AGM Belief Revision Research Articles

Logic-based updating

We build on AGM belief revision (Alchourrón et al. (1985)) and propose a class of updating rules called pragmatic rules. Pragmatic updating applies to multiple priors and requires that the agent's posteriors be the subset of her priors under which the realized event occurs with probability 1, if such priors exist. We construct a propositional language based on qualitative probability and demonstrate the strong relation between belief updating rules and belief revision rules in this language. We show that an updating rule is consistent with AGM belief revision if and only if it is pragmatic. While maximum likelihood updating is pragmatic in general, full-Bayesian updating is not. We characterize maximum likelihood updating within the AGM framework, and show that full-Bayesian updating can be obtained by dropping one of AGM's postulates.

Difference-Making Conditionals and Connexivity

Today there is a wealth of fascinating studies of connexive logical systems. But sometimes it looks as if connexive logic is still in search of a convincing interpretation that explains in intuitive terms why the connexive principles should be valid. In this paper I argue that difference-making conditionals as presented in Rott (Review of Symbolic Logic 15, 2022) offer one principled way of interpreting connexive principles. From a philosophical point of view, the idea of difference-making demands full, unrestricted connexivity, because neither logical truths nor contradictions or other absurdities can ever ‘make a difference’ (i.e., be relevantly connected) to anything. However, difference-making conditionals have so far been only partially connexive. I show how the existing analysis of difference-making conditionals can be reshaped to obtain full connexivity. The classical AGM belief revision model is replaced by a conceivability-limited revision model that serves as the semantic base for the analysis. The key point of the latter is that the agent should never accept any absurdities.

Filtered Belief Revision: Syntax and Semantics

In an earlier paper [Rational choice and AGM belief revision, Artificial Intelligence, 2009] a correspondence was established between the set-theoretic structures of revealed-preference theory (developed in economics) and the syntactic belief revision functions of the AGM theory (developed in philosophy and computer science). In this paper we extend the re-interpretation of those structures in terms of one-shot belief revision by relating them to the trichotomous attitude towards information studied in Garapa (Rev Symb Logic, 1–21, 2020) where information may be either (1) fully accepted or (2) rejected or (3) taken seriously but not fully accepted. We begin by introducing the syntactic notion of filtered belief revision and providing a characterization of it in terms of a mixture of both AGM revision and contraction. We then establish a correspondence between the proposed notion of filtered belief revision and the above-mentioned set-theoretic structures, interpreted as semantic partial belief revision structures. We also provide an interpretation of the trichotomous attitude towards information in terms of the degree of implausibility of the information.

Paraconsistent Belief Revision: An Algebraic Investigation

This paper offers a logico-algebraic investigation of AGM belief revision based on the logic of paradox (LP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathrm {LP}$$\\end{document}). First, we define a concrete belief revision operator for LP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathrm {LP}$$\\end{document}, proving that it satisfies a generalised version of the traditional AGM postulates. Moreover, we investigate to what extent the Levi and Harper identities, in their classical formulation, can be applied to a paraconsistent account of revision. We show that a generalised Levi-type identity still yields paraconsistent-based revisions that are fully compatible with the AGM postulates. The main outcome is that, once the classical AGM framework is lifted up to an appropriate level of generality, it still appears as a regulative ideal for treating of paraconsistent-based epistemic operators.

Belief base change as priority change: A study based on dynamic epistemic logic

AGM's belief revision is one of the main paradigms in the study of belief change operations. In this context, belief bases (prioritised bases) have been primarily used to specify the agent's belief state. While the connection of iterated AGM-like operations and their encoding in dynamic epistemic logics have been studied before, few works considered how well-known postulates from iterated belief revision theory can be characterised by means of belief bases. Particularly, it has been shown that some postulates can be characterised through transformations in priority graphs, while others may not be represented that way. This work investigates the expressive power of prioritized bases, employing priority graphs as a representation for an agent's belief state and of transformations on such bases as representations for iterated relational belief change operators. As such, we propose a new representation for an agent's belief state, which we show can be used to characterize different iterated belief change postulates not previously representable using transformations on priority graphs.

Dynamic Preference Logic meets iterated belief change: Representation results and postulates characterization

AGM's belief revision is one of the main paradigms in the study of belief change operations. Recently, several logics for belief and information change have been proposed in the literature and used to encode belief change operations in rich and expressive semantic frameworks. While the connections of AGM-like operations and their encoding in dynamic doxastic logics have been studied before by the work of Segerberg, most works on the area of Dynamic Epistemic Logics (DEL) have not, to our knowledge, attempted to use those logics as tools to investigate mathematical properties of belief change operators. This work investigates how Dynamic Preference Logic, a logic in the DEL family, can be used to study properties of dynamic belief change operators, focusing on well-known postulates of iterated belief change.

PROBABILISTIC STABILITY, AGM REVISION OPERATORS AND MAXIMUM ENTROPY

AbstractSeveral authors have investigated the question of whether canonical logic-based accounts of belief revision, and especially the theory of AGM revision operators, are compatible with the dynamics of Bayesian conditioning. Here we show that Leitgeb’s stability rule for acceptance, which has been offered as a possible solution to the Lottery paradox, allows to bridge AGM revision and Bayesian update: using the stability rule, we prove that AGM revision operators emerge from Bayesian conditioning by an application of the principle of maximum entropy. In situations of information loss, or whenever the agent relies on a qualitative description of her information state—such as a plausibility ranking over hypotheses, or a belief set—the dynamics of AGM belief revision are compatible with Bayesian conditioning; indeed, through the maximum entropy principle, conditioning naturally generates AGM revision operators. This mitigates an impossibility theorem of Lin and Kelly for tracking Bayesian conditioning with AGM revision, and suggests an approach to the compatibility problem that highlights the information loss incurred by acceptance rules in passing from probabilistic to qualitative representations of belief.

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.

Filtered Belief Revision and Generalized Choice Structures

In an earlier paper [Rational choice and AGM belief revision, Artificial Intelligence, 2009] a correspondence was established between the choice structures of revealed-preference theory (developed in economics) and the syntactic belief revision functions of the AGM theory (developed in philosophy and computer science). In this paper we extend the re-interpretation of (a generalized notion of) choice structure in terms of belief revision by adding: (1) the possibility that an item of information'' might be discarded as not credible (thus dropping the AGM success axiom) and (2) the possibility that an item of information, while not accepted as fully credible, may still be taken seriously'' (we call such items of information allowable''). We establish a correspondence between generalized choice structures (GCS) and AGM belief revision; furthermore, we provide a syntactic characterization of the proposed notion of belief revision, which we call filtered belief revision.

Credible Information, Allowable Information and Belief Revision - Extended Abstract

In an earlier paper [Rational choice and AGM belief revision, Artificial Intelligence, 2009] a correspondence was established between the choice structures of revealed-preference theory (developed in economics) and the syntactic belief revision functions of the AGM theory (developed in philosophy and computer science). In this paper we extend the re-interpretation of (a generalized notion of) choice structure in terms of belief revision by adding: (1) the possibility that an item of "information" might be discarded as not credible (thus dropping the AGM success axiom) and (2) the possibility that an item of information, while not accepted as fully credible, may still be "taken seriously" (we call such items of information "allowable"). We establish a correspondence between generalized choice structures (GCS) and AGM belief revision; furthermore, we provide a syntactic analysis of the proposed notion of belief revision, which we call filtered belief revision.

Bayesian updating rules and AGM belief revision

We interpret the problem of updating beliefs as a choice problem (selecting a posterior from a set of admissible posteriors) with a reference point (prior). We use AGM belief revision to define the support of admissible posteriors after arrival of information, which applies also to zero probability events. We study two classes of updating rules for probabilities: 1) “lexicographic” updating rules where posteriors are given by a lexicographic probability system 2) “minimum distance” updating rules which select the posterior closest to the prior by some metric. We show that an updating rule is lexicographic if and only if it is Bayesian, AGM-consistent and satisfies a weak form of path independence. While not all lexicographic updating rules have a minimum distance representation, we study a sub-class of lexicographic rules, which we call “support-dependent” rules, which admit a minimum distance representation. Finally, we apply our approach to the problem of updating preferences.

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.

Judgment aggregation and minimal change: a model of consensus formation by belief revision

When a group of agents attempts to reach an agreement on certain issues, it is usually desirable that the resulting consensus be as close as possible to the original judgments of the individuals. However, when these judgments are logically connected to further beliefs, the notion of closeness should also take into account to what extent the individuals would have to revise their entire belief set to reach an agreement. In this work, we present a model for generation of agreement with respect to a given agenda which allows individual epistemic entrenchment to influence the value of the consensus. While the postulates for the transformation function and their construction resemble those of AGM belief revision, the notion of an agenda is adapted from the theory of judgment aggregation. This allows our model to connect both frameworks.

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.

Argument Revision

Understanding the dynamics of argumentation systems is a crucial component in the development of computational models of argument that are used as representations of belief. To that end, in this article, we introduce a model of Argument Revision, presented in terms of the contraction and revision of a system of structured argumentation. Argument Revision is influenced by the AGM model of belief revision, but with certain key differences. First, Argument Revision involves modifying the underlying model (system of argumentation) from which beliefs are derived, allowing for a finer-grained approach to modifying beliefs. Secondly, the richer structure provided by a system of argumentation permits a determination of minimal change based on quantifiable effects on the system as opposed to qualitative criteria such as entrenchment orderings. Argument Revision does, however, retain a close link to the AGM approach to belief revision. A basic set of postulates for rational revisions and contractions in Argument Revision is proposed; these postulates are influenced by, and capture the spirit of, those found in AGM belief revision. After specifying a determination of minimal change, based on measurable effects on the system, we conclude the article by going on to show how Argument Revision can be used as a strategic tool by a participant in a multi-agent dialogue, assisting with commitment retraction and dishonesty. In systems of argumentation that contain even small knowledge bases, it is difficult for a dialogue participant to fully assess the impact of seemingly trivial changes to that knowledge base, or other parts of the system; we demonstrate, by means of an example, that Argument Revision solves this problem through a determination of minimal change that is justifiable and intuitive.

Rethinking common belief, revision, and backward induction

Whether rationality and common belief in rationality jointly entail the backward inductive outcome in centipede games has long been debated. Stalnaker’s compelling negative argument appeals to the AGM belief revision postulates to argue that off-path moves may be rational, given the revisions they may prompt. I counter that the structure of common belief and the principles of AGM justify an additional assumption about revision. I then prove that, given my proposed constraint, for all finite, n-player, extensive form, perfect information games with a unique backward inductive solution, if there is initial common belief in rationality, then backward induction is guaranteed.

Revising beliefs on the basis of evidence

Approaches to belief revision most commonly deal with categorical information: an agent has a set of beliefs and the goal is to consistently incorporate a new item of information given by a formula. However, most information about the real world is not categorical. In revision, one may circumvent this fact by assuming that, in some fashion or other, an agent has elected to accept a formula ϕ, and the task of revision is to consistently incorporate ϕ into its belief corpus. Nonetheless, it is worth asking whether probabilistic information and noncategorical beliefs may be reconciled with, or even inform, approaches to revision. In this paper, one such account is presented. An agent receives uncertain information as input, and its probabilities on (a finite set of) possible worlds are updated via Bayesian conditioning. A set of formulas among the noncategorical beliefs is identified as the agent’s categorical belief set. The effect of this updating on the belief set is examined with respect to its appropriateness as a revision operator. We show that few of the classical AGM belief revision postulates are satisfied by this approach. Most significantly, though not surprisingly, the success postulate is not guaranteed to hold. However it does hold after a sufficient number of iterations. As well, it proves to be the case that in revising by a formula consistent with the agent’s beliefs, revision does not correspond to expansion. Postulates for iterated revision also examined, and it proves to be the case that most such postulates also do not hold. On the other hand, limiting cases of the presented approach correspond to specific approaches to revision that have appeared in the literature.

Belief Change in Branching Time: AGM-consistency and Iterated Revision

We study belief change in the branching-time structures introduced in Bonanno (Artif Intell 171:144–160, 2007). First, we identify a property of branching-time frames that is equivalent (when the set of states is finite) to AGM-consistency, which is defined as follows. A frame is AGM-consistent if the partial belief revision function associated with an arbitrary state-instant pair and an arbitrary model based on that frame can be extended to a full belief revision function that satisfies the AGM postulates. Second, we provide a set of modal axioms that characterize the class of AGM-consistent frames within the modal logic introduced in Bonanno (Artif Intell 171:144–160, 2007). Third, we introduce a generalization of AGM belief revision functions that allows a clear statement of principles of iterated belief revision and discuss iterated revision both semantically and syntactically.

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.