The axiom of recovery, while capturing a central intuition regarding belief change, has been the source of much controversy. We argue briefly against putative counterexamples to the axiom—while agreeing that some of their insight deserves to be preserved—and present additional recovery-like axioms in a framework that uses epistemic states, which encode preferences, as the object of revisions. This makes iterated revision possible and renders explicit the connection between iterated belief change and the axiom of recovery. We provide a representation theorem (...) that connects the semantic conditions we impose on iterated revision and our additional syntactical properties. We show interesting similarities between our framework and that of Darwiche–Pearl (Artificial Intelligence 89:1–29 1997). In particular, we show that intuitions underlying the controversial (C2) postulate are captured by the recovery axiom and our recovery-like postulates (the latter can be seen as weakenings of (C2)). We present postulates for contraction, in the same spirit as the Darwiche–Pearl postulates for revision, and provide a theorem that connects our syntactic postulates with a set of semantic conditions. Lastly, we show a connection between the contraction postulates and a generalisation of the recovery axiom. (shrink)

When a belief set is contracted only some beliefs are eligible for removal. By introducing eligibility for removal as a new semantic primitive for contraction and combining it with epistemic entrenchment we get a contraction operator with a number of interesting properties. By placing some minimal constraint upon eligibility we get an explicit contraction recipe that exactly characterises the so called interpolation thesis, a thesis that states upper and lower bounds for the amount of information to be given up in (...) contraction. As a result we drop the controversial property of recovery. By placing additional constraints on eligibility we get representation theorems for a number of contraction operators of varying strength. In addition it is shown that recovery contraction is a special case that we get if eligibility is explicitly constructed in terms of logical relevance. (shrink)

In studies of multi-agent interaction, especially in game theory, the notion of equilibrium often plays a prominent role. A typical scenario for the belief merging problem is one in which several agents pool their beliefs together to form a consistent "group" picture of the world. The aim of this paper is to define and study new notions of equilibria in belief merging. To do so, we assume the agents arrive at consistency via the use of a social belief removal function, (...) in which each agent, using his own individual removal function, removes some belief from his stock of beliefs. We examine several notions of equilibria in this setting, assuming a general framework for individual belief removal due to Booth et al. We look at their inter-relations as well as prove their existence or otherwise. We also show how our equilibria can be seen as a generalisation of the idea of taking maximal consistent subsets of agents. (shrink)

Most belief change operators in the AGM tradition assume an underlying plausibility ordering over the possible worlds which is transitive and complete. A unifying structure for these operators, based on supplementing the plausibility ordering with a second, guiding, relation over the worlds was presented in Booth et al. (Artif Intell 174:1339-1368, 2010). However it is not always reasonable to assume completeness of the underlying ordering. In this paper we generalise the structure of Booth et al. (Artif Intell 174: 1339-1368, 2010) (...) to allow incomparabilities between worlds. We axiomatise the resulting class of belief removal functions, and show that it includes an important family of removal functions based on finite prioritised belief bases. (shrink)

This book provides a critical examination of how the choice of what to believe is represented in the standard model of belief change. In particular the use of possible worlds and infinite remainders as objects of choice is critically examined. Descriptors are introduced as a versatile tool for expressing the success conditions of belief change, addressing both local and global descriptor revision. The book presents dynamic descriptors such as Ramsey descriptors that convey how an agent’s beliefs tend to be changed (...) in response to different inputs. It also explores sentential revision and demonstrates how local and global operations of revision by a sentence can be derived as a special case of descriptor revision. Lastly, the book examines revocation, a generalization of contraction in which a specified sentence is removed in a process that may possibly also involve the addition of some new information to the belief set. (shrink)

A representation theorem is obtained for contraction operators that are based on Levi's recent proposal that selection functions should be applied to the set of saturatable contractions, rather than to maximal subsets as in the AGM framework. Furthermore, it is shown that Levi's proposal to base the selection on a weakly monotonic measure of informational value guarantees the satisfaction of both of Gärdenfors' supplementary postulates for contraction. These results indicate that Levi has succeeded in constructing a well-behaved operation of contraction (...) that does not satisfy the postulate of recovery. (shrink)

In this paper it is argued that, in order to solve the problem of iterated belief change, both the belief state and its input should be represented as epistemic entrenchment (EE) relations. A belief revision operation is constructed that updates a given EE relation to a new one in light of an evidential EE relation. It is shown that the operation in question satisfies generalized versions of the Gärdenfors revision postulates. The account offered is motivated by Spohn's ordinal conditionalization functions, (...) and can be seen as the Jeffrization of a proposal considered by Rott. (shrink)

In this paper, it is argued that both the belief state and its input should be represented as epistemic entrenchment (EE) relations. A belief revision operation is constructed that updates a given EE relation to a new one in light of an evidential EE relation, and an axiomatic characterization of this operation is given. Unlike most belief revision operations, the one developed here can handle both multiple belief revision and iterated belief revision.

Scientific inquiry is represented as a process of rational hypothesis revision in the face of data. For the concept of rationality, we rely on the theory of belief dynamics as developed in [5, 9]. Among other things, it is shown that if belief states are left unclosed under deductive logic then scientific theories can be expanded in a uniform, consistent fashion that allows inquiry to proceed by any method of hypothesis revision based on "kernel" contraction. In contrast, if belief states (...) are closed under logic, then no such expansion is possible. (shrink)

Scientific inquiry is represented as a process of rational hypothesis revision in the face of data. For the concept of rationality, we rely on the theory of belief dynamics as developed in [5, 9]. Among other things, it is shown that if belief states are left unclosed under deductive logic then scientific theories can be expanded in a uniform, consistent fashion that allows inquiry to proceed by any method of hypothesis revision based on “kernel” contraction. In contrast, if belief states (...) are closed under logic, then no such expansion is possible. (shrink)

Generalizations of partial meet contraction are introduced that start out from the observation that only some of the logically closed subsets of the original belief set are at all viable as contraction outcomes. Belief contraction should proceed by selection among these viable options. Several contraction operators that are based on such selection mechanisms are introduced and then axiomatically characterized. These constructions are more general than the belief base approach. It is shown that partial meet contraction is exactly characterized by adding (...) to one of these constructions the condition that all logically closed subsets of the belief set can be obtained as the outcome of a single (multiple) contraction. Examples are provided showing the counter-intuitive consequences of that condition, thus confirming the credibility of the proposed generalization of the AGM framework. (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.

ABSTRACT In his paper ?On Having Bad Contractions, Or: No Room for Recovery? [Te97], N. Tennant attacks the AGM research program of belief revision. We show that he misrepresents the state of affairs in this field of research.

Belief revision theories aim to model the dynamics of epistemic states. Besides beliefs, epistemic states comprise most importantly justificational structures. Typically, belief revision theories, however, model the dynamics of beliefs while neglecting justificational structures over and above logical relations. Despite some awareness that this approach is problematic, how devastating the consequences of this neglect are has not yet been fully grasped. In this paper, I argue that taking justificational structures into account could solve four well-known problems of belief revision.

The postulate of Recovery, among the six postulates for theory contraction, formulated and studied by Alchourrón, Gärdenfors and Makinson is the one that has provoked most controversy. In this article we construct withdrawal functions that do not satisfy Recovery, but try to preserve minimal change, and relate these withdrawal functions with the AGM contraction functions.

Semi-contraction is a withdrawal operation defined by Fermé in "On the logic of theory change: Contraction without recovery." In this paper we propose: (1) an axiomatic characterization of semi-contraction; (2) an alternative construction for semi-contraction based on semi-saturatable sets, inspired by Levi's saturatable sets; (3) a special kind of semi-contraction that satisfies the Lindström and Rabinowicz interpolation thesis.

links to current studies in the theory of scientific discovery. Our own theory is elaborated in four papers accessible in pdf format through the links on the left.