Modern belief revision theory is based to a large extent on partial meet contraction that was introduced in the seminal article by Carlos Alchourrón, Peter Gärdenfors, and David Makinson that appeared in 1985. In the same year, Alchourrón and Makinson published a significantly different approach to the same problem, called safe contraction. Since then, safe contraction has received much less attention than partial meet contraction. The present paper summarizes the current state of knowledge on safe contraction, provides some new results (...) and offers a list of unsolved problems that are in need of investigation. (shrink)

Prioritized bases, i.e., weakly ordered sets of sentences, have been used for specifying an agent’s ‘basic’ or ‘explicit’ beliefs, or alternatively for compactly encoding an agent’s belief state without the claim that the elements of a base are in any sense basic. This paper focuses on the second interpretation and shows how a shifting of priorities in prioritized bases can be used for a simple, constructive and intuitive way of representing a large variety of methods for the change of belief (...) states—methods that have usually been characterized semantically by a system-of-spheres modeling. Among the methods represented are ‘radical’, ‘conservative’ and ‘moderate’ revision, ‘revision by comparison’ in its raising and lowering variants, as well as various constructions for belief expansion and contraction. Importantly, none of these methods makes any use of numbers. (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)

After a number of decades of research into the dynamics of rational belief, the belief revision theory community remains split on the appropriate handling of sequences of changes in view, the issue of so-called iterated revision. It has long been suggested that the matter is at least partly settled by facts pertaining to the results of various single revisions of one’s initial state of belief. Recent work has pushed this thesis further, offering various strong principles that ultimately result in a (...) wholesale reduction of iterated to one-shot revision. The present paper offers grounds to hold that these principles should be significantly weakened and that the reductionist thesis should ultimately be rejected. Furthermore, the considerations provided suggest a close connection between the logic of iterated belief change and the logic of evidential relevance. (shrink)

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)

This is a discussion of the problem of extending the basic AGM belief revision theory to iterated belief revision: the problem of formulating rules, not only for revising a basic belief state in response to potential new information, but also for revising one’s revision rules in response to potential new information. The emphasis in the paper is on foundational questions about the nature of and motivation for various constraints, and about the methodology of the evaluation of putative counterexamples to proposed (...) constraints. Some specific constraints that have been proposed are criticized. The paper emphasizes the importance of meta-information—information about one’s sources of information—and argues that little of substance can be said about constraints on iterated belief revision at a level of abstraction that lacks the resources for explicit representation of meta-information. (shrink)

In this paper I discuss the foundations of a formal theory of coherent and conservative belief change that is (a) suitable to be used as a method for constructing iterated changes of belief, (b) sensitive to the history of earlier belief changes, and (c) independent of any form of dispositional coherence. I review various ways to conceive the relationship between the beliefs actually held by an agent and her belief change strategies (that also deal with potential belief sets), show the (...) problems they suffer from, and suggest that belief states should be represented by unary revision functions that take sequences of inputs. Three concepts of coherence implicit in current theories of belief change are distinguished: synchronic, diachronic and dispositional coherence. Diachronic coherence is essentially identified with what is known as conservatism in epistemology. The present paper elaborates on the philosophical motivation of the general framework; formal details and results are provided in a companion paper. (shrink)

Belief revision theory studies how an ideal doxastic agent should revise her beliefs when she receives new information. In part I I will first present the AGM theory of belief revision (Alchourrón & Gärdenfors & Makinson 1985). Then I will focus on the problem of iterated belief revisions.

Belief revision theory studies how an ideal doxastic agent should revise her beliefs when she receives new information. In part I, I have first presented the AGM theory of belief revision. Then I have focused on the problem of iterated belief revisions. In part II, I will first present ranking theory (Spohn 1988). Then I will show how it solves the problem of iterated belief revisions. I will conclude by sketching two areas of future research.

According to the Ramsey Test, conditionals reflect changes of beliefs: α > β is accepted in a belief state iff β is accepted in the minimal revision of it that is necessary to accommodate α. Since Gärdenfors’s seminal paper of 1986, a series of impossibility theorems (“triviality theorems”) has seemed to show that the Ramsey test is not a viable analysis of conditionals if it is combined with AGM-type belief revision models. I argue that it is possible to endorse that (...) Ramsey test for conditionals while staying true to the spirit of AGM. A main focus lies on AGM’s condition of Preservation according to which the original belief set should be fully retained after a revision by information that is consistent with it. I use concrete representations of belief states and (iterated) revisions of belief states as semantic models for (nested) conditionals. Among the four most natural qualitative models for iterated belief change, two are identified that indeed allow us to combine the Ramsey test with Preservation in the language containing only flat conditionals of the form α > β. It is shown, however, that Preservation for this simple language enforces a violation of Preservation for nested conditionals of the form α > (β > γ). In such languages, no two belief sets are ordered by strict subset inclusion. I argue that it has been wrong right from the start to expect that Preservation holds in languages containing nested conditionals. (shrink)

The contributions to the Special Issue on Multiple Belief Change, Iterated Belief Change and Preference Aggregation are divided into three parts. Four contributions are grouped under the heading "multiple belief change" (Part I, with authors M. Falappa, E. Fermé, G. Kern-Isberner, P. Peppas, M. Reis, and G. Simari), five contributions under the heading "iterated belief change" (Part II, with authors G. Bonanno, S.O. Hansson, A. Nayak, M. Orgun, R. Ramachandran, H. Rott, and E. Weydert). These papers do not only pick (...) up the particular questions raised, but also extend and modify the framework of Alchourrón, Gärdenfors and Makinson. Part III deals with preference aggregation and consists of one contribution (by F. Herzberg and D. Eckert). (shrink)

In this paper we investigate three approaches to iterated contraction, namely: the Moderate (or Priority) contraction, the Natural (or Conservative) contraction, and the Lexicographic contraction. We characterise these three contraction functions using certain, arguably plausible, properties of an iterated contraction function. While we provide the characterisation of the first two contraction operations using rationality postulates of the standard variety for iterated contraction, we found doing the same for the Lexicographic contraction more challenging. We provide its characterisation using a variation of (...) Epistemic ranking function instead. (shrink)

This paper presents the model of ‘bounded revision’ that is based on two-dimensional revision functions taking as arguments pairs consisting of an input sentence and a reference sentence. The key idea is that the input sentence is accepted as far as (and just a little further than) the reference sentence is ‘cotenable’ with it. Bounded revision satisfies the AGM axioms as well as the Same Beliefs Condition (SBC) saying that the set of beliefs accepted after the revision does not depend (...) on the reference sentence (although the posterior belief state does depend on it). Bounded revision satisfies the Darwiche–Pearl (DP) axioms for iterated belief change. If the reference sentence is fixed to be a tautology or a contradiction, two well-known one-dimensional revision operations result. Bounded revision thus naturally fills the space between conservative revision (also known as natural revision) and moderate revision (also known as lexicographic revision). I compare this approach to the two-dimensional model of ‘revision by comparison’ investigated by Fermé and Rott (Artif Intell 157:5–47, 2004 ) that satisfies neither the SBC nor the DP axioms. I conclude that two-dimensional revision operations add substantially to the expressive power of qualitative approaches that do not make use of numbers as measures of degrees of belief. (shrink)

This article provides a discussion of the principle of transmission of evidential support across entailment from the perspective of belief revision theory in the AGM tradition. After outlining and briefly defending a small number of basic principles of belief change, which include a number of belief contraction analogues of the Darwiche-Pearl postulates for iterated revision, a proposal is then made concerning the connection between evidential beliefs and belief change policies in rational agents. This proposal is found to be suffcient to (...) establish the truth of a much-discussed intuition regarding transmission failure. (shrink)

We investigate the process of truth-seeking by iterated belief revision with higher-level doxastic information . We elaborate further on the main results in Baltag and Smets (Proceedings of TARK, 2009a , Proceedings of WOLLIC’09 LNAI 5514, 2009b ), applying them to the issue of convergence to truth . We study the conditions under which the belief revision induced by a series of truthful iterated upgrades eventually stabilizes on true beliefs. We give two different conditions ensuring that beliefs converge to “full” (...) (complete) truth , as well as a condition ensuring only that they converge to true (but not necessarily complete) beliefs. (shrink)

In the context of a general framework for belief dynamics which interprets revision as doxastic constraint satisfaction, we discuss a proposal for revising quasi-probabilistic belief measures with finite sets of graded conditionals. The belief states are ranking measures with divisible values (generalizing Spohn’s epistemology), and the conditionals are interpreted as ranking constraints. The approach is inspired by the minimal information paradigm and based on the principle-guided canonical construction of a ranking model of the input conditionals. This is achieved by extending (...) techniques known from conditional default reasoning. We give an overview of how it handles different principles for conditional and parallel revision and compare it with similar accounts. (shrink)

Various theories try to give accounts of how measures of this confidence do or ought to behave, both as far as the internal mental consistency of the agent as ...

First, ranking functions are argued to be superior to AGM belief revision theory in two crucial respects. Second, it is shown how ranking functions are uniquely reflected in iterated belief change. More precisely, conditions on threefold contractions are specified which suffice for representing contractions by a ranking function uniquely up to multiplication by a positive integer. Thus, an important advantage AGM theory seemed to have over ranking functions proves to be spurious.

"A Survey of Ranking Theory": The paper gives an up-to-date survey of ranking theory. It carefully explains the basics. It elaborates on the ranking theoretic explication of reasons and their balance. It explains the dynamics of belief statable in ranking terms and indicates how the ranks can thereby be measured. It suggests how the theory of Bayesian nets can be carried over to ranking theory. It indicates what it might mean to objectify ranks. It discusses the formal and the philosophical (...) aspects of the tight relation and the complementarity of ranks and probabilities. It closes with comparative remarks on predecessors and other philosophical proposals as well as formal models developed in AI. (shrink)

Ranking theory delivers an account of iterated contraction; each ranking function induces a specific iterated contraction behavior. The paper shows how to reconstruct a ranking function from its iterated contraction behavior uniquely up to multiplicative constant and thus how to measure ranks on a ratio scale. Thereby, it also shows how to completely axiomatize that behavior. The complete set of laws of iterated contraction it specifies amend the laws hitherto discussed in the literature.

In this article, we propose a belief revision approach for families of (non-classical) logics whose semantics are first-order axiomatisable. Given any such (non-classical) logic , the approach enables the definition of belief revision operators for , in terms of a belief revision operation satisfying the postulates for revision theory proposed by Alchourrrdenfors and Makinson (AGM revision, Alchourrukasiewicz's many-valued logic. In addition, we present a general methodology to translate algebraic logics into classical logic. For the examples provided, we analyse in what (...) circumstances the properties of the AGM revision are preserved and discuss the advantages of the approach from both theoretical and practical viewpoints. (shrink)

This paper provides algorithmic options for belief revision of a database receiving an infinite stream of inputs. At stage , the database is ¡£¢ , receiving the input ¤ ¢ . The revision algorithms for moving to the new database ¡ ¢¦¥¨§© ¡ ¢ ¤ ¢ take into account the history of previous revisions actually executed as well as possible revision options which were discarded at the time but may now be pursued. The appropriate methodology for carrying this out is (...) Labelled Deductive Systems. (shrink)

The Spohnian paradigm of ranking functions is in many respects like an order-of-magnitude reverse of subjective probability theory. Unlike probabilities, however, ranking functions are only indirectly—via a pointwise ranking function on the underlying set of possibilities W —defined on a field of propositions A over W. This research note shows under which conditions ranking functions on a field of propositions A over W and rankings on a language L are induced by pointwise ranking functions on W and the set of (...) models for L, ModL, respectively. (shrink)

Degrees of belief are familiar to all of us. Our confidence in the truth of some propositions is higher than our confidence in the truth of other propositions. We are pretty confident that our computers will boot when we push their power button, but we are much more confident that the sun will rise tomorrow. Degrees of belief formally represent the strength with which we believe the truth of various propositions. The higher an agent’s degree of belief for a particular (...) proposition, the higher her confidence in the truth of that proposition. For instance, Sophia’s degree of belief that it will be sunny in Vienna tomorrow might be .52, whereas her degree of belief that the train will leave on time might be .23. The precise meaning of these statements depends, of course, on the underlying theory of degrees of belief. These theories offer a formal tool to measure degrees of belief, to investigate the relations between various degrees of belief in different propositions, and to normatively evaluate degrees of belief. (shrink)

Belief revision theory concerns methods for reformulating an agent's epistemic state when the agent's beliefs are refuted by new information. The usual guiding principle in the design of such methods is to preserve as much of the agent's epistemic state as possible when the state is revised. Learning theoretic research focuses, instead, on a learning method's reliability or ability to converge to true, informative beliefs over a wide range of possible environments. This paper bridges the two perspectives by assessing the (...) reliability of several proposed belief revision operators. Stringent conceptions of minimal change are shown to occasion a limitation called inductive amnesia: they can predict the future only if they cannot remember the past. Avoidance of inductive amnesia can therefore function as a plausible and hitherto unrecognized constraint on the design of belief revision operators. (shrink)

Following the pioneer work of Bruno De Finetti [12], conditional probability spaces (allowing for conditioning with events of measure zero) have been studied since (at least) the 1950's. Perhaps the most salient axiomatizations are Karl Popper's in [31], and Alfred Renyi's in [33]. Nonstandard probability spaces [34] are a well know alternative to this approach. Vann McGee proposed in [30] a result relating both approaches by showing that the standard values of infinitesimal probability functions are representable as Popper functions, and (...) that every Popper function is representable in terms of the standard real values of some infinitesimal measure. Our main goal in this article is to study the constraints on (qualitative and probabilistic) change imposed by an extended version of McGee's result. We focus on an extension capable of allowing for iterated changes of view. Such extension, we argue, seems to be needed in almost all considered applications. Since most of the available axiomatizations stipulate (definitionally) important constraints on iterated change, we propose a non-questionbegging framework, Iterative Probability Systems (IPS) and we show that every Popper function can be regarded as a Bayesian IPS. A generalized version of McGee's result is then proved and several of its consequences considered. In particular we note that our proof requires the imposition of Cumulativity, i.e. the principle that a proposition that is accepted at any stage of an iterative process of acceptance will continue to be accepted at any later stage. The plausibility and range of applicability of Cumulativity is then studied. In particular we appeal to a method for defining belief from conditional probability (first proposed in [42] and then slightly modified in [6] and [3]) in order to characterize the notion of qualitative change induced by Cumulative models of probability kinematics. The resulting cumulative notion is then compared with existing axiomatizations of belief change and probabilistic supposition. We also consider applications in the probabilistic accounts of conditionals [1] and [30]. (shrink)

Discussions of the issue of iterated belief revision are commonly accompanied by the presentation of three “concrete” operators: natural, restrained and lexicographic. This raises a natural question: What is so distinctive about these three particular methods? Indeed, the common axiomatic ground for work on iterated revision, the AGM and Darwiche-Pearl postulates, leaves open a whole range of alternative proposals. In this paper, we show that it is satisfaction of an additional principle of “Independence of Irrelevant Alternatives”, inspired by the literature (...) on Social Choice, that unites and sets apart our three “elementary” revision operators. A parallel treatment of iterated belief contraction is also given, yielding a family of elementary contraction operators that includes, besides the well-known “conservative” and “moderate” operators, a new contraction operator that is related to restrained revision. (shrink)

Revision operation is the consistent expansion of a theory by a new belief-representing sentence. We consider that in a paraconsistent setting this desideratum can be accomplished in at least three distinct ways: the output of a revision operation should be either non-trivial or non-contradictory (in general or relative to the new belief). In this paper those distinctions will be explored in the constructive level by showing how the remainder sets could be refined, capturing the key concepts of paraconsistency in a (...) dynamical scenario. These are preliminaries results of a wider project on Paraconsistent Belief Change conduced by the authors. (shrink)

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

Suppositional theories of conditionals take apparent similarities between supposition and conditionals as a starting point, appealing to features of the former to provide an account of the latter. This paper develops a novel form of suppositional theory, one which characterizes the relationship at the level of semantics rather than at the level of speech acts. In the course of doing so, it considers a range of novel data which shed additional light on how conditionals and supposition interact.

Analyzing situations where information is partial, incomplete or contradictory has created a demand for quantitative belief measures that are weaker than classic probability theory. In this paper, we compare two frameworks that have been proposed for this task, Dempster-Shafer theory and non-standard probability theory based on Belnap-Dunn logic. We show the two frameworks to assume orthogonal perspectives on informational shortcomings, but also provide a partial correspondence result. Lastly, we also compare various dynamical rules of the two frameworks, all seen as (...) generalizations of classic Bayes’ conditioning. (shrink)

Ranking theory is one of the salient formal representations of doxastic states. It differs from others in being able to represent belief in a proposition (= taking it to be true), to also represent degrees of belief (i.e. beliefs as more or less firm), and thus to generally account for the dynamics of these beliefs. It does so on the basis of fundamental and compelling rationality postulates and is hence one way of explicating the rational structure of doxastic states. Thereby (...) it provides foundations for accounts of defeasible or nonmonotonic reasoning. It has widespread applications in philosophy, it proves to be most useful in Artificial Intelligence, and it has started to find applications as a model of reasoning in psychology. (shrink)

Darwiche and Pearl’s seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. Most suggestions have resulted in a form of ‘reductionism’ that identifies belief states with orderings of worlds. However, this position has recently been criticised as being unacceptably strong. Other proposals, such as the popular principle (P), aka ‘Independence’, characteristic of ‘admissible’ operators, remain commendably more modest. In this (...) paper, we supplement the DP postulates and (P) with a number of novel conditions. While the DP postulates constrain the relation between a prior and a posterior conditional belief set, our new principles notably govern the relation between two posterior conditional belief sets obtained from a common prior by different revisions. We show that operators from the resulting family, which subsumes both lexicographic and restrained revision, can be represented as relating belief states associated with a ‘proper ordinal interval’ (POI) assignment, a structure more fine-grained than a simple ordering of worlds. We close the paper by noting that these operators satisfy iterated versions of many AGM era postulates, including Superexpansion, that are not sound for admissible operators in general. (shrink)

Given the role consensus is supposed to play in the social aspects of inquiry and deliberation, it is important that we may always identify a consensus as the basis of joint inquiry and deliberation. However, it turns out that if we think of an agent revising her beliefs to reach a consensus, then, on the received view of belief revision, AGM belief revision theory, certain simple and compelling consensus positions are not always available.

This book illustrates the program of Logical-Informational Dynamics. Rational agents exploit the information available in the world in delicate ways, adopt a wide range of epistemic attitudes, and in that process, constantly change the world itself. Logical-Informational Dynamics is about logical systems putting such activities at center stage, focusing on the events by which we acquire information and change attitudes. Its contributions show many current logics of information and change at work, often in multi-agent settings where social behavior is essential, (...) and often stressing Johan van Benthem's pioneering work in establishing this program. However, this is not a Festschrift, but a rich tapestry for a field with a wealth of strands of its own. The reader will see the state of the art in such topics as information update, belief change, preference, learning over time, and strategic interaction in games. Moreover, no tight boundary has been enforced, and some chapters add more general mathematical or philosophical foundations or links to current trends in computer science. The theme of this book lies at the interface of many disciplines. Logic is the main methodology, but the various chapters cross easily between mathematics, computer science, philosophy, linguistics, cognitive and social sciences, while also ranging from pure theory to empirical work. Accordingly, the authors of this book represent a wide variety of original thinkers from different research communities. And their interconnected themes challenge at the same time how we think of logic, philosophy and computation. Thus, very much in line with van Benthem's work over many decades, the volume shows how all these disciplines form a natural unity in the perspective of dynamic logicians (broadly conceived) exploring their new themes today. And at the same time, in doing so, it offers a broader conception of logic with a certain grandeur, moving its horizons beyond the traditional study of consequence relations. (shrink)

In the companion paper (Towards a “sophisticated” model of belief dynamics. Part I), a general framework for realistic modelling of instantaneous states of belief and of the operations involving them was presented and motivated. In this paper, the framework is applied to the case of belief revision. A model of belief revision shall be obtained which, firstly, recovers the Gärdenfors postulates in a well-specified, natural yet simple class of particular circumstances; secondly, can accommodate iterated revisions, recovering several proposed revision operators (...) for iterated revision as special cases; and finally, offers an analysis of Rott’s recent counterexample to several Gärdenfors postulates [32], elucidating in what sense it fails to be one of the special cases to which these postulates apply. (shrink)

The 1985 paper by Carlos Alchourrón, Peter Gärdenfors, and David Makinson, “On the Logic of Theory Change: Partial Meet Contraction and Revision Functions” was the starting-point of a large and rapidly growing literature that employs formal models in the investigation of changes in belief states and databases. In this review, the first twenty-five years of this development are summarized. The topics covered include equivalent characterizations of AGM operations, extended representations of the belief states, change operators not included in the original (...) framework, iterated change, applications of the model, its connections with other formal frameworks, computatibility of AGM operations, and criticism of the model. (shrink)

The question I am addressing in this paper is the following: how is it possible to empirically test, or confirm, counterfactuals? After motivating this question in Section 1, I will look at two approaches to counterfactuals, and at how counterfactuals can be empirically tested, or confirmed, if at all, on these accounts in Section 2. I will then digress into the philosophy of probability in Section 3. The reason for this digression is that I want to use the way observable (...) absolute and relative frequencies, two empirical notions, are used to empirically test, or confirm, hypotheses about objective chances, a metaphysical notion, as a role-model. Specifically, I want to use this probabilistic account of the testing of chance hypotheses as a role-model for the account of the testing of counterfactuals, another metaphysical notion, that I will present in Sections 4 to 8. I will conclude by comparing my proposal to one non-probabilistic and one probabilistic alternative in Section 9. (shrink)

Conditionals are most important objects in knowledge representation, commonsense reasoning and belief revision. Due to their non-classical nature, however, they are not easily dealt with. This paper presents a new approach to conditionals, which is apt to capture their dynamic power particularly well. We show how this approach can be applied to represent conditional knowledge inductively, and to guide revisions of epistemic states by sets of beliefs. In particular, we generalize system-Z* as an appropriate counterpart to maximum entropy-representations in a (...) semi-quantitative setting, and provide a theoretical justification to make its basic ideas usable also for belief revision. (shrink)

In ‘belief revision’ a theory is revised with a formula φ resulting in a revised theory . Typically, is in , one has to give up belief in by a process of retraction, and φ is in . We propose to model belief revision in a dynamic epistemic logic. In this setting, we typically have an information state (pointed Kripke model) for the theory wherein the agent believes the negation of the revision formula, i.e., wherein is true. The revision with (...) φ is a program *φ that transforms this information state into a new information state. The transformation is described by a dynamic modal operator [*φ], that is interpreted as a binary relation [ [*φ] ] between information states. The next information state is computed from the current information state and the belief revision formula. If the revision is successful, the agent believes φ in the resulting state, i.e., Bφ is then true. To make this work, as information states we propose ‘doxastic epistemic models’ that represent both knowledge and degrees of belief. These are multi-modal and multi-agent Kripke models. They are constructed from preference relations for agents, and they satisfy various characterizable multi-agent frame properties. Iterated, revocable, and higher-order belief revision are all quite natural in this setting. We present, for an example, five different ways of such dynamic belief revision. One can also see that as a non-deterministic epistemic action with two alternatives, where one is preferred over the other, and there is a natural generalization to general epistemic actions with preferences. (shrink)

In this paper we propose a conditional logic called IBC to represent iterated belief revision systems. We propose a set of postulates for iterated revision which are a small variant of Darwiche and Pearl''s ones. The conditional logic IBC has a standard semantics in terms of selection function models and provides a natural representation of epistemic states. We establish a correspondence between iterated belief revision systems and IBC-models. Our representation theorem does not entail Gärdenfors'' Triviality Result.

This paper describes an approach for reasoning in a dynamic domain with nondeterministic actions in which an agent’s beliefs correspond to the simplest, or most plausible, course of events consistent with the agent’s observations and beliefs. The account is based on an epistemic extension of the situation calculus, a first-order theory of reasoning about action that accommodates sensing actions. In particular, the account is based on a qualitative theory of nondeterminism. Our position is that for commonsense reasoning, the world is (...) most usefully regarded as deterministic, and that nondeterminism is an epistemic phenomenon, arising from an agent’s limited awareness and perception. The account offers several advantages: an agent has a set of categorical beliefs, yet can deal with equally-likely outcomes or with outcomes of differing plausibility. The agent maintains as its set of contingent beliefs the most plausible, or simplest, picture of the world, consistent with its beliefs and actions it believes it executed; yet it may modify these in light of later information. (shrink)

The idea of preserving conditional beliefs emerged recently as a new paradigm apt to guide the revision of epistemic states. Conditionals are substantially different from propositional beliefs and need specific treatment. In this paper, we present a new approach to conditionals, capturing particularly well their dynamic part as revision policies. We thoroughly axiomatize a principle of conditional preservation as an indifference property with respect to conditional structures of worlds. This principle is developed in a semi-quantitative setting, so as to reveal (...) its fundamental meaning for belief revision in quantitative as well as in qualitative frameworks. In fact, it is shown to cover other proposed approaches to conditional preservation. (shrink)

Postulational approaches attempt to understand the dynamics of belief revision by appealing to no more than the set of beliefs held by an agent and the logical relations between them. It is argued there that such an approach cannot work. A proper account of belief revision must also appeal to the arguments supporting beliefs, and recognize that those arguments can be defeasible. If we begin with a mature epistemological theory that accommodates this, it can be seen that the belief revision (...) operators on which the postulational theories are based are ill-defined. It is further argued that there is no way to repair the definitions so as to retain the spirit of those theory. Belief revision is better studied from within an independently motivated epistemological theory. (shrink)