Belief revision is the task of modifying a knowledge base when new information becomes available, while also respecting a number of desirable properties. Classical belief revision schemes have been already specialised to \emph{binary decision diagrams} (BDDs), the classical formalism to compactly represent propositional knowledge. These results also apply to \emph{ordered} BDDs (OBDDs), a special class of BDDs, designed to guarantee canonicity. Yet, those revisions cannot be applied to \emph{sentential decision diagrams} (SDDs), a typically more compact but still canonical class of Boolean circuits, which generalizes OBDDs, while not being a subclass of BDDs. Here we fill this gap by deriving a general revision algorithm for SDDs based on a syntactic characterisation of Dalal revision. A specialised procedure for DNFs is also presented. Preliminary experiments performed with randomly generated knowledge bases show the advantages of directly perform revision within SDD formalism.
On Definite Iterated Belief Revision with Belief Algebras
School of Mathematics, Southwest Jiaotong University, China（数学学院，西南交通大学）；School of Computing and Artificial Intelligence, Southwest Jiaotong University, China（计算与人工智能学院，西南交通大学）；LIRMM UMR 5506, University of Montpellier & CNRS, France（蒙彼利埃大学及CNRS LIRMM研究中心）
Indian Statistical Institute（印度统计研究所）；Jadavpur University（贾达普大学）
A belief base revision is developed. The belief base is represented using Unified Answer Set Programs which is capable of representing imprecise and uncertain information and perform nonomonotonic reasoning with them. The base revision operator is developed using Removed Set Revision strategy. The operator is characterized with respect to the postulates for base revisions operator satisfies.
The (extended) AGM postulates for belief revision seem to deal with the revision of a given theory K by an arbitrary formula, but not to constrain the revisions of two different theories by the same formula. A new postulate is proposed and compared with other similar postulates that have been proposed in the literature. The AGM revisions that satisfy this new postulate stand in one-to-one correspondence with the rational, consistency-preserving relations. This correspondence is described explicitly. Two viewpoints on iterative revisions are distinguished and discussed.
Université de Lorraine（洛林大学）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）；Université de Strasbourg（斯特拉斯堡大学）；ENGEES（斯特拉斯堡国立水与环境工程学院）
Belief revision is an operation that aims at modifying old be-liefs so that they become consistent with new ones. The issue of belief revision has been studied in various formalisms, in particular, in qualitative algebras (QAs) in which the result is a disjunction of belief bases that is not necessarily repre-sentable in a QA. This motivates the study of belief revision in formalisms extending QAs, namely, their propositional clo-sures: in such a closure, the result of belief revision belongs to the formalism. Moreover, this makes it possible to define a contraction operator thanks to the Harp…
We propose a new approach to belief revision that provides a way to change knowledge bases with a minimum of effort. We call this way of revising belief states optimal belief revision. Our revision method gives special attention to the fact that most belief revision processes are directed to a specific informational objective. This approach to belief change is founded on notions such as optimal context and accessibility. For the sentential model of belief states we provide both a formal description of contexts as sub-theories determined by three parameters and a method to construct contexts. N…
Université de Lorraine（洛林大学）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）；Université de Strasbourg（斯特拉斯堡大学）；ENGEES（斯特拉斯堡国立水与环境工程学院）
Belief revision is an operation that aims at modifying old beliefs so that they become consistent with new ones. The issue of belief revision has been studied in various formalisms, in particular, in qualitative algebras (QAs) in which the result is a disjunction of belief bases that is not necessarily representable in a QA. This motivates the study of belief revision in formalisms extending QAs, namely, their propositional closures: in such a closure, the result of belief revision belongs to the formalism. Moreover, this makes it possible to define a contraction operator thanks to the Harper …
In a probability-based reasoning system, Bayes' theorem and its variations are often used to revise the system's beliefs. However, if the explicit conditions and the implicit conditions of probability assignments `me properly distinguished, it follows that Bayes' theorem is not a generally applicable revision rule. Upon properly distinguishing belief revision from belief updating, we see that Jeffrey's rule and its variations are not revision rules, either. Without these distinctions, the limitation of the Bayesian approach is often ignored or underestimated. Revision, in its general form, can…
The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. In a companion paper (Friedman & Halpern, 1997), we introduce a new framework to model belief change. This framework combines temporal and epistemic modalities with a notion of plausibility, allowing us to examine the change of beliefs over time. In this paper, we show how belief revision and belief update can be captured in our framework. This allows us to compare the assumptions made by each method, and to…
A vast and interesting family of natural semantics for belief revision is defined. Suppose one is given a distance d between any two models. One may then define the revision of a theory K by a formula a as the theory defined by the set of all those models of a that are closest, by d, to the set of models of K. This family is characterized by a set of rationality postulates that extends the AGM postulates. The new postulates describe properties of iterated revisions.
In general, the best explanation for a given observation makes no promises on how good it is with respect to other alternative explanations. A major deficiency of message-passing schemes for belief revision in Bayesian networks is their inability to generate alternatives beyond the second best. In this paper, we present a general approach based on linear constraint systems that naturally generates alternative explanations in an orderly and highly efficient manner. This approach is then applied to cost-based abduction problems as well as belief revision in Bayesian net works.
How Do People Revise Inconsistent Beliefs? Examining Belief Revision in Humans with User Studies
Washington University in St. Louis（华盛顿大学圣路易斯分校）；Imperial College London（伦敦帝国学院）；Artificial Intelligence Research Institute (IIIA-CSIC)（人工智能研究所（IIIA-CSIC））
A common assumption in belief revision is that the reliability of the information sources is either given, derived from temporal information, or the same for all. This article does not describe a new semantics for integration but the problem of obtaining the reliability of the sources given the result of a previous merging. As an example, the relative reliability of two sensors can be assessed given some certain observation, and allows for subsequent mergings of data coming from them.
Institut Supérieur d’Informatique et de Multimédia, Université de Sfax（斯法克斯大学高等信息与多媒体学院）；Laboratoire OLID (LR19ES21), Institut Supérieur de Gestion Industrielle, Université de Sfax（斯法克斯大学高等工业管理学院OLID实验室（LR19ES21））；Institut des Hautes Etudes Commerciales, Université de Sfax（斯法克斯大学高等商业研究学院）
This paper deals with belief base revision that is a form of belief change consisting of the incorporation of new facts into an agent's beliefs represented by a finite set of propositional formulas. In the aim to guarantee more reliability and rationality for real applications while performing revision, we propose the idea of credible belief base revision yielding to define two new formula-based revision operators using the suitable tools offered by evidence theory. These operators, uniformly presented in the same spirit of others in [9], stem from consistent subbases maximal with respect to c…
Northrop Research and Technology Center（诺斯罗普研究与技术中心）
This paper describes a formal system of belief revision developed by Wolfgang Spohn and shows that this system has a parallel implementation that can be derived from an influence diagram in a manner similar to that in which Bayesian networks are derived. The proof rests upon completeness results for an axiomatization of the notion of conditional independence, with the Spohn system being used as a semantics for the relation of conditional independence.
This paper extends the applications of belief-networks to include the revision of belief commitments, i.e., the categorical acceptance of a subset of hypotheses which, together, constitute the most satisfactory explanation of the evidence at hand. A coherent model of non-monotonic reasoning is established and distributed algorithms for belief revision are presented. We show that, in singly connected networks, the most satisfactory explanation can be found in linear time by a message-passing algorithm similar to the one used in belief updating. In multiply-connected networks, the problem may be…
Centre for Artificial Intelligence Research（人工智能研究中心）；University of KwaZulu-Natal（夸祖鲁-纳塔尔大学）；CSIR Meraka（南非科学与工业研究理事会梅拉卡研究所）
I propose a framework for an agent to change its probabilistic beliefs when a new piece of propositional information $α$ is observed. Traditionally, belief change occurs by either a revision process or by an update process, depending on whether the agent is informed with $α$ in a static world or, respectively, whether $α$ is a 'signal' from the environment due to an event occurring. Boutilier suggested a unified model of qualitative belief change, which "combines aspects of revision and update, providing a more realistic characterization of belief change." In this paper, I propose a unified mo…
Institut de Recherche en Informatique de Toulouse (IRIT) - CNRS（图卢兹计算机科学研究所（IRIT）- 法国国家科学研究中心）；Universite Paul Sabatier（保罗·萨巴蒂埃大学）
This paper discusses belief revision under uncertain inputs in the framework of possibility theory. Revision can be based on two possible definitions of the conditioning operation, one based on min operator which requires a purely ordinal scale only, and another based on product, for which a richer structure is needed, and which is a particular case of Dempster's rule of conditioning. Besides, revision under uncertain inputs can be understood in two different ways depending on whether the input is viewed, or not, as a constraint to enforce. Moreover, it is shown that M.A. Williams' transmutati…
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 of the suggestions made 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' revision operators, remain commendably more modest. In this paper, we s…
We are interested in belief revision involving conditional statements where the antecedent is almost certainly false. To represent such problems, we use Ordinal Conditional Functions that may take infinite values. We model belief change in this context through simple arithmetical operations that allow us to capture the intuition that certain antecedents can not be validated by any number of observations. We frame our approach as a form of finite belief improvement, and we propose a model of conditional belief revision in which only the "right" hypothetical levels of implausibility are revised.
FernUniversität in Hagen（哈根远程大学）；TU Dortmund University（多特蒙德工业大学）
The research on non-prioritized revision studies revision operators which do not accept all new beliefs. In this paper, we contribute to this line of research by introducing the concept of dynamic-limited revision, which are revisions expressible by a total preorder over a limited set of worlds. For a belief change operator, we consider the scope, which consists of those beliefs which yield success of revision. We show that for each set satisfying single sentence closure and disjunction completeness there exists a dynamic-limited revision having the union of this set with the beliefs set as sc…
SATEN is an object-oriented web-based extraction and belief revision engine. It runs on any computer via a Java 1.1 enabled browser such as Netscape 4. SATEN performs belief revision based on the AGM approach. The extraction and belief revision reasoning engines operate on a user specified ranking of information. One of the features of SATEN is that it can be used to integrate mutually inconsistent commensuate rankings into a consistent ranking.
We address the problem of belief change in (nonmonotonic) logic programming under answer set semantics. Unlike previous approaches to belief change in logic programming, our formal techniques are analogous to those of distance-based belief revision in propositional logic. In developing our results, we build upon the model theory of logic programs furnished by SE models. Since SE models provide a formal, monotonic characterisation of logic programs, we can adapt techniques from the area of belief revision to belief change in logic programs. We introduce methods for revising and merging logic pr…
British Columbia Institute of Technology（不列颠哥伦比亚理工学院）
Belief revision is the process in which an agent incorporates a new piece of information together with a pre-existing set of beliefs. When the new information comes in the form of a report from another agent, then it is clear that we must first determine whether or not that agent should be trusted. In this paper, we provide a formal approach to modeling trust as a pre-processing step before belief revision. We emphasize that trust is not simply a relation between agents; the trust that one agent has in another is often restricted to a particular domain of expertise. We demonstrate that this fo…
British Columbia Institute of Technology（不列颠哥伦比亚理工学院）；Simon Fraser University（西蒙菲莎大学）
In action domains where agents may have erroneous beliefs, reasoning about the effects of actions involves reasoning about belief change. In this paper, we use a transition system approach to reason about the evolution of an agents beliefs as actions are executed. Some actions cause an agent to perform belief revision while others cause an agent to perform belief update, but the interaction between revision and update can be non-elementary. We present a set of rationality properties describing the interaction between revision and update, and we introduce a new class of belief change operators …
Iterated Belief Change is the research area that investigates principles for the dynamics of beliefs over (possibly unlimited) many subsequent belief changes. In this paper, we demonstrate how iterated belief change is connected to computation. In particular, we show that iterative belief revision is Turing complete, even under the condition that broadly accepted principles like the Darwiche-Pearl postulates for iterated revision hold.
Institute for Logic, Language and Computation（逻辑、语言与计算研究所）；The University of Amsterdam（阿姆斯特丹大学）
Prominent approaches to belief revision prescribe the adoption of a new belief that is as close as possible to the prior belief, in a process that, even in the standard case, can be described as attempting to minimize surprise. Here we extend the existing model by proposing a measure of surprise, dubbed relative surprise, in which surprise is computed with respect not just to the prior belief, but also to the broader context provided by the new information, using a measure derived from familiar distance notions between truth-value assignments. We characterize the surprise minimization revision…
Indian Statistical Institute（印度统计研究所）；Jadavpur University（贾达普大学）
Bilattice-based triangle provides an elegant algebraic structure for reasoning with vague and uncertain information. But the truth and knowledge ordering of intervals in bilattice-based triangle can not handle repetitive belief revisions which is an essential characteristic of nonmonotonic reasoning. Moreover the ordering induced over the intervals by the bilattice-based triangle is not sometimes intuitive. In this work, we construct an alternative algebraic structure, namely preorder-based triangle and we formulate proper logical connectives for this. It is also demonstrated that Preorder-bas…
In this paper we propose a new family of Belief Conditioning Rules (BCRs) for belief revision. These rules are not directly related with the fusion of several sources of evidence but with the revision of a belief assignment available at a given time according to the new truth (i.e. conditioning constraint) one has about the space of solutions of the problem.
The field of iterated belief change has focused mainly on revision, with the other main operator of AGM belief change theory, i.e. contraction, receiving relatively little attention. In this paper we extend the Harper Identity from single-step change to define iterated contraction in terms of iterated revision. Specifically, just as the Harper Identity provides a recipe for defining the belief set resulting from contracting A in terms of (i) the initial belief set and (ii) the belief set resulting from revision by not-A, we look at ways to define the plausibility ordering over worlds resulting…
We present a general, consistency-based framework for belief change. Informally, in revising K by A, we begin with A and incorporate as much of K as consistently possible. Formally, a knowledge base K and sentence A are expressed, via renaming propositions in K, in separate languages. Using a maximization process, we assume the languages are the same insofar as consistently possible. Lastly, we express the resultant knowledge base in a single language. There may be more than one way in which A can be so extended by K: in choice revision, one such ``extension'' represents the revised state; alt…
La Trobe University（拉筹伯大学）；Cardiff University（卡迪夫大学）
The belief revision literature has largely focussed on the issue of how to revise one's beliefs in the light of information regarding matters of fact. Here we turn to an important but comparatively neglected issue: How might one extend a revision operator to handle conditionals as input? Our approach to this question of 'conditional revision' is distinctive insofar as it abstracts from the controversial details of how to revise by factual sentences. We introduce a 'plug and play' method for uniquely extending any iterated belief revision operator to the conditional case. The flexibility of our…
Interval Orders, Biorders and Credibility-limited Belief Revision
Cardiff University, United Kingdom（Cardiff大学，英国）；Université Sorbonne Paris Nord, Inserm, Sorbonne Université, Limics（巴黎-索邦大学，Inserm，索邦大学，Limics）；CAIR, University of Cape Town, South Africa（开普敦大学，南非）；ISTI-CNR, Pisa, Italy（意大利比萨CNR ISTI）
Several forms of iterable belief change exist, differing in the kind of change and its strength: some operators introduce formulae, others remove them; some add formulae unconditionally, others only as additions to the previous beliefs; some only relative to the current situation, others in all possible cases. A sequence of changes may involve several of them: for example, the first step is a revision, the second a contraction and the third a refinement of the previous beliefs. The ten operators considered in this article are shown to be all reducible to three: lexicographic revision, refineme…
SNePS is a mature knowledge representation, reasoning, and acting system that has long contained a belief revision subsystem, called SNeBR. SNeBR is triggered when an explicit contradiction is introduced into the SNePS belief space, either because of a user's new assertion, or because of a user's query. SNeBR then makes the user decide what belief to remove from the belief space in order to restore consistency, although it provides information to help the user in making that decision. We have recently added automatic belief revision to SNeBR, by which, under certain circumstances, SNeBR decide…
The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. In a companion paper, we introduce a new framework to model belief change. This framework combines temporal and epistemic modalities with a notion of plausibility, allowing us to examine the change of beliefs over time. In this paper, we show how belief revision and belief update can be captured in our framework. This allows us to compare the assumptions made by each method, and to better understand the prin…
AGM's belief revision is one of the main paradigms in the study of belief change operations. In this context, belief bases (prioritised bases) have been largely used to specify the agent's belief state - whether representing the agent's `explicit beliefs' or as a computational model for her belief state. While the connection of iterated AGM-like operations and their encoding in dynamic epistemic logics have been studied before, few works considered how well-known postulates from iterated belief revision theory can be characterised by means of belief bases and their counterpart in a dynamic epi…
Descriptor revision by Hansson is a framework for addressing the problem of belief change. In descriptor revision, different kinds of change processes are dealt with in a joint framework. Individual change requirements are qualified by specific success conditions expressed by a belief descriptor, and belief descriptors can be combined by logical connectives. This is in contrast to the currently dominating AGM paradigm shaped by Alchourrón, Gärdenfors, and Makinson, where different kinds of changes, like a revision or a contraction, are dealt with separately. In this article, we investigate the…
FernUniversität in Hagen（哈根开放大学）；Technical University Dortmund（多特蒙德工业大学）
According to Boutillier, Darwiche, Pearl and others, principles for iterated revision can be characterised in terms of changing beliefs about conditionals. For iterated contraction a similar formulation is not known. This is especially because for iterated belief change the connection between revision and contraction via the Levi and Harper identity is not straightforward, and therefore, characterisation results do not transfer easily between iterated revision and contraction. In this article, we develop an axiomatisation of iterated contraction in terms of changing conditional beliefs. We pro…
Centrale Supelec（中央理工-高等电力学院）；Université Paris-Saclay（巴黎萨克雷大学）；Université Paris-Dauphine（巴黎多芬大学）；CNRS（法国国家科学研究中心）；Télécom ParisTech（巴黎电信学院）
Belief revision of knowledge bases represented by a set of sentences in a given logic has been extensively studied but for specific logics, mainly propositional, and also recently Horn and description logics. Here, we propose to generalize this operation from a model-theoretic point of view, by defining revision in an abstract model theory known under the name of satisfaction systems. In this framework, we generalize to any satisfaction systems the characterization of the well known AGM postulates given by Katsuno and Mendelzon for propositional logic in terms of minimal change among interpret…
Imaging is a form of probabilistic belief change which could be employed for both revision and update. In this paper, we propose a new framework for probabilistic belief change based on imaging, called Expected Distance Imaging (EDI). EDI is sufficiently general to define Bayesian conditioning and other forms of imaging previously defined in the literature. We argue that, and investigate how, EDI can be used for both revision and update. EDI's definition depends crucially on a weight function whose properties are studied and whose effect on belief change operations is analysed. Finally, four E…
We present a method for relevance sensitive non-monotonic inference from belief sequences which incorporates insights pertaining to prioritized inference and relevance sensitive, inconsistency tolerant belief revision. Our model uses a finite, logically open sequence of propositional formulas as a representation for beliefs and defines a notion of inference from maxiconsistent subsets of formulas guided by two orderings: a temporal sequencing and an ordering based on relevance relations between the conclusion and formulas in the sequence. The relevance relations are ternary (using context as a…
The AGM model is the most remarkable framework for modeling belief revision. However, it is not perfect in all aspects. Paraconsistent belief revision, multi-agent belief revision and non-prioritized belief revision are three different extensions to AGM to address three important criticisms applied to it. In this article, we propose a framework based on AGM that takes a position in each of these categories. Also, we discuss some features of our framework and study the satisfiability of AGM postulates in this new context.
University of Illinois at Chicago（伊利诺伊大学芝加哥分校）；MTA-SZTE Research Group on Artificial Intelligence（MTA-SZTE人工智能研究组）
A formal framework is given for the characterizability of a class of belief revision operators, defined using minimization over a class of partial preorders, by postulates. It is shown that for partial orders characterizability implies a definability property of the class of partial orders in monadic second-order logic. Based on a non-definability result for a class of partial orders, an example is given of a non-characterizable class of revision operators. This appears to be the first non-characterizability result in belief revision.
University of New Mexico（新墨西哥大学）；ONERA（法国国家航空航天研究院）
In this paper we extend the new family of (quantitative) Belief Conditioning Rules (BCR) recently developed in the Dezert-Smarandache Theory (DSmT) to their qualitative counterpart for belief revision. Since the revision of quantitative as well as qualitative belief assignment given the occurrence of a new event (the conditioning constraint) can be done in many possible ways, we present here only what we consider as the most appealing Qualitative Belief Conditioning Rules (QBCR) which allow to revise the belief directly with words and linguistic labels and thus avoids the introduction of ad-ho…
In this paper an approach to automated deduction under uncertainty,based on possibilistic logic, is proposed ; for that purpose we deal with clauses weighted by a degree which is a lower bound of a necessity or a possibility measure, according to the nature of the uncertainty. Two resolution rules are used for coping with the different situations, and the refutation method can be generalized. Besides the lower bounds are allowed to be functions of variables involved in the clause, which gives hypothetical reasoning capabilities. The relation between our approach and the idea of minimizing abno…
The AGM theory of belief revision has become an important paradigm for investigating rational belief changes. Unfortunately, researchers working in this paradigm have restricted much of their attention to rather simple representations of belief states, namely logically closed sets of propositional sentences. In our opinion, this has resulted in a too abstract categorisation of belief change operations: expansion, revision, or contraction. Occasionally, in the AGM paradigm, also probabilistic belief changes have been considered, and it is widely accepted that the probabilistic version of expans…
