Gricean Belief Change

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

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 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.     

Contraction: On the Decision-Theoretical Origins of Minimal Change and Entrenchment

We present a decision-theoretically motivated notion of contraction which, we claim, encodes the principles of minimal change and entrenchment. Contraction is seen as an operation whose goal is to minimize loses of informational value. The operation is also compatible with the principle that in contracting A one should preserve the sentences better entrenched than A (when the belief set contains A). Even when the principle of minimal change and the latter motivation for entrenchment figure prominently among the basic intuitions in the works of, among others, Quine and Ullian (1978), Levi (1980, 1991), Harman (1988) and Gärdenfors (1988), formal accounts of belief change (AGM, KM – see Gärdenfors (1988); Katsuno and Mendelzon (1991)) have abandoned both principles (see Rott (2000)). We argue for the principles and we show how to construct a contraction operation, which obeys both. An axiom system is proposed. We also prove that the decision-theoretic notion of contraction can be completely characterized in terms of the given axioms. Proving this type of completeness result is a well-known open problem in the field, whose solution requires employing both decision-theoretical techniques and logical methods recently used in belief change.     

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.     

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.     

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     

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     

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.     

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.     

Belief Revision,Rational Choice and the Unity of Reason

Hans Rott has argued, most recently in his book Change, Choice and Inference, that certain formal correspondences between belief revision and rational choice have important philosophical implications, claiming that the former strongly indicate the unity of practical and theoretical reason as well as the primacy of practical reason. In this paper, I confront Rott's argument with three serious challenges. My conclusion is that, while Rott's work is indisputable as a formal achievement, the philosophical consequences he wants to draw are not forthcoming. This revised version was published online in August 2006 with corrections to the Cover Date.     

Truth in Fiction,Impossible Worlds,and Belief Revision

We present a theory of truth in fiction that improves on Lewis's [1978] ‘Analysis 2’ in two ways. First, we expand Lewis's possible worlds apparatus by adding non-normal or impossible worlds. Second, we model truth in fiction as (make-believed) belief revision via ideas from dynamic epistemic logic. We explain the major objections raised against Lewis's original view and show that our theory overcomes them.     

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。     

大学生精神信仰的现状研究

本研究首次关注大学生的精神信仰,通过问卷对1100名大学生调查,发现大学生精神信仰存在如下特点：社会信仰占优势,其次依次为实用信仰和超自然信仰;民族主义、生命崇拜和国家主义位居前三位,宗教信仰、金钱崇拜和神灵崇拜位居后三位。     

3～6岁儿童信念理解能力的发展研究

研究设计了冲突真实信念任务,用于考察儿童对真实信念的理解;并利用区分信念、冲突真实信念和意外地点的错误信念任务,考察儿童理解信念推理基本规则、真实信念和错误信念的发展顺序。97名3~6岁儿童完成了测试。结果显示,3岁儿童能理解信念推理的基本规则,5岁儿童能理解真实信念,6岁儿童能理解错误信念。结果支持了儿童先理解真实信念,后理解错误信念的发展模式;也说明在理解信念以前儿童已能掌握信念推理的基本规则。     

Exploiting the Wisdom of Others to Make Better Decisions: Suspending Judgment Reduces Egocentrism and Increases Accuracy

Although decision makers often consult other people's opinions to improve their decisions, they fail to do so optimally. One main obstacle to incorporating others' opinions efficiently is one's own opinion. We theorize that decision makers could improve their performance by suspending their own judgment. In three studies, participants used others' opinions to estimate uncertain quantities (the caloric value of foods). In the full‐view condition, participants could form independent estimates prior to receiving others' opinions, whereas participants in the blindfold condition could not form prior opinions. We obtained an intriguing blindfold effect. In all studies, the blindfolded participants provided more accurate estimates than did the full‐view participants. Several policy‐capturing measures indicated that the advantage of the blindfolded participants was due to their unbiased weighting of others' opinions. The full‐view participants, in contrast, adhered to their prior opinion and thus failed to exploit the information contained in others' opinions. Moreover, in all three studies, the blindfolded participants were not cognizant of their advantage and expressed less confidence in their estimates than did the full‐view participants. The results are discussed in relation to theories of opinion revision and group decision making. Copyright © 2011 John Wiley & Sons, Ltd.