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)

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.

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)

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, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron 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 Gardenfors 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 Gardenfors investigated, with a further representation theorem established. (shrink)

This paper dwells upon formal models of changes of beliefs, or theories, which are expressed in languages containing a binary conditional connective. After defining the basic concept of a (non-trivial) belief revision model. I present a simple proof of Gärdenfors''s (1986) triviality theorem. I claim that on a proper understanding of this theorem we must give up the thesis that consistent revisions (additions) are to be equated with logical expansions. If negated or might conditionals are interpreted on the basis of (...) autoepistemic omniscience, or if autoepistemic modalities (Moore) are admitted, even more severe triviality results ensue. It is argued that additions cannot be philosophically construed as parasitic (Levi) on expansions. In conclusion I outline somed logical consequences of the fact that we must not expect monotonic revisions in languages including conditionals. (shrink)

This paper provides an interpretation of the Routley-Meyer semantics for a weak negation-free relevant logic using Israel and Perry's theory of information. In particular, Routley and Meyer's ternary accessibility relation is given an interpretation in information-theoretic terms.

In this paper we set out a semantics for relevant (counterfactual) conditionals. We combine the Routley-Meyer semantics for relevant logic with a semantics for conditionals based on selection functions. The resulting models characterize a family of conditional logics free from fallacies of relevance, in particular counternecessities and conditionals with necessary consequents receive a non-trivial treatment.

Gärdenfors' impossibility theorem draws attention to certain formal difficulties in defining a conditional connective from a notion of theory revision, via the Ramsey test. We show that these difficulties are not avoided by taking the background inference operation to be non-monotonic.

The last section made it clear that an analysis which at first seems to fail is viable after all. It is viable if we let it depend on a partition function to be provided by the context of conversation. This analysis leaves certain traits of the partition function open. I have tried to show that this should be so. Specifying these traits as Pollock does leads to wrong predictions. And leaving them open endows counterfactuals with just the right amount of (...) variability and vagueness. (shrink)

Kernel contraction is a natural nonrelational generalization of safe contraction. All partial meet contractions are kernel contractions, but the converse relationship does not hold. Kernel contraction is axiomatically characterized. It is shown to be better suited than partial meet contraction for formal treatments of iterated belief change.

This paper summarizes and systematizes recent and ongoing work on non-prioritized belief change, i.e., belief revision in which the new information has no special priority due to its novelty.

The purpose of this note is to formulate some weaker versions of the so called Ramsey test that do not entail the following unacceptable consequenceIf A and C are already accepted in K, then if A, then C is also accepted in K. and to show that these versions still lead to the same triviality result when combined with a preservation criterion.

This essay describes a general approach to building perturbation-tolerant autonomous systems, based on the conviction that artificial agents should be able to notice when something is amiss, assess the anomaly, and guide a solution into place. This basic strategy of self-guided learning is termed the metacognitive loop; it involves the system monitoring, reasoning about, and, when necessary, altering its own decision-making components. This paper (a) argues that equipping agents with a metacognitive loop can help to overcome the brittleness problem, (b) (...) details the metacognitive loop and its relation to our ongoing work on time-sensitive commonsense reasoning, (c) describes specific, implemented systems whose perturbation tolerance was improved by adding a metacognitive loop, and (d) outlines both short-term and long-term research agendas. (shrink)