Infinitary Belief Revision

This paper extends the AGM theory of belief revision to accommodate infinitary belief change. We generalize both axiomatization and modeling of the AGM theory. We show that most properties of the AGM belief change operations are preserved by the generalized operations whereas the infinitary belief change operations have their special properties. We prove that the extended axiomatic system for the generalized belief change operators with a Limit Postulate properly specifies infinite belief change. This framework provides a basis for first-order belief revision and the theory of revising a belief state by a belief state.     

A Model for Structural Changes of Belief

The paper suggests a way of modeling belief changes within the tradition of formal belief revision theories. The present model extends the scope of traditional proposals, such as AGM, so as to take care of “structural belief changes” – a type of radical shifts that is best illustrated with, but not limited to, instances of scientific discovery; we obtain AGM expansions and contractions as limiting cases. The representation strategy relies on a non-standard use of a semantic machinery. More precisely, the model seeks to correlate knowledge states with interpretations of a given formal language L, in such a way that the epistemic state of an agent at a given time gives rise to a picture of how things could be, if there weren’t anything else to know. Interpretations of L proceed along supervaluational ideas; hence, the model as a whole can be seen as a particular application of supervaluational semantics to epistemic matters. Presented by Hannes Leitgeb     

A Sequent Formulation of Conditional Logic Based on Belief Change Operations

Peter Gärdenfors has developed a semantics for conditional logic, based on the operations of expansion and revision applied to states of information. The account amounts to a formalisation of the Ramsey test for conditionals. A conditional A > B is declared accepted in a state of information K if B is accepted in the state of information which is the result of revising K with respect to A. While Gärdenfors's account takes the truth-functional part of the logic as given, the present paper proposes a semantics entirely based on epistemic states and operations on these states. The semantics is accompanied by a syntactic treatment of conditional logic which is formally similar to Gentzen's sequent formulation of natural deduction rules. Three of David Lewis's systems of conditional logic are represented. The formulations are attractive by virtue of their transparency and simplicity.     

Non-Prioritized Ranked Belief Change

Traditional accounts of belief change have been criticized for placing undue emphasis on the new belief provided as input. A recent proposal to address such issues is a framework for non-prioritized belief change based on default theories (Ghose and Goebel, 1998). A novel feature of this approach is the introduction of disbeliefs alongside beliefs which allows for a view of belief contraction as independently useful, instead of just being seen as an intermediate step in the process of belief revision. This approach is, however, restrictive in assuming a linear ordering of reliability on the received inputs. In this paper, we replace the linear ordering with a preference ranking on inputs from which a total preorder on inputs can be induced. This extension brings along with it the problem of dealing with inputs of equal rank. We provide a semantic solution to this problem which contains, as a special case, AGM belief change on closed theories.     

Implementation of Belief Change Operators Using BDDs

While the theory of belief change has attracted a lot of interest from researchers, work on implementing belief change and actually putting it to use in real-world problems is still scarce. In this paper, we present an implementation of propositional belief change using Binary Decision Diagrams. Upper complexity bounds for the algorithm are presented and discussed. The approach is presented both in the general case, as well as on specific belief change operators from the literature. In an effort to gain a better understanding of the empirical efficiency of the algorithms involved, a fault diagnosis problem on combinational circuits is presented, implemented and evaluated.     

On Revising Fuzzy Belief Bases

We look at the problem of revising fuzzy belief bases, i.e., belief base revision in which both formulas in the base as well as revision-input formulas can come attached with varying degrees. Working within a very general framework for fuzzy logic which is able to capture certain types of uncertainty calculi as well as truth-functional fuzzy logics, we show how the idea of rational change from “crisp” base revision, as embodied by the idea of partial meet (base) revision, can be faithfully extended to revising fuzzy belief bases. We present and axiomatise an operation of partial meet fuzzy base revision and illustrate how the operation works in several important special instances of the framework. We also axiomatise the related operation of partial meet fuzzy base contraction.This paper is an extended version of a paper presented at the Nineteenth Conference on Uncertainty in Arti.cial Intelligence (UAI’03).     

Basic Infobase Change

Generalisations of theory change involving arbitrary sets of wffs instead of belief sets have become known as base change. In one view, a base should be thought of as providing more structure to its generated belief set, and can be used to determine the theory change operation associated with a base change operation. In this paper we extend a proposal along these lines by Meyer et al. We take an infobase as a finite sequence of wffs, with each element in the sequence being seen as an independently obtained bit of information, and define appropriate infobase change operations. The associated theory change operations satisfy the AGM postulates for theory change. Since an infobase change operation produces a new infobase, it allows for iterated infobase change. We measure iterated infobase change against the postulates proposed by Darwiche et al. and Lehmann.     

Iterated Belief Change and the Recovery Axiom

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. Portions of this paper were originally presented at ECAI 2002.     

信念修正的AGM理论

信念修正问题是一个富有活力的,正在发展的研究主题。这个主题包括了一大批背景不同、形态各异的理论。阿尔罗若(C．E．Alchourron)、加德福斯(P．Gardenfors)和梅金森(D．Markinson)共同建立的信念修正理论(简称AGM理论)是其中形成比较早的、影响最大的理论。本文说明信念修正的基本概念,并且对AGM理论进行述评.     

Scientific Discovery on Positive Data via Belief Revision

A model of inductive inquiry is defined within a first-order context. Intuitively, the model pictures inquiry as a game between Nature and a scientist. To begin the game, a nonlogical vocabulary is agreed upon by the two players along with a partition of a class of structures for that vocabulary. Next, Nature secretly chooses one structure (the real world) from some cell of the partition. She then presents the scientist with a sequence of atomic facts about the chosen structure. With each new datum the scientist announces a guess about the cell to which the chosen structure belongs. To succeed in his inquiry, the scientist's successive conjectures must be correct all but finitely often, that is, the conjectures must converge in the limit to the correct cell. A special kind of scientist selects his hypotheses on the basis of a belief revision operator. We show that reliance on belief revision allows scientists to solve a wide class of problems.     

Local pragmatics in a Gricean framework

The pragmatic framework developed by H.P. Grice in “Logic and Conversation” explains how a speaker can mean something more than, or different from, the conventional meaning of the sentence she utters. But it has been argued that the framework cannot give a similar explanation for cases where these pragmatic effects impact the understood content of an embedded clause, such as the antecedent of a conditional, a clausal disjunct, or the clausal complement of a verb. In this paper, I show that such an explanation is available. One of the central arguments of the paper (Section 2) is that in a significant subset of cases, local pragmatic effects are a consequence of a global (utterance-level) pragmatic requirement. In these cases, local pragmatic effects are a consequence of ‘acting locally’ to resolve a potential global pragmatic violation. These cases do not require us to posit application of pragmatic principles (Maxims of Conversation) to the contents of embedded clauses. The account does, though, require the assumption that interpreters can identify and reason about the contents of unasserted sub-parts of sentences, an assumption that I motivate in section 3. Building on this, in section 4 of the paper, I argue that once we have recognized that interpreters can, and do, reason independently about the contents of non-asserted clauses, it becomes unproblematic to assume that in some cases, Gricean conversational principles do apply directly to these contents, providing an alternative route to account for local pragmatic effects. In revisiting the ideas of this paper in my response to the commentaries, I consider in more detail the revisions to Grice’s broader program that are necessitated by these moves, in particular acknowledging the problematicity of Grice’s notion of what is said. I argue that the starting point for Gricean reconstructions should instead be merely what is expressed, which carries no pragmatic commitments regarding what is speaker meant.     

A Single Counterexample Leads to Moral Belief Revision

What kind of evidence will lead people to revise their moral beliefs? Moral beliefs are often strongly held convictions, and existing research has shown that morality is rooted in emotion and socialization rather than deliberative reasoning. In addition, more general issues—such as confirmation bias—further impede coherent belief revision. Here, we explored a unique means for inducing belief revision. In two experiments, participants considered a moral dilemma in which an overwhelming majority of people judged that it was inappropriate to take action to maximize utility. Their judgments contradicted a utilitarian principle they otherwise strongly endorsed. Exposure to this scenario led participants to revise their belief in the utilitarian principle, and this revision persisted over several hours. This method provides a new avenue for inducing belief revision.     

Prior knowledge and subtyping effects in children's category learning

Two experiments examined how 5- and 10-year-old children revise their category representations when exposed to exemplars that are congruent or incongruent with existing knowledge. During training children were presented with exemplars containing features that were congruent or incongruent with children's social stereotypes together with a stereotype-neutral feature. In the knowledge-subtyping condition this neutral feature predicted the stereotype-congruence of the other features. In the knowledge-standard condition the neutral feature was uncorrelated with stereotype-congruence. At test children made judgements about feature co-occurrence within the learned category. In each experiment these judgements were influenced by both stereotypical beliefs and exemplar observation. Stereotypical beliefs, however, had a greater influence on co-occurrence judgements in the knowledge-subtyping than in the standard conditions. In Experiment 2 these effects were shown to generalize to judgements about features that were not presented during training. These results challenge current models of knowledge-based categorization by showing that exemplar structure determines whether novel exemplar features are incorporated into category representations.     

Temporal Interaction of Information and Belief

The temporal updating of an agent’s beliefs in response to a flow of information is modeled in a simple modal logic that, for every date t, contains a normal belief operator B _t and a non-normal information operator I _t which is analogous to the ‘only knowing’ operator discussed in the computer science literature. Soundness and completeness of the logic are proved and the relationship between the proposed logic, the AGM theory of belief revision and the notion of plausibility is discussed. A first draft of this paper was presented at the Workshop on Belief Change in Rational Agents: Perspectives from Artificial Intelligence, Philosophy and Economics, Dagstuhl (Germany), August 2005. Special Issue Formal Epistemology II. Edited by Branden Fitelson     

Dynamic doxastic logic: why,how, and where to?

We investigate the research programme of dynamic doxastic logic (DDL) and analyze its underlying methodology. The Ramsey test for conditionals is used to characterize the logical and philosophical differences between two paradigmatic systems, AGM and KGM, which we develop and compare axiomatically and semantically. The importance of Gärdenfors’s impossibility result on the Ramsey test is highlighted by a comparison with Arrow’s impossibility result on social choice. We end with an outlook on the prospects and the future of DDL.     

外表真实区别、表征变化和错误信念的任务分析

自20世纪80年代以来,“心理理论”已成为发展心理学的研究热点和最活跃、最多产的领域。为了分析和比较“心理理论”的实验任务,该研究以济南市3所幼儿园中的233名3—6岁儿童为有效被试。进行了“意外转移。和“欺骗外表”两种心理理论实验任务。得出如下主要结论：(1)意外转移任务中内隐错误信念显著难于标准错误信念,易化错误信念与标准错误信念的难度不存在显著差异。(2)欺骗外表任务中外表真实区别难度显著低于表征变化和错误信念。(3)意外转移任务的错误信念显著难于欺骗外表任务的错误信念。