F. P. Ramsey proposed the following test in . 'If A, then B' must be accepted with respect to the current epistemic state iff the minimal hypothetical change of it needed to accept A also requires accepting B. In this article we propose a formulation of , which unlike some of its predecessors, is compatible with our best theory of belief revision, the so-called AGM theory , chapters 1-5 for a survey). The new test, which, (...) we claim, encodes some of the crucial insights defended by F. P. Ramsey in , is used to study the conditionals epistemically validated by the AGM postulates. Our notion of validity is compared with the notion of negative validity used by Gärdenfors in . It is observed that the notions of PV and NV will in general differ and that when these differences arise it is the notion of PV that is preferable. Finally we compare our formulation of the Ramsey test with a previous formulation offered by Gärdenfors . We show that any attempt to interpret as delivering acceptance conditions for Ramsey's conditionals is doomed to failure. (shrink)

Consider a rational agent X at certain point of time t. X's epistemic state can be represented in different ways.

We consider the dispute between causal decision theorists and evidential decision theorists over Newcomb-like problems. We introduce a framework relating causation and directed graphs developed by Spirtes et al. (1993) and evaluate several arguments in this context. We argue that much of the debate between the two camps is misplaced; the disputes turn on the distinction between conditioning on an event E as against conditioning on an event I which is an action to bring about E. We give the essential (...) machinery for calculating the effect of an intervention and consider recent work which extends the basic account given here to the case where causal Knowledge is incomplete. (shrink)