On uniform belief revision

2020 ◽  
Vol 30 (7) ◽  
pp. 1357-1376
Author(s):  
Theofanis Aravanis
Keyword(s):  
Present Article ◽  
Belief Revision ◽  
Possible Worlds ◽  
Belief Change ◽  
Rational Belief ◽  
Iterated Revision ◽  
Interesting Class ◽  
Total Preorder ◽  
Revision Function

Abstract Rational belief-change policies are encoded in the so-called AGM revision functions, defined in the prominent work of Alchourrón, Gärdenfors and Makinson. The present article studies an interesting class of well-behaved AGM revision functions, called herein uniform-revision operators (or UR operators, for short). Each UR operator is uniquely defined by means of a single total preorder over all possible worlds, a fact that in turn entails a significantly lower representational cost, relative to an arbitrary AGM revision function, and an embedded solution to the iterated-revision problem, at no extra representational cost. Herein, we first demonstrate how weaker, more expressive—yet, more representationally expensive—types of uniform revision can be defined. Furthermore, we prove that UR operators, essentially, generalize a significant type of belief change, namely, parametrized-difference revision. Lastly, we show that they are (to some extent) relevance-sensitive, as well as that they respect the so-called principle of kinetic consistency.

scholarly journals Incompatibilities Between Iterated and Relevance-Sensitive Belief Revision

2020 ◽  
Vol 69 ◽  
pp. 85-108
Author(s):  
Theofanis Aravanis ◽  
Pavlos Peppas ◽  
Mary-Anne Williams
Keyword(s):  
Belief Revision ◽  
Belief Change ◽  
Strong Sense ◽  
Revision Process ◽  
Entire Class ◽  
Iterated Revision ◽  
Formal Framework ◽  
Knowledge Dynamics

The AGM paradigm for belief change, as originally introduced by Alchourron, Gärdenfors and Makinson, lacks any guidelines for the process of iterated revision. One of the most influential work addressing this problem is Darwiche and Pearl's approach (DP approach, for short), which, despite its well-documented shortcomings, remains to this date the most dominant. In this article, we make further observations on the DP approach. In particular, we prove that the DP postulates are, in a strong sense, inconsistent with Parikh's relevance-sensitive axiom (P), extending previous initial conflicts. Immediate consequences of this result are that an entire class of intuitive revision operators, which includes Dalal's operator, violates the DP postulates, as well as that the Independence postulate and Spohn's conditionalization are inconsistent with axiom (P). The whole study, essentially, indicates that two fundamental aspects of the revision process, namely, iteration and relevance, are in deep conflict, and opens the discussion for a potential reconciliation towards a comprehensive formal framework for knowledge dynamics.

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.

(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.

scholarly journals Modeling Belief in Dynamic Systems, Part II: Revision and Update

1999 ◽  
Vol 10 ◽  
pp. 117-167 ◽  
Author(s):  
N. Friedman ◽  
J. Y. Halpern
Keyword(s):  
Artificial Intelligence ◽  
Belief Revision ◽  
Dynamic Systems ◽  
Belief Change ◽  
Companion Paper ◽  
Minimal Change ◽  
Special Cases ◽  
Epistemic Modalities ◽  
Over Time ◽  
New Framework

The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. In a companion paper (Friedman & Halpern, 1997), we introduce a new framework to model belief change. This framework combines temporal and epistemic modalities with a notion of plausibility, allowing us to examine the change of beliefs over time. In this paper, we show how belief revision and belief update can be captured in our framework. This allows us to compare the assumptions made by each method, and to better understand the principles underlying them. In particular, it shows that Katsuno and Mendelzon's notion of belief update (Katsuno & Mendelzon, 1991a) depends on several strong assumptions that may limit its applicability in artificial intelligence. Finally, our analysis allow us to identify a notion of minimal change that underlies a broad range of belief change operations including revision and update.

scholarly journals Revision and Conditional Inference for Abstract Dialectical Frameworks

2021 ◽  
Author(s):  
Jesse Heyninck ◽  
Gabriele Kern-Isberner ◽  
Tjitze Rienstra ◽  
Kenneth Skiba ◽  
Matthias Thimm
Keyword(s):  
Belief Revision ◽  
Research Topic ◽  
Conditional Inference ◽  
Ramsey Test ◽  
The One ◽  
Exact Relationship ◽  
Nonmonotonic Inference ◽  
Total Preorder

For propositional beliefs, there are well-established connections between belief revision, defeasible conditionals and nonmonotonic inference. In argumentative contexts, such connections have not yet been investigated. On the one hand, the exact relationship between formal argumentation and nonmonotonic inference relations is a research topic that keeps on eluding researchers despite recently intensified efforts, whereas argumentative revision has been studied in numerous works during recent years. In this paper, we show that similar relationships between belief revision, defeasible conditionals and nonmonotonic inference hold in argumentative contexts as well. We first define revision operators for abstract dialectical frameworks, and use such revision operators to define dynamic conditionals by means of the Ramsey test. We show that such conditionals can be equivalently defined using a total preorder over three-valued interpretations, and study the inferential behaviour of the resulting conditional inference relations.

A study of possible-worlds semantics of relevance-sensitive belief revision

2020 ◽  
Vol 30 (5) ◽  
pp. 1125-1142
Author(s):  
Theofanis Aravanis ◽  
Pavlos Peppas ◽  
Mary-Anne Williams
Keyword(s):  
Belief Revision ◽  
Possible Worlds ◽  
Strong Version ◽  
Possible Worlds Semantics ◽  
Significant Drop ◽  
Natural Connection ◽  
Global And Local ◽  
Shed Light

Abstract Parikh’s relevance-sensitive axiom (P) for belief revision is open to two different interpretations, i.e. the weak and the strong version of (P), both of which are plausible depending on the context. Given that strong (P) has not received the attention it deserves, in this article, an extended examination of it is conducted. In particular, we point out interesting properties of the semantic characterization of the strong version of (P), as well as a vital feature of it that, potentially, results in a significant drop on the resources required for an implementation of a belief-revision system. Lastly, we shed light on the natural connection between global and local revision functions, via their corresponding semantic characterization, hence, a means for constructing global revision functions from local ones, and vice versa, is provided.

Book Review: Neil Tennant, Changes of Mind: An Essay on Rational Belief Revision

Studia Logica ◽  
2015 ◽  
Vol 103 (1) ◽  
pp. 227-231
Author(s):  
Nina Gierasimczuk
Keyword(s):  
Belief Revision ◽  
Rational Belief

scholarly journals Belief Revision Operators with Varying Attitudes Towards Initial Beliefs

2019 ◽  
Author(s):  
Adrian Haret ◽  
Stefan Woltran
Keyword(s):  
Decision Theory ◽  
Knowledge Base ◽  
Belief Revision ◽  
Possible Worlds ◽  
New Information ◽  
New Type ◽  
Conservative Attitude

Classical axiomatizations of belief revision include a postulate stating that if new information is consistent with initial beliefs, then revision amounts to simply adding the new information to the original knowledge base. This postulate assumes a conservative attitude towards initial beliefs, in the sense that an agent faced with the need to revise them will seek to preserve initial beliefs as much as possible. In this work we look at operators that can assume different attitudes towards original beliefs. We provide axiomatizations of these operators by varying the aforementioned postulate and obtain representation results that characterize the new types of operators using preorders on possible worlds. We also present concrete examples for each new type of operator, adapting notions from decision theory.

scholarly journals A Unifying Framework for Probabilistic Belief Revision

2017 ◽  
Author(s):  
Zhiqiang Zhuang ◽  
James Delgrande ◽  
Abhaya Nayak ◽  
Abdul Sattar
Keyword(s):  
Belief Revision ◽  
Representation Theorem ◽  
Probabilistic Logic ◽  
Basic Principles ◽  
Probabilistic Information ◽  
Probabilistic Setting ◽  
Revision Function

In this paper we provide a general, unifying framework for probabilistic belief revision. We first introduce a probabilistic logic called p-logic that is capable of representing and reasoning with basic probabilistic information. With p-logic as the background logic, we define a revision function called p-revision that resembles partial meet revision in the AGM framework. We provide a representation theorem for p-revision which shows that it can be characterised by the set of basic AGM revision postulates. P-revision represents an "all purpose" method for revising probabilistic information that can be used for, but not limited to, the revision problems behind Bayesian conditionalisation, Jeffrey conditionalisation, and Lewis's imaging. Importantly, p-revision subsumes all three approaches indicating that Bayesian conditionalisation, Jeffrey conditionalisation, and Lewis' imaging all obey the basic principles of AGM revision. As well our investigation sheds light on the corresponding operation of AGM expansion in the probabilistic setting.

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