AGM Theory Of Belief Revision Research Articles

DYNAMIC HYPERINTENSIONAL BELIEF REVISION

AbstractWe propose a dynamic hyperintensional logic of belief revision for non-omniscient agents, reducing the logical omniscience phenomena affecting standard doxastic/epistemic logic as well as AGM belief revision theory. Our agents don’t know all a priori truths; their belief states are not closed under classical logical consequence; and their belief update policies are such that logically or necessarily equivalent contents can lead to different revisions. We model both plain and conditional belief, then focus on dynamic belief revision. The key idea we exploit to achieve non-omniscience focuses on topic- or subject matter-sensitivity: a feature of belief states which is gaining growing attention in the recent literature.

Theory Choice, Theory Change, and Inductive Truth-Conduciveness

(I) Synchronic norms of theory choice, a traditional concern in scientific methodology, restrict the theories one can choose in light of given information. (II) Diachronic norms of theory change, as studied in belief revision, restrict how one should change one’s current beliefs in light of new information. (III) Learning norms concern how best to arrive at true beliefs. In this paper, we undertake to forge some rigorous logical relations between the three topics. Concerning (III), we explicate inductive truth conduciveness in terms of optimally direct convergence to the truth, where optimal directness is explicated in terms of reversals and cycles of opinion prior to convergence. Concerning (I), we explicate Ockham’s razor and related principles of choice in terms of the information topology of the empirical problem context and show that the principles are necessary for reversal or cycle optimal convergence to the truth. Concerning (II), we weaken the standard principles of agm belief revision theory in intuitive ways that are also necessary (and in some cases, sufficient) for reversal or cycle optimal convergence. Then we show that some of our weakened principles of change entail corresponding principles of choice, completing the triangle of relations between (I), (II), and (III).

Simple Hyperintensional Belief Revision

I present a possible worlds semantics for a hyperintensional belief revision operator, which reduces the logical idealization of cognitive agents affecting similar operators in doxastic and epistemic logics, as well as in standard AGM belief revision theory. (Revised) belief states are not closed under classical logical consequence; revising by inconsistent information does not perforce lead to trivialization; and revision can be subject to ‘framing effects’: logically or necessarily equivalent contents can lead to different revisions. Such results are obtained without resorting to non-classical logics, or to non-normal or impossible worlds semantics. The framework combines, instead, a standard semantics for propositional S5 with a simple mereology of contents.

Unanimous Consensus Against AGM?

Given the role consensus is supposed to play in the social aspects of inquiry and deliberation, it is important that we may always identify a consensus as the basis of joint inquiry and deliberation. However, it turns out that if we think of an agent revising her beliefs to reach a consensus, then, on the received view of belief revision, AGM belief revision theory, certain simple and compelling consensus positions are not always available.

Supporters and Underminers: Reply to Chandler

I argue that two of the standard axioms of the AGM theory of belief revision stand in the way of it serving as the basis for an adequate account of defeasible reasoning, because they respectively disallow the adoption of beliefs not logically entailed by those previously learned and the abandonment of those not contradicted by them.

A non-linear dynamical approach to belief revision in cognitive behavioral therapy.

Belief revision is the key change mechanism underlying the psychological intervention known as cognitive behavioral therapy (CBT). It both motivates and reinforces new behavior. In this review we analyze and apply a novel approach to this process based on AGM theory of belief revision, named after its proponents, Carlos Alchourrón, Peter Gärdenfors and David Makinson. AGM is a set-theoretical model. We reconceptualize it as describing a non-linear, dynamical system that occurs within a semantic space, which can be represented as a phase plane comprising all of the brain's attentional, cognitive, affective and physiological resources. Triggering events, such as anxiety-producing or depressing situations in the real world, or their imaginal equivalents, mobilize these assets so they converge on an equilibrium point. A preference function then evaluates and integrates evidentiary data associated with individual beliefs, selecting some of them and comprising them into a belief set, which is a metastable state. Belief sets evolve in time from one metastable state to another. In the phase space, this evolution creates a heteroclinic channel. AGM regulates this process and characterizes the outcome at each equilibrium point. Its objective is to define the necessary and sufficient conditions for belief revision by simultaneously minimizing the set of new beliefs that have to be adopted, and the set of old beliefs that have to be discarded or reformulated. Using AGM, belief revision can be modeled using three (and only three) fundamental syntactical operations performed on belief sets, which are expansion; revision; and contraction. Expansion is like adding a new belief without changing any old ones. Revision is like adding a new belief and changing old, inconsistent ones. Contraction is like changing an old belief without adding any new ones. We provide operationalized examples of this process in action.

Belief Revision II: Ranking Theory

AbstractBelief revision theory studies how an ideal doxastic agent should revise her beliefs when she receives new information. In part I, I have first presented the AGM theory of belief revision. Then I have focused on the problem of iterated belief revisions. In part II, I will first present ranking theory (Spohn 1988). Then I will show how it solves the problem of iterated belief revisions. I will conclude by sketching two areas of future research.

Belief Revision I: The AGM Theory

AbstractBelief revision theory studies how an ideal doxastic agent should revise her beliefs when she receives new information. In part I I will first present the AGM theory of belief revision (Alchourrón & Gärdenfors & Makinson 1985). Then I will focus on the problem of iterated belief revisions.

On AGM for Non-Classical Logics

The AGM theory of belief revision provides a formal framework to represent the dynamics of epistemic states. In this framework, the beliefs of the agent are usually represented as logical formulas while the change operations are constrained by rationality postulates. In the original proposal, the logic underlying the reasoning was supposed to be supraclassical, among other properties. In this paper, we present some of the existing work in adapting the AGM theory for non-classical logics and discuss their interconnections and what is still missing for each approach.

Private announcement and belief expansion: an internal perspective

AGM belief revision theory and the BMS framework of dynamic epistemic logic both deal with the formalization of belief change, the former in a single-agent setting and the latter in a multi-agent setting. In this article, we study the relation between these two formalisms.To be fair,we restrict our attention to the AGM operation of expansion since the original BMS framework does not allow for belief revision. The generalization of the AGM operation of revision to the multi-agent setting is dealt with in the companion paper [Aucher (2010, Logic Journal of the IGPL, 18, 530–558)]. Besides, because AGM theory follows the internal approach, instead of the original BMS framework we define and deal with its internal version. This allows us to show that the AGM operation of expansion can naturally be viewed in the multi-agent setting of the BMS framework as the operation of private announcement, which goes against the claims of [van Ditmarsch, van der Hoek and Kooi (2004, Advances in Modal Logic, 335–346)]. In parallel, we also provide conditions under which seriality of accessibility relations is preserved during an update, in the BMS framework as well as its internal version: it is a preliminary step towards the introduction of revision mechanisms into these frameworks.

Generalizing AGM to a multi-agent setting

We generalize AGM belief revision theory to the multi-agent case. To do so, we first generalize the semantics of the single-agent case, based on the notion of interpretation, to the multi-agent case. Then we show that, thanks to the shape of our new semantics, all the results of the AGM framework transfer. Afterwards we investigate some postulates that are specific to our multi-agent setting. Finally, we give an example of revision operator that fulfills one of these new postulates and give an example of revision on a concrete example.

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.

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.

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.

Conditional Doxastic Models: A Qualitative Approach to Dynamic Belief Revision

In this paper, we present a semantical approach to multi-agent belief revision and belief update. For this, we introduce relational structures called conditional doxastic models (CDM's, for short). We show this setting to be equivalent to an epistemic version of the classical AGM Belief Revision theory. We present a logic of conditional beliefs that is complete w.r.t. CDM's. Moving then to belief updates (sometimes called “dynamic” belief revision) induced by epistemic actions, we consider two particular cases: public announcements and private announcements to subgroups of agents. We show how the standard semantics for these types of updates can be appropriately modified in order to apply it to CDM's, thus incorporating belief revision into our notion of update. We provide a complete axiomatization of the corresponding dynamic doxastic logics. As an application, we solve a “cheating version” of the Muddy Children Puzzle.

Structured Clusters: A Framework to Reason with Contradictory Interests

This paper presents a framework in which priorities in a belief base can be specified and used in the resolution of conflicts. Priorities are given in terms of a partial pre-order associated with the sentences in the base. When the new information is given the highest priority, it is accepted, thus complying with the success postulate of the AGM theory of belief revision. However, in general, priorities can be specified in a very flexible way and an input sentence placed anywhere in the previous ordering. The result or conclusion of a belief base can be computed into a sentence, allowing the method to be used in the reasoning of more complex structures where nodes in the structure are themselves prioritized bases. Embedded groups of prioritized bases are recursively resolved before the embedding structure is. The method combines reasoning about inconsistency and priorities in an elegant way.

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.

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.

Providing foundations for coherentism

We prove that four theses commonly associated with coherentism are incompatible with the representation of a belief state as a logically closed set of sentences. The result is applied to the conventional coherence interpretation of the AGM theory of belief revision, which appears not to be tenable. Our argument also counts against the coherentistic acceptability of a certain form of propositional holism. We argue that the problems arise as an effect of ignoring the distinction between derived and non-derived beliefs, and we suggest that the kind of coherence relevant to epistemic justification is the coherence of non-derived beliefs.