A Qualitative Theory of Dynamic Interactive Belief Revision (original) (raw)

Dynamic logic for belief revision

Journal of Applied Non-Classical Logics, 2007

We show how belief revision can be treated systematically in the format of dynamicepistemic logic, when operators of conditional belief are added. The core engine consists of definable update rules for changing plausibility relations between worlds, which have been proposed independently in the dynamic-epistemic literature on preference change. Our analysis yields two new types of modal result. First, we obtain complete logics for concrete mechanisms of belief revision, based on compositional reduction axioms. Next, we show how various abstract postulates for belief revision can be analyzed by standard modal frame correspondences for model-changing operations.

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.

Conditional Doxastic Models: A Qualitative Approach to Dynamic Belief Revision

Electronic Notes in Theoretical Computer Science, 2006

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.

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

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.

A simple modal logic for belief revision : Extended Abstract

2005

The notions of static belief and of belief revision have been extensively studied in the literature. However, there is a surprising lack of uniformity in the two approaches. In the philosophy and logic literature the notion of static belief has been studied mainly within the context of modal logic. On the syntactic side a belief operator B is introduced, with the intended interpretation of B as “the individual believes that ”. Various properties of beliefs are then expressed by means of axioms, such as the positive introspection axiom B ! BB , which says that if the individual believes then she believes that she believes . On the semantic side Kripke structures are used, consisting of a set of states (or possible worlds) together with a binary relation B on , with the interpretation of B as “at state the individual considers state possible”. The connection between syntax and semantics is then obtained by means of a valuation V which associates with every atomic sentence p the set of...

A Semantics for Hyperintensional Belief Revision Based on Information Bases

Studia Logica, 2021

I propose a novel hyperintensional semantics for belief revision and a corresponding system of dynamic doxastic logic. The main goal of the framework is to reduce some of the idealisations that are common in the belief revision literature and in dynamic epistemic logic. The models of the new framework are primarily based on potentially incomplete or inconsistent collections of information, represented by situations in a situation space. I propose that by shifting the representational focus of doxastic models from belief sets to collections of information, and by defining changes of beliefs as artifacts of changes of information, we can achieve a more realistic account of belief representation and belief change. The proposed dynamic operation suggests a non-classical way of changing beliefs: belief revision occurs in non-explosive environments which allow for a non-monotonic and hyperintensional belief dynamics. A logic that is sound with respect to the semantics is also provided.

Dynamic Hyperintensional Belief Revision - Review of Symbolic Logic

Review of Symbolic Logic, 2020

We 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.

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.

A Simple Modal Logic for Belief Revision

Synthese, 2005

We propose a modal logic based on three operators, representing intial beliefs, information and revised beliefs. Three simple axioms are used to provide a sound and complete axiomatization of the qualitative part of Bayes' rule. Some theorems of this logic are derived concerning the interaction between current beliefs and future beliefs. Information flows and iterated revision are also discussed.