Belief Revision by Sets of Sentences

The aim of this paper is to extend the system of belief revision developed by Alchourron,Gaerdenfors and Makinson(AGM)to a more general framework.This extension enables a treatment of revision not only by single sentences but also by any sets of entences,especially by infinite sets.The extended revision and contraction operators will be called general ones,respectively.A group of postulates for each operator is provided in such a way that it coincides with AGM‘s in the limit case.A notion of the nice-ordering partition is introduced to characterize the general contraction opeation.A computation-oriented approach is provided for belief revision operations.     

Belief revision in a microworld

Gardenfors et al. proposed a metatheory for reasoning about rational ideal agents revision of beliefs. They provide a set of postulates and consequent theorems which characterize and constrain all revision algorithms. Since the primary thrust of most dynamic revision schemes are presently foundational in nature while the Gardenfors approach is based on coherence, we investigate these postulates as an alternative. In a microworld setting of blocks, actions are defined in terms of the basic Gardenfors operators of revision, expansion and contraction of theories. States of the blocks world are captured as canonical theories. Laws of the world are codified as the most entrenched formulas using the entrenchment relation of the Gardenfors postulates. It is thereby shown that linear planning is adequately handled. The equivalence of laws with pre- and post-conditions in the blocks world is suggested, and the need for strong ontology revision is shown for a modification of the microworld.     

A Fuzzy Dynamic Belief Logic System

In this paper, we develop a fuzzy dynamic belief revision logic system. In our system, propositions take truth values in a set of multiple fuzzy linguistic terms, which people use in everyday life. And we use a uninorm operator to aggregate the linguistic truth values of the same proposition but drawn from two different rules because uninorms can reflect well that the aggregated result of two somehow negative truth values of the same proposition should be more negative, the aggregated result of two somehow positive ones should be more positive, and the result of a negative one and a positive one is a compromise. In this system, the belief on a proposition is the linguistic truth of the proposition in the most possible world according to the current preference over all possible worlds. In the light of new information, the preference degrees of possible worlds will be updated. Accordingly, the most possible world will be changed to another and thus an old belief on a propositional formula will be changed to the linguistic truth of the proposition in the new most possible world. Moreover, we prove the soundness and completeness of our fuzzy dynamic belief revision system. In addition, we also prove that our belief revision method in fuzzy environment satisfies some relevant ones of standard AGM postulates (named after the names of their proponents, Alchourrón, Gärdenfors, and Makinson).     

Axiomatic characterization of the AGM theory of belief revision in a temporal logic

Since belief revision deals with the interaction of belief and information over time, branching-time temporal logic seems a natural setting for a theory of belief change. We propose two extensions of a modal logic that, besides the next-time temporal operator, contains a belief operator and an information operator. The first logic is shown to provide an axiomatic characterization of the first six postulates of the AGM theory of belief revision, while the second, stronger, logic provides an axiomatic characterization of the full set of AGM postulates.     

Coherence approach to logic program revision

In this paper, we present a new approach to the problem of revising extended programs; we base this approach on the coherence theory initially advocated by Gardenfors for belief revision. Our approach resolves contradiction by removing only conflicting information, not the believed source of it, and therefore, keeps information loss minimal. Furthermore, since there is no need to search for problematic assumptions, as is done in the traditional assumption-removal approach, our approach provides a skeptical revision semantics that is tractable. We define the skeptical and credulous coherence semantics and show that both semantics can be characterized in terms of the fixpoint semantics of a revised program using a simple program-revision technique. These semantics provide a suitable framework for knowledge and belief revision in the context of logic programs. Semantical properties and advantages of the proposed revision semantics are also analyzed     

Belief revision in structured probabilistic argumentation

In real-world applications, knowledge bases consisting of all the available information for a specific domain, along with the current state of affairs, will typically contain contradictory data, coming from different sources, as well as data with varying degrees of uncertainty attached. An important aspect of the effort associated with maintaining such knowledge bases is deciding what information is no longer useful; pieces of information may be outdated; may come from sources that have recently been discovered to be of low quality; or abundant evidence may be available that contradicts them. In this paper, we propose a probabilistic structured argumentation framework that arises from the extension of Presumptive Defeasible Logic Programming (PreDeLP) with probabilistic models, and argue that this formalism is capable of addressing these basic issues. The formalism is capable of handling contradictory and uncertain data, and we study non-prioritized belief revision over probabilistic PreDeLP programs that can help with knowledge-base maintenance. For belief revision, we propose a set of rationality postulates — based on well-known ones developed for classical knowledge bases — that characterize how these belief revision operations should behave, and study classes of operators along with theoretical relationships with the proposed postulates, including representation theorems stating the equivalence between classes of operators and their associated postulates. We then demonstrate how our framework can be used to address the attribution problem in cyber security/cyber warfare.     

Preferential belief change using generalized epistemic entrenchment

A sentence A is epistemically less entrenched in a belief state K than a sentence B if and only if a person in belief state K who is forced to give up either A or B will give up A and hold on to B. This is the fundamental idea of epistemic entrenchment as introduced by Gärdenfors (1988) and elaborated by Gärdenfors and Makinson (1988). Another distinguishing feature of relations of epistemic entrenchment is that they permit particularly simple and elegant construction recipes for minimal changes of belief states. These relations, however, are required to satisfy rather demanding conditions. In the present paper we liberalize the concept of epistemic entrenchment by removing connectivity, minimality and maximality conditions. Correspondingly, we achieve a liberalization of the concept of rational belief change that does no longer presuppose the postulates of success and rational monotony. We show that the central results of Gärdenfors and Makinson are preserved in our more flexible setting. Moreover, the generalized concept of epistemic entrenchment turns out to be applicable also to relational and iterated belief changes.     

Iterated belief revision, revised

The AGM postulates for belief revision, augmented by the DP postulates for iterated belief revision, provide widely accepted criteria for the design of operators by which intelligent agents adapt their beliefs incrementally to new information. These postulates alone, however, are too permissive: They support operators by which all newly acquired information is canceled as soon as an agent learns a fact that contradicts some of its current beliefs. In this paper, we present a formal analysis of the deficiency of the standard postulates alone, and we show how to solve the problem by an additional postulate of independence. We give a representation theorem for this postulate and prove that it is compatible with AGM and DP.     

Seeing Is Believing

In this paper a formal framework is proposed in which variousinformative actions are combined, corresponding to the different ways in whichrational agents can acquire information. In order to solve the variousconflicts that could possibly occur when acquiring information fromdifferent sources, we propose a classification of the informationthat an agent possesses according to credibility. Based on this classification, we formalize what itmeans for agents to have seen or heard something, or to believesomething by default. We present a formalization of observations,communication actions, and the attempted jumps to conclusions thatconstitutes default reasoning. To implement these informative actionswe use a general belief revision action which satisfies theAGM postulates; dependent on the credibility of the incominginformation this revision action acts on one or more parts ofthe classified belief sets of the agents. The abilities of agents formalizeboth the limited capacities of agents to acquire information, and the preference of one kind of information acquisition to another. A very important feature of our approach is that it shows how to integratevarious aspects of agency, in particular the (informational) attitudesof dealing with information from observation, communication and defaultreasoning into one coherent framework, both model-theoretically andsyntactically.     

On the Logic of Theory Change: Contraction without Recovery

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.     

Agent信念的遗忘修正方法

为了使信念修正能够满足最小改变原则,首先基于遗忘理论定义遗忘收缩算子,并且证明该算子满足必要AGM收缩假定;然后通过Levi Identity构建遗忘修正算子;最后给出遗忘修正方法和多次遗忘修正算法。实例分析表明,算法具有可行性和有效性,能够得到较满意的修正结果。     

Prioritized assertional-based removed sets revision of <Emphasis Type="Italic">DL</Emphasis>-<Emphasis Type="Italic">Lite</Emphasis> belief bases

In real world applications, information is often provided by multiple sources having different priority levels reflecting for instance their reliability. This paper investigates ”Prioritized Removed Sets Revision” (PRSR) for revising stratified DL-Lite knowledge bases when a new sure piece of information, called the input, is added. The strategy of revision is based on inconsistency minimization and consists in determining smallest subsets of assertions (prioritized removed sets) that should be dropped from the current stratified knowledge base in order to restore consistency and accept the input. We consider different forms of input: A membership assertion, a positive or a negative inclusion axiom. To characterize our revision approach, we first rephrase Hansson’s postulates for belief bases revision within a DL-Lite setting, we then give logical properties of PRSR operators. In some situations, the revision process leads to several possible revised knowledge bases where defining a selection function is required to keep results within DL-Lite fragment. The last part of the paper shows how to use the notion of hitting set in order to compute the PRSR outcome. We also study the complexity of PRSR operators, and show that, in some cases, the computational complexity of the result can be performed in polynomial time.     

Belief Fusion: Aggregating Pedigreed Belief States

We introduce a new operator – belief fusion– which aggregates the beliefs of two agents, each informed by a subset of sources ranked by reliability. In the process we definepedigreed belief states, which enrich standard belief states with the source of each piece of information. We note that the fusion operator satisfies the invariants of idempotence, associativity, and commutativity. As a result, it can be iterated without difficulty. We also define belief diffusion; whereas fusion generally produces a belief state with more information than is possessed by either of its two arguments, diffusion produces a state with less information. Fusion and diffusion are symmetric operators, and together define a distributive lattice. Finally, we show that AGM revision can be viewed as fusion between a novice and an expert. This revised version was published online in August 2006 with corrections to the Cover Date.     

Belief Revision: A Critique

We examine carefully the rationale underlying the approaches to belief change taken in the literature, and highlight what we view as methodological problems. We argue that to study belief change carefully, we must be quite explicit about the “ontology” or scenario underlying the belief change process. This is something that has been missing in previous work, with its focus on postulates. Our analysis shows that we must pay particular attention to two issues that have often been taken for granted: the first is how we model the agent's epistemic state. (Do we use a set of beliefs, or a richer structure, such as an ordering on worlds? And if we use a set of beliefs, in what language are these beliefs are expressed?) We show that even postulates that have been called “beyond controversy” are unreasonable when the agent's beliefs include beliefs about her own epistemic state as well as the external world. The second is the status of observations. (Are observations known to be true, or just believed? In the latter case, how firm is the belief?) Issues regarding the status of observations arise particularly when we consider iterated belief revision, and we must confront the possibility of revising by φ and then by ¬ φ.     

Belief function combination and conflict management

Within the framework of evidence theory, data fusion consists in obtaining a single belief function by the combination of several belief functions resulting from distinct information sources. The most popular rule of combination, called Dempster's rule of combination (or the orthogonal sum), has several interesting mathematical properties such as commutativity or associativity. However, combining belief functions with this operator implies normalizing the results by scaling them proportionally to the conflicting mass in order to keep some basic properties. Although this normalization seems logical, several authors have criticized it and some have proposed other solutions. In particular, Dempster's combination operator is a poor solution for the management of the conflict between the various information sources at the normalization step. Conflict management is a major problem especially during the fusion of many information sources. Indeed, the conflict increases with the number of information sources. That is why a strategy for re-assigning the conflicting mass is essential. In this paper, we define a formalism to describe a family of combination operators. So, we propose to develop a generic framework in order to unify several classical rules of combination. We also propose other combination rules allowing an arbitrary or adapted assignment of the conflicting mass to subsets.     

Encompassing full nonmonotonicity within belief modification activity

 In this paper, starting from an analysis of the general activity of belief modification, the concept of full nonmonotonicity is introduced and discussed. Such concept is based on the identification of two different types of nonmonotonicity and includes all the cases of belief modification that may occur in reasoning activity. This distinction cannot be encompassed by the most known nonmonotonic logic formalisms nor by the classical view of conditioning and belief revision axiomatically set up by Gardenfors [9]. A conceptual model able to correctly capture fully nonmonotonic reasoning is discussed: such model includes an explicit representation for the concepts of uncertainty about the applicability of a piece of knowledge and of reasoning attitude. Finally, the issue of formalizing fully nonmonotonic reasoning is discussed and preliminary formalization proposals are introduced.     

Iterated Belief Change

Most existing formalizations treat belief change as a single-step process, and ignore several problems that become important when a theory, or belief state, is revised over several steps. This paper identifies these problems, and argues for the need to retain all of the multiple possible outcomes of a belief change step, and for a framework in which the effects of a belief change step persist as long as is consistently possible. To demonstrate that such a formalization is indeed possible, we develop a framework, which uses the language of PJ-default logic (Delgrande and Jackson 1991) to represent a belief state, and which enables the effects of a belief change step to persist by propagating belief constraints . Belief change in this framework maps one belief state to another, where each belief state is a collection of theories given by the set of extensions of the PJ-default theory representing that belief state. Belief constraints do not need to be separately recorded; they are encoded as clearly identifiable components of a PJ-default theory. The framework meets the requirements for iterated belief change that we identify and satisfies most of the AGM postulates (Alchourrón, Gärdenfors, and Makinson 1985) as well.     

信任函数组合与局部冲突处理

在证据理论框架中,数据融合是将几个来自不同证据源的信任函数组合成一个信任函数,Dempster组合规则是人们常用的方法,但由于此规则是通过按比例放大组合后焦元的基本信任指派值而使其满足信任函数的标准定义,尽管这一标准化方法有逻辑上的解释,但还是招致诸多批评,并提出了一些修正的组合规则。Dempster组合规则尤其在较强冲突情形下其组合结果是不符合常理的,因此不同证据源的冲突处理是信息融合的主要问题。该文通过分析比较已有的主要组合规则,提出了一种处理冲突的新方法--局部冲突处理法,此方法可克服已有方法的缺点,而且组合结果更加合理。     

Prime forms and minimal change in propositional belief bases

This paper proposes to use prime implicants and prime implicates normal forms to represent belief sets. This representation is used, on the one hand, to define syntactical versions of belief change operators that also satisfy the rationality postulates but present better complexity properties than those proposed in the literature and, on the other hand, to propose a new minimal distance that adopts as a minimal belief unit a “fact”, defined as a prime implicate of the belief set, instead of the usually adopted Hamming distance, i.e., the number of propositional symbols on which the models differ. Some experiments are also presented that show that this new minimal distance allows to define belief change operators that usually preserve more information of the original belief set.     

A sound and complete R-calculi with respect to contraction and minimal change

AGM postulates are for belief revision (revision by a single belief), and DP postulates are for iterated revision (revision by a finite sequence of beliefs). R-calculus is given for R-configurations Δ|Γ, where Δ is a set of atomic formulas or the negations of atomic formulas, and Γ is a finite set of formulas. We shall give two R-calculi C and M (sets of deduction rules) such that for any finite consistent sets Γ, Δ of formulas in the propositional logic, there is a consistent set Θ ? Γ of formulas such that Δ|Γ ? Δ, Θ is provable and Θ is a contraction of Γ by Δ or a minimal change of Γ by Δ; and prove that C and M are sound and complete with respect to the contraction and the minimal change, respectively.