Probabilistic dynamic belief revision [Journal Paper] (original) (raw)

Probabilistic Dynamic Belief Revision

2007

We investigate the discrete (finite) case of the Popper-Renyi theory of conditional probability, introducing discrete conditional probabilis-tic models for knowledge and conditional belief, and comparing them with the more standard plausibility models. We also consider a related notion, that of safe belief, which is a weak (non-negatively introspective) type of " knowledge ". We develop a probabilistic version of this concept (" degree of safety ") and we analyze its role in games. We completely axiomatize the logic of conditional belief, knowledge and safe belief over conditional probabilistic models. We develop a theory of probabilistic dynamic belief revision, introducing " action models " and a notion of probabilistic update product, that comes together with appropriate reduction laws.

From conditional probability to the logic of doxastic actions

2007

We investigate the discrete (finite) case of the Popper-Renyi theory of conditional probability, introducing discrete conditional probabilistic models for (multi-agent) knowledge and conditional belief, and comparing them with the more standard plausibility models. We also consider a related notion, that of safe belief, which is a weak (non-negatively introspective) type of “knowledge”, and we analyze its role in games. We completely axiomatize the logic of conditional belief, knowledge and safe belief. We develop a theory of dynamic belief revision over probabilistic models, by introducing “action models” and a notion of update, and showing how various belief-revisions policies considered in the literature, as well as various forms of communication and other belief-changing events, can be represented in this setting. We give a complete and decidable set of axioms for a qualitative dynamic logic of belief-revising actions over probabilistic models.

Dynamic Logics of Belief Change

2015

This chapter gives an overview of current dynamic logics that describe belief update and revision, both for single agents and in multi-agent settings. We employ a mixture of ideas from AGM belief revision theory and dynamic-epistemic logics of information-driven agency. After describing the basic background, we review logics of various kinds of beliefs based on plausibility models, and then go on to various sorts of belief change engendered by changes in current models through hard and soft information. We present matching complete logics with dynamic-epistemic recursion axioms, and develop a very general perspective on belief change by the use of event models and priority update. The chapter continues with three topics that naturally complement the setting of single steps of belief change: connections with probabilistic approaches to belief change, long-term temporal process structure including links with formal learning theory, and multi-agent scenarios of information flow and belief revision in games and social networks. We end with a discussion of alternative approaches, further directions, and windows to the broader literature, while links with relevant philosophical traditions are discussed throughout.

Heirarchies of Beliefs and Interactive Epistemology in Dynamic Games

Game Theory in the Tradition of Bob …, 2002

We show h o w to extend the construction of in nite hierachies of beliefs Zamir 1985, Brandenburger and from the case of probability measures to the case of conditional probability systems CPSs de ned with respect to a xed collection of relevant h ypotheses. The set of hierarchies of CPSs satisfying common certainty of coherency conditional on every relevant h ypothesis corresponds to a universal type space. This construction provides a uni ed framework to analyze the epistemic foundations of solution concepts for dynamic games. As an illustration, we derive some results about conditional common certainty of rationality and rationalizability i n m ultistage games with observed actions.

Dynamic Belief Revision over Multi-Agent Plausibility Models

2006

In this paper, we develop a notion of doxastic actions, general enough to cover all examples of communication actions and most other belief-changing actions encountered in the literature, but also flexible enough to deal with the issue of (static and dynamic) revision of beliefs. This can be seen as a natural extension of the work in [3, 4] on “epistemic actions”, incorporating ideas from the semantics of belief revision and of conditional belief, along the lines pioneered in [2] and [11], but using the conditional belief approach adopted in [22, 10, 9] and adapted in [25] to the context of dynamic belief revision.

On the revision of probabilistic belief states

1995

Abstract In this paper we describe two approaches to the revision of probability functions. We assume that a probabilistic state of belief is captured by a counterfactual probability or Popper function, the revision of which determines a new Popper function. We describe methods whereby the original function determines the nature of the revised function. The first is based on a probabilistic extension of Spohn's OCFs, whereas the second exploits the structure implicit in the Popper function itself.

The Algebra of Multi-Agent Dynamic Belief Revision

Electronic Notes in Theoretical Computer Science, 2006

We refine our algebraic axiomatization in of epistemic actions and epistemic update (notions defined in using Kripke-style semantics), to incorporate a mechanism for dynamic belief revision in a multi-agent setting. We encode revision as a particular form of epistemic update, as a result of which we can revise with epistemic propositions as well as facts, we can also revise theories about actions as well as about states of the worlds, and we can do multi-agent belief revision. We show how our setting can be applied to a cheating version of the muddy children puzzle where by using this logic, after the cheating happens, honest children will not get contradictory beliefs.

The Logic of Conditional Doxastic Actions: A theory of dynamic multi-agent belief revision

2000

be Abstract. We present a logic of conditional doxastic actions, obtained by incorporating ideas from belief revision theory into the usual dynamic logic of epistemic actions. We do this by extending to actions the setting of epistemic plausibility models , developed in Baltag and Smets (2006) for representing (static) conditional beliefs. We introduce a natural extension of the notion of