SOME COMPLETENESS THEOREMS IN THE DYNAMIC DOXASTIC LOGIC OF ITERATED BELIEF REVISION

2010 ◽  
Vol 3 (2) ◽  
pp. 228-246 ◽  
Author(s):  
KRISTER SEGERBERG
Keyword(s):  
Belief Revision ◽  
Belief Change ◽  
Doxastic Logic ◽  
New Information ◽  
Incoming Information ◽  
Iterated Belief Revision ◽  
Dynamic Doxastic Logic ◽  
Completeness Theorems ◽  
Nested Beliefs

The success of the AGM paradigm—the theory of belief change initiated by Alchourrón, Gärdenfors, and Makinson—is remarkable, as even a quick look at the literature it has generated will testify. But it is also remarkable, at least in hindsight, how limited was the original effort. For example, the theory concerns the beliefs of just one agent; all incoming information is accepted; belief change is uniquely determined by the new information; there is no provision for nested beliefs. And perhaps most surprising: there is no analysis of iterated change.In this paper it is that last restriction that is at issue. Our medium of study is dynamic doxastic logic (DDL). The success of the AGM paradigm The particular contribution of the paper is detailed completeness proofs for three dynamic doxastic logics of iterated belief revision.The problem of extending the AGM paradigm to include iterated change has been discussed for years, but systematic discussions have appeared only recently (see Segerberg, 2007 and forthcoming, but also van Benthem, 2007; Rott, 2006; Zvesper, 2007).

scholarly journals A Semantics for Hyperintensional Belief Revision Based on Information Bases

Studia Logica ◽  
2021 ◽  
Author(s):  
Sena Bozdag
Keyword(s):  
Belief Revision ◽  
Epistemic Logic ◽  
Belief Change ◽  
Dynamic Epistemic Logic ◽  
Doxastic Logic ◽  
Dynamic Operation ◽  
Belief Dynamics ◽  
Dynamic Doxastic Logic ◽  
New Framework

AbstractI 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.

(DIS)BELIEF CHANGE AND ARGUED FEED-BACK DIALOG

2005 ◽  
Vol 13 (05) ◽  
pp. 511-538
Author(s):  
LAURENT PERRUSSEL ◽  
JEAN-MARC THÉVENIN
Keyword(s):  
Belief Revision ◽  
Belief Change ◽  
Preference Relation ◽  
Belief State ◽  
Temporal Aspects ◽  
Incoming Information ◽  
Multi Agent

This paper focuses on the features of belief change in a multi-agent context where agents consider beliefs and disbeliefs. Disbeliefs represent explicit ignorance and are useful to prevent agents to entail conclusions due to their ignorance. Agents receive messages holding information from other agents and change their belief state accordingly. An agent may refuse to adopt incoming information if it prefers its own (dis)beliefs. For this, each agent maintains a preference relation over its own beliefs and disbeliefs in order to decide if it accepts or rejects incoming information whenever inconsistencies occur. This preference relation may be built by considering several criteria such as the reliability of the sender of statements or temporal aspects. This process leads to non-prioritized belief revision. In this context we first present the * and − operators which allow an agent to revise, respectively contract, its belief state in a non-prioritized way when it receives an incoming belief, respectively disbelief. We show that these operators behave properly. Based on this we then illustrate how the receiver and the sender may argue when the incoming (dis)belief is refused. We describe pieces of dialog where (i) the sender tries to convince the receiver by sending arguments in favor of the original (dis)belief and (ii) the receiver justifies its refusal by sending arguments against the original (dis)belief. We show that the notion of acceptability of these arguments can be represented in a simple way by using the non-prioritized change operators * and −. The advantage of argumentation dialogs is twofold. First whenever arguments are acceptable the sender or the receiver reconsider its belief state; the main result is an improvement of the reconsidered belief state. Second the sender may not be aware of some sets of rules which act as constraints to reach a specific conclusion and discover them through argumentation dialogs.

A Weighted-Logic Representation of C-Revising Ordinal Conditional Functions

2020 ◽  
Vol 28 (04) ◽  
pp. 569-589
Author(s):  
Safia Laaziz ◽  
Younes Zeboudj ◽  
Salem Benferhat ◽  
Faiza Haned Khellaf
Keyword(s):  
Information System ◽  
Belief Revision ◽  
Belief Change ◽  
Possibility Theory ◽  
Knowledge Bases ◽  
Compact Representation ◽  
Natural Representation ◽  
Uncertainty Distribution ◽  
Semantic Level ◽  
New Information

The problem of belief change is considered as a major issue in managing the dynamics of an information system. It consists in modifying an uncertainty distribution, representing agents’ beliefs, in the light of a new information. In this paper, we focus on the so-called multiple iterated belief revision or C-revision, proposed for conditioning or revising uncertain distributions under uncertain inputs. Uncertainty distributions are represented in terms of ordinal conditional functions. We will use prioritized or weighted knowledge bases as a compact representation of uncertainty distributions. The input information leading to a revision of an uncertainty distribution is also represented by a set of consistent weighted formulas. This paper shows that C-revision, defined at a semantic level using ordinal conditional functions, has a very natural representation using weighted knowledge bases. We propose simple syntactic methods for revising weighted knowledge bases, that are semantically meaningful in the frameworks of possibility theory and ordinal conditional functions. In particular, we show that the space complexity of the proposed syntactic C-revision is linear with respect to the size of initial weighted knowledge bases.

scholarly journals Ranking kinematics for revising by contextual information

2021 ◽  
Author(s):  
Meliha Sezgin ◽  
Gabriele Kern-Isberner ◽  
Christoph Beierle
Keyword(s):  
Belief Revision ◽  
Belief Change ◽  
Contextual Information ◽  
Proof Of Concept ◽  
Ranking Functions ◽  
Ramsey Test ◽  
Local Contexts ◽  
Iterated Belief Revision ◽  
Probability Kinematics ◽  
Set Up

AbstractProbability kinematics is a leading paradigm in probabilistic belief change. It is based on the idea that conditional beliefs should be independent from changes of their antecedents’ probabilities. In this paper, we propose a re-interpretation of this paradigm for Spohn’s ranking functions which we call Generalized Ranking Kinematics as a new principle for iterated belief revision of ranking functions by sets of conditional beliefs with respect to their specific subcontext. By taking into account semantical independencies, we can reduce the complexity of the revision task to local contexts. We show that global belief revision can be set up from revisions on the local contexts via a merging operator. Furthermore, we formalize a variant of the Ramsey-Test based on the idea of local contexts which connects conditional and propositional revision in a straightforward way. We extend the belief change methodology of c-revisions to strategic c-revisions which will serve as a proof of concept.

scholarly journals Iterated Belief Base Revision: A Dynamic Epistemic Logic Approach

2019 ◽  
Vol 33 ◽  
pp. 3076-3083 ◽  
Author(s):  
Marlo Souza ◽  
Álvaro Moreira ◽  
Renata Vieira
Keyword(s):  
Belief Revision ◽  
Epistemic Logic ◽  
Belief Change ◽  
Dynamic Epistemic Logic ◽  
Belief State ◽  
Revision Operation ◽  
Belief Bases ◽  
Negative Results ◽  
Base Revision ◽  
Iterated Belief Revision

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 largely used to specify the agent’s belief state - whether representing the agent’s ‘explicit beliefs’ or as a computational model for her 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 and their counterpart in dynamic epistemic logic. This work investigates how priority graphs, a syntactic representation of preference relations deeply connected to prioritised bases, can be used to characterise belief change operators, focusing on well-known postulates of Iterated Belief Change. We provide syntactic representations of belief change operators in a dynamic context, as well as new negative results regarding the possibility of representing an iterated belief revision operation using transformations on priority graphs.

scholarly journals Iterated contraction of propositions and conditionals under the principle of conditional preservation

10.29007/3q8l ◽  
2018 ◽  
Author(s):  
Gabriele Kern-Isberner ◽  
Tanja Bock ◽  
Kai Sauerwald ◽  
Christoph Beierle
Keyword(s):  
Belief Revision ◽  
Belief Change ◽  
Ranking Function ◽  
Ranking Functions ◽  
Belief Contraction ◽  
Seminal Work ◽  
Iterated Belief Revision ◽  
Iterated Contraction

Research on iterated belief change has focussed mostly on belief revision, only few papers have addressed iterated belief contraction. Most prominently, Darwiche and Pearl published seminal work on iterated belief revision the leading paradigm of which is the so-called principle of conditional preservation. In this paper, we use this principle in a thoroughly axiomatized form to develop iterated belief contraction operators for Spohn's ranking functions. We show that it allows for setting up constructive approaches to tackling the problem of how to contract a ranking function by a proposition or a conditional, respectively, and that semantic principles can also be derived from it for the purely qualitative case.

A Semantic Approach to Non-prioritized Belief Revision

2020 ◽  
Author(s):  
Elise Perrotin ◽  
Fernando R Velázquez-Quesada
Keyword(s):  
Belief Revision ◽  
Belief Change ◽  
Current Model ◽  
General Setting ◽  
Semantic Approach ◽  
Incoming Information ◽  
The One ◽  
The Right ◽  
The Given ◽  
The Way

Abstract Belief revision is concerned with belief change fired by incoming information. Despite the variety of frameworks representing it, most revision policies share one crucial feature: incoming information outweighs current information and hence, in case of conflict, incoming information will prevail. However, if one is interested in representing the way actual humans revise their beliefs, one might not always want for the agent to blindly believe everything they are told. This manuscript presents a semantic approach to non-prioritized belief revision. It uses plausibility models for depicting an agent’s beliefs, and model operations for displaying the way beliefs change. The first proposal, semantically-based screened revision, compares the current model with the one the revision would yield, accepting or rejecting the incoming information depending on whether the ‘differences’ between these models go beyond a given threshold. The second proposal, semantically-based gradual revision, turns the binary decision of acceptance or rejection into a more general setting in which a revision always occurs, with the threshold used rather to choose ‘the right revision’ for the given input and model.

scholarly journals An Epistemological Study of Theory Change

2021 ◽  
Author(s):  
Theofanis Aravanis
Keyword(s):  
Belief Revision ◽  
Belief Change ◽  
Theory Change ◽  
Rational Belief ◽  
Dominant Model ◽  
Traditional Philosophy ◽  
New Information ◽  
Formal Framework ◽  
The Face ◽  
Main Shortcoming

Belief Revision is a well-established field of research that deals with how agents rationally change their minds in the face of new information. The milestone of Belief Revision is a general and versatile formal framework introduced by Alchourrón, Gärdenfors and Makinson, known as the AGM paradigm, which has been, to this date, the dominant model within the field. A main shortcoming of the AGM paradigm, as originally proposed, is its lack of any guidelines for relevant change. To remedy this weakness, Parikh proposed a relevance-sensitive axiom, which applies on splittable theories; i.e., theories that can be divided into syntax-disjoint compartments. The aim of this article is to provide an epistemological interpretation of the dynamics (revision) of splittable theories, from the perspective of Kuhn's inuential work on the evolution of scientific knowledge, through the consideration of principal belief-change scenarios. The whole study establishes a conceptual bridge between rational belief revision and traditional philosophy of science, which sheds light on the application of formal epistemological tools on the dynamics of knowledge.

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