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.     

A Paraconsistent Theory Of Belief Revision

This paper presents a theory of belief revision that allows people to come tobelieve in contradictions. The AGM theory of belief revision takes revision,in part, to be consistency maintenance. The present theory replacesconsistency with a weaker property called coherence. In addition to herbelief set, we take a set of statements that she rejects. These two sets arecoherent if they do not overlap. On this theory, belief revision maintains coherence.     

The Stability Theory of Knowledge and Belief Revision: Comments on Rott

In this commentary on Rotts paper Stability, Strength and Sensitivity: Converting Belief into Knowledge, I discuss two problems of the stability theory of knowledge which are pointed out by Rott. I conclude that these problems offer no reason for rejecting the stability theory, but might be grounds for deviating from the standard AGM account of belief revision which Rott presupposes.     

Symmetry and Belief Revision

This paper continues the recent tradition of investigating iterated AGM revision by reasoning directly about the dynamics for total pre-order (“implausibility ordering”) representations of AGM revision functions. We reorient discussion, however, by proving that symmetry considerations, almost by themselves, suffice to determine a particular, AGM-friendly implausibility ordering dynamics due to Spohn 1988, which we call “J-revision”. After exploring the connections between implausibility ordering dynamics and the social choice theory of Arrow 1963, we provide symmetry arguments in the social choice-theoretic framework for an interesting generalization of J-revision due to Nayak 1994. We conclude by arguing that the symmetry principles that uniquely favor J-revision and its generalizations are importantly expressive of the purely qualitative framework for representing beliefs that distinguishes the AGM program. Our results therefore comprehensively vindicate Spohn's 1988 conjecture that essentially J-revision is the best that can be done by way of a purely qualitative model of belief revision. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mighty Belief Revision

Journal of Philosophical Logic - Belief revision theories standardly endorse a principle of intensionality to the effect that ideal doxastic agents do not discriminate between pieces of information...     

Iterated Belief Revision

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.

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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.     

Moore's Paradox and Akratic Belief

G.E. Moore noticed the oddity of statements like: “It's raining, but I don't believe it.” This oddity is often seen as analogous to the oddity of believing akratically, or believing what one believes one should not believe, and has been appealed to in denying the possibility of akratic belief. I describe a Belief Akratic's Paradox, analogous to Moore's paradox and centered on sentences such as: “I believe it's raining, but I shouldn't believe it.” I then defend the possibility of akratic belief against appeals to this analogy, arguing both that akratic belief does not require belief‐akratic‐paradoxical belief, and that the latter is importantly different from Moorean belief. I conclude by considering the implications of these arguments for an understanding of both Moorean and akratic belief.     

Revocable Belief Revision

Krister Segerberg proposed irrevocable belief revision, to be contrasted with standard belief revision, in a setting wherein belief of propositional formulas is modelled explicitly. This suggests that in standard belief revision is revocable: one should be able to unmake (‘revoke’) the fresh belief in the revision formula, given yet further information that contradicts it. In a dynamic epistemic logical setting for belief revision, for multiple agents, we investigate what the requirements are for revocable belief revision. By this we not merely mean recovering belief in non-modal propositions, as in the recovery principle for belief contraction, but recovering belief in modal propositions: beliefs about beliefs. These requirements are almost never met, a surprising result.     

The Modal Logic of Bayesian Belief Revision

In Bayesian belief revision a Bayesian agent revises his prior belief by conditionalizing the prior on some evidence using Bayes’ rule. We define a hierarchy of modal logics that capture the logical features of Bayesian belief revision. Elements in the hierarchy are distinguished by the cardinality of the set of elementary propositions on which the agent’s prior is defined. Inclusions among the modal logics in the hierarchy are determined. By linking the modal logics in the hierarchy to the strongest modal companion of Medvedev’s logic of finite problems it is shown that the modal logic of belief revision determined by probabilities on a finite set of elementary propositions is not finitely axiomatizable.

     

Truth-Tracking by Belief Revision

Studia Logica - We study the learning power of iterated belief revision methods. Successful learning is understood as convergence to correct, i.e., true, beliefs. We focus on the issue of...     

Resource Bounded Belief Revision

The AGM paradigm for belief revision provides a very elegant and powerful framework for reasoning about idealized agents. The paradigm assumes that the modeled agent is a perfect reasoner with infinite memory. In this paper we propose a framework to reason about non-ideal agents that generalizes the AGM paradigm. We first introduce a structure to represent an agent's belief states that distinguishes different status of beliefs according to whether or not they are explicitly represented, whether they are currently active and whether they are fully accepted or provisional. Then we define a set of basic operations that change the status of beliefs and show how these operations can be used to model agents with different capacities. We also show how different operations of belief change described in the literature can be seen as special cases of our theory.     

Belief Revision And Epistemology

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.     

Moore's Paradox And Self-Ascribed Belief

Moore's paradox arises from the logicaloddity of sentences of the form`P and I do not believe that P'or `P and I believe that not-P'. Thiskind of sentence is logically peculiarbecause it is absurd to assert it, although it isnot a logical contradiction. In this paperI offer a new proposal. I argue that Moore's paradox arises because there is a defaultprocedure for evaluating a self-ascribed belief sentence and one is presumptivelyjustified in believing that one believes a sentence when one sincerely assents to it.     

逻辑心理主义：一种信念修正的视角

以穆勒为代表的逻辑心理主义与以弗雷格为代表的反心理主义之间的争论由来已久。逻辑心理主义认为,逻辑是心理学的一部分或是其分支,具有描述性;反心理主义则认为,应当把心理的东西从逻辑中剔除,逻辑只是规范性的。信念修正理论虽具有规范性特质,但是当信念状态层级从低层级走向高层级时,其规范性解释力度则会降低,这表明信念状态的改变会受到经验描述的影响,信念修正理论研究有从规范性走向描述性的层级区分。信念修正理论一定程度上能为弱逻辑心理主义在逻辑中的合法性提供支持,并将心理主义与反心理主义聚焦在人即主体上。     

Iterated Belief Revision and Conditional Logic

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.     

Contraction in Interrogative Belief Revision

In the paper “On the role of the research agenda in epistemic change”, Olsson and Westlund have suggested that the notion of epistemic state employed in the standard framework of belief revision (Alchourrón et al. 1985; G?rdenfors 1988) should be extended to include a representation of the agent’s research agenda (Olsson and Westlund 2006). The resulting framework will here be referred to as interrogative belief revision. In this paper, I attempt to deal with the problem of how research agendas should change in contraction, a problem largely left open by Olsson and Westlund. Two desiderata of an appropriate solution are suggested: one is a principle of continuity, stating that changes in the research agenda should somehow reflect that certain long term research interests are kept fixed. The other desideratum, which is based on part of Olsson and Westlund’s motivation for adding research agendas to the epistemic states, is that we should be able to account for how contraction may serve to open up new, fruitful hypotheses for investigation. In order to achieve these desiderata, I base my solution on a revised version of Olsson and Westlund’s notion of epistemic state.     

Moore's Paradox and the Structure of Conscious Belief

Propositions such as are paradoxical, in that even though they can be true, they cannot be truly asserted or believed. This is Moore's paradox. Sydney Shoemaker has recently argued that the paradox arises from a constitutive relation that holds between first- and second-order beliefs. This paper explores this approach to the paradox. Although Shoemaker's own account of the paradox is rejected, a different account along similar lines is endorsed. At the core of the endorsed account is the claim that conscious beliefs are always partly about themselves; it will be shown to follow from this that conscious beliefs in Moorean propositions are self-contradictory.     

A Survey of non-Prioritized Belief Revision

This paper summarizes and systematizes recent and ongoing work on non-prioritized belief change, i.e., belief revision in which the new information has no special priority due to its novelty.