By replacement is meant an operation that replaces one sentence by another in a belief set. Replacement can be used as a kind of Sheffer stroke for belief change, since contraction, revision, and expansion can all be defined in terms of it. Replacement can also be defined either in terms of contraction or in terms of revision. Close connections are shown to hold between axioms for replacement and axioms for contraction and revision. Partial meet replacement is axiomatically characterized. It is (...) shown that this operation can have outcomes that are not obtainable through either partial meet contraction or partial meet revision. (shrink)

Two of the major problems in AGM-style belief revision, namely the difficulties in accounting for iterated change and for Ramsey test conditionals, have satisfactory solutions in descriptor revision. In descriptor revision, the input is a metalinguistic sentence specifying the success condition of the operation. The choice mechanism selects one of the potential outcomes in which the success condition is satisfied. Iteration of this operation is unproblematic. Ramsey test conditionals can be introduced without giving rise to the paradoxical results that they (...) generate in other systems. In addition to standard Ramsey test conditionals, a more general variant of epistemic conditionals is defined, representing statements of the form ”if the belief state is changed to satisfy condition A then it will satisfy condition B”. An axiomatic characterization of such descriptor conditionals is presented. It is related in intricate ways to the KLM postulates for cumulative reasoning. (shrink)

We argue that giving up on the closure of rational belief under conjunction comes with a substantial price. Either rational belief is closed under conjunction, or else the epistemology of belief has a serious diachronic deficit over and above the synchronic failures of conjunctive closure. The argument for this, which can be viewed as a sequel to the preface paradox, is called the ‘review paradox'; it is presented in four distinct, but closely related versions.

Straightforward theory revision, taking into account as effectively as possible the established nomic possibilities and, on their basis induced empirical laws, is conducive for (unstratified) nomic truth approximation. The question this paper asks is: is it possible to reconstruct the relevant theory revision steps, on the basis of incoming evidence, in AGM-terms? A positive answer will be given in two rounds, first for the case in which the initial theory is compatible with the established empirical laws, then for the case (...) in which it is incompatible with at least one such a law. (shrink)

The splitting theorem says that any set of formulae has a finest representation as a family of letter-disjoint sets. Parikh formulated this for classical propositional logic, proved it in the finite case, used it to formulate a criterion for relevance in belief change, and showed that AGMpartial meet revision can fail the criterion. In this paper we make three further contributions. We begin by establishing a new version of the well-known interpolation theorem, which we call parallel interpolation, use it to (...) prove the splitting theorem in the infinite case, and show how AGM belief change operations may be modified, if desired, so as to ensure satisfaction of Parikh’s relevance criterion. (shrink)

Specified meet contraction is the operation defined by the identity where ∼ is full meet contraction and f is a sentential selector, a function from sentences to sentences. With suitable conditions on the sentential selector, specified meet contraction coincides with the partial meet contractions that yield a finite-based contraction outcome if the original belief set is finite-based. In terms of cognitive realism, specified meet contraction has an advantage over partial meet contraction in that the selection mechanism operates on sentences rather (...) than on temporary infinite structures (remainders) that are cognitively inaccessible. Specified meet contraction provides a versatile framework in which other types of contraction, such as severe withdrawal and base-generated contraction, can be expressed with suitably chosen properties of the sentential selector. (shrink)

An operator of belief change is reconstructible as another such operator if and only if any outcome that can be obtained with the former can also be obtained with the latter. Two operators are mutually reconstructible if they generate exactly the same set of outcomes. The relations of reconstructibility among fifteen operators of contraction, including the common AGM contraction operators, are completely characterized. Furthermore, the additional such relations are characterized that arise if all belief sets are required to be finite-based (...) or if the language is finite. These results are significant for the choice of a formal model to represent how real-world agents change their beliefs. In particular, if two contraction operators are mutually reconstructible, then that limits the types of considerations that can legitimately be invoked in favour of one over the other. (shrink)

The basic assumption of repertoire contraction is that only some of the logically closed subsets of the original belief set are viable as contraction outcomes. Contraction takes the form of choosing directly among these viable outcomes, rather than among cognitively more far-fetched objects such as possible worlds or maximal consistent subsets of the original belief set. In this first investigation of repertoire contraction, postulates for various variants of the operation are introduced. Necessary and sufficient conditions are given for when repertoire (...) contraction coincides with AGM contraction or with operations generated by AGM-style contraction on a belief base. A close connection is shown to hold between repertoire contraction and specified meet contraction. (shrink)

A descriptor is a set of sentences that are truth-functional combinations of expressions of the form \ , where \ is a metalinguistic belief predicate and p a sentence in the object language in which beliefs are expressed. Descriptor revision ) is an operation of belief change that takes us from a belief set K to a new belief set \ where \ is a descriptor representing the success condition. Previously studied operations of belief change are special cases of descriptor (...) revision, hence sentential revision can be represented as \ , contraction as \ , multiple contraction as \ , replacement as \ , etc. General models of descriptor revision are constructed and axiomatically characterized. The common selection mechanisms of AGM style belief change cannot be used, but they can be replaced by choice functions operating directly on the set of potential outcomes . The restrictions of this construction to sentential revision ) and sentential contraction give rise to operations with plausible properties that are also studied in some some detail. (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 model of coherentist belief contraction is constructed. The outcome of belief contraction is required to be one of the coherent subsets of the original belief set, and a set of plausible properties is proposed for this set of coherent subsets. The contraction operators obtained in this way are shown to coincide with well-known belief base operations. This connection between coherentist and "foundationalist" approaches to belief change has important implications for the philosophical interpretation of models of belief change.

Traditionally, belief change is modelled as the construction of a belief set that satisfies a success condition. The success condition is usually that a specified sentence should be believed or not believed. Furthermore, most models of belief change employ a select-and-intersect strategy. This means that a selection is made among primary objects that satisfy the success condition, and the intersection of the selected objects is taken as outcome of the operation. However, the select-and-intersect method is difficult to justify, in particular (...) since the primary objects are not themselves plausible outcome candidates. Some of the most controversial features of belief change theory, such as recovery and the impossibility of Ramsey test conditionals, are closely connected with the select-and-intersect method. It is proposed that a selection mechanism should instead operate directly on the potential outcomes, and select only one of them. In this way many of the problems that are associated with the select-and-intersect method can be avoided. This model is simpler than previous models in the important Ockhamist sense of doing away with intermediate, cognitively inaccessible objects. However, the role of simplicity as a choice criterion in the direct selection among potential outcomes is left as an open issue. (shrink)

Blockage contraction is an operation of belief contraction that acts directly on the outcome set, i.e. the set of logically closed subsets of the original belief set K that are potential contraction outcomes. Blocking is represented by a binary relation on the outcome set. If a potential outcome X blocks another potential outcome Y, and X does not imply the sentence p to be contracted, then Y ≠ K ÷ p. The contraction outcome K ÷ p is equal to the (...) (unique) inclusion-maximal unblocked element of the outcome set that does not imply p. Conditions on the blocking relation are specified that ensure the existence of such a unique inclusion-maximal set for all sentences p. Blockage contraction is axiomatically characterized and its relations to AGM-style operations are investigated. In a finite-based framework, every transitively relational partial meet contraction is also a blockage contraction. (shrink)

Although the AGM theory established a paradigm for the theory of belief revision, which is generally regarded as a kind of standard in the field, it is also frequently criticized as inadequate because it neglects justificational structures. Other theories of belief revision are similarly remiss in this regard. So far, little has been done to address this shortcoming. This paper aims to fill this gap. Following a critical analysis of the AGM theory, a justification operator is introduced as a formal (...) means to incorporate justificational structures into a belief revision theory. An AGM style belief revision theory is proposed that is based on such a justification operator. The theory is presented in an axiomatic form. Representation theorems link the axioms with constructive belief change mechanisms. The proposed theory addresses the problems of the AGM theory and similar approaches that neglect justificational structures. (shrink)

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 AGM success postulates for belief expansions and revisions have been widely criticized. This has resulted in the development of a number of non-prioritized belief change theories that violate these postulates. It is shown that we must also discard the monotony postulate for belief expansions if we abandon the success postulates. Non-prioritized belief change theories should instead fulfill a weaker postulate, which we call Conditional Monotony.

Belief Revision addresses the problem of rationally incorporating pieces of new information into an agent’s belief state. In the AGM paradigm, the most used framework in Belief Revision, primacy is given to the new information, which is fully incorporated into the agent’s belief state. However, in real situations, one may want to reject the new information or only accept a part of it. A constructive model called Selective Revision was proposed to meet this need but, as in the AGM framework, (...) focused on belief sets. In this paper we adapt the selective revision operators, that were proposed for belief sets, to the belief base context, obtaining a model in which an agent’s epistemic state is represented by a belief base and that allows the acceptance of only part of the new information. We present several representation theorems for selective base revision operators based on different base revision operators. (shrink)

This work considers the formalisation of the merging process of stratified belief bases, where beliefs are stored in different layers or strata. Their strata are ranked, following a total order, employing the value the agent using the belief base assigns to these beliefs. The agent uses an argumentation mechanism to reason from the belief base and obtain the final inferences. We present two ways of merging stratified belief bases: the first is defined by merging two strata without belief preservation, and (...) the second by merging two strata with belief preservation. For these operators, as layers merge, it is possible that some information has to be deleted from the stratum to maintain consistency. The latter merge operator will be defined as performing their actions so that information removed from the stratum is preserved after the merging by moving it to a stratum containing information perceived as having a lower value and where those beliefs may trigger a new revision, possibly starting a cascading effect. (shrink)

One of the standard principles of rationality guiding traditional accounts of belief change is the principle of minimal change: a reasoner's belief corpus should be modified in a minimal fashion when assimilating new information. This rationality principle has stood belief change in good stead. However, it does not deal properly with all belief change scenarios. We introduce a novel account of belief change motivated by one of Grice's maxims of conversational implicature: the reasoner's belief corpus is modified in a minimal (...) fashion to assimilate exactly the new information. In this form of belief change, when the reasoner revises by new information p ∨ q their belief corpus is modified so that p∨q is believed but stronger propositions like p∧q are not, no matter what beliefs are in the reasoner's initial corpus. We term this conservative belief change since the revised belief corpus is a conservative extension of the original belief corpus given the new information. (shrink)

An important trend in contemporary epistemology centers on elaborating an old idea of pragmatist pedigree: theory selection (and in general the process of changing view and fixing beliefs) presupposes epistemic values. This article focuses on analyzing the case where epistemic values are indeterminate or when the sources of valuation are multiple (epistemic values like coherence and simplicity need not order options in compatible ways). According to the theory that thus arises epistemic alternatives need not be fully ordered by an underlying (...) notion of information-value and therefore the usual economic techniques of optimization cannot be applied in order to compute optimal contractions. But in cases of this sort it is still rational to maximize, i.e. to deem an option as choosable when it is not known to be worse that any other. We present here basic results about a notion of liberal contraction based on maximizing quasi-orderings. This requires the previous solution of some open problems in the theory of rational choice functions, namely a full characterization of choice functions rationalizable in terms of maximization of quasi-transitive relations. We conclude by discussing the problem of what is the adequate feasible set for calculating maximizing solutions for contraction problems and by considering the epistemological roots of some counterexamples against the most fundamental axioms on choice functions (like α). While the first part of the paper shows how economic insights can be used to improve our understanding of the principles of belief formation and change, this final section reverses this strategy by showing the utility of epistemological insights and techniques for providing invariance conditions capable of regulating the applicability of the pure principles of choice. (shrink)

Review of Olsson, Erik J. and Enqvist, Sebastian , Belief Revision meets Philosophy of Science.

This is an essay on the understanding of disposition concepts, which exploits the Ramsey test semantics of conditionals for a refined conditional analysis of dispositions. I will show that this semantics allows for a more accurate account of disposition concepts than the standard semantics of conditionals by David Lewis. This includes dealing with the counterexamples to the conditional analysis, which are known as finks, antidotes, and mimics.

I propose a novel hyperintensional semantics for belief revision and a corresponding system of dynamic doxastic logic. The main goal of the framework is to reduce some of the idealisations that are common in the belief revision literature and in dynamic epistemic logic. The models of the new framework are primarily based on potentially incomplete or inconsistent collections of information, represented by situations in a situation space. I propose that by shifting the representational focus of doxastic models from belief sets (...) to collections of information, and by defining changes of beliefs as artifacts of changes of information, we can achieve a more realistic account of belief representation and belief change. The proposed dynamic operation suggests a non-classical way of changing beliefs: belief revision occurs in non-explosive environments which allow for a non-monotonic and hyperintensional belief dynamics. A logic that is sound with respect to the semantics is also provided. (shrink)

This paper adds evidence structure to standard models of belief, in the form of families of sets of worlds. We show how these more fine-grained models support natural actions of “evidence management”, ranging from update with external new information to internal rearrangement. We show how this perspective leads to new richer languages for existing neighborhood semantics for modal logic. Our main results are relative completeness theorems for the resulting dynamic logic of evidence.

The present paper aims to complement causal model approaches to causal explanation by Woodward [15], Halpern and Pearl [5], and Strevens [14]. It centres on a strengthened Ramsey Test of conditionals: α ≫ γ iff, after sus- pending judgment about α and γ, an agent can infer γ from the supposition of α. It has been shown by Andreas and Gu ̈nther [1] that such a conditional can be used as starting point of an analysis of ‘because’ in natural language. (...) In what follows, we shall refine this analysis so as to yield a fully fledged account of causal explanation. (shrink)