scholarly journals A Characterization of Probability-based Dichotomous Belief Revision

Studia Logica ◽  
2021 ◽  
Author(s):  
Sven Ove Hansson
Keyword(s):  
Belief Revision ◽  
Probabilistic Models ◽  
Belief Change ◽  
Negligible Probability ◽  
Future Information ◽  
Belief Set

AbstractThis article investigates the properties of multistate top revision, a dichotomous (AGM-style) model of belief revision that is based on an underlying model of probability revision. A proposition is included in the belief set if and only if its probability is either 1 or infinitesimally close to 1. Infinitesimal probabilities are used to keep track of propositions that are currently considered to have negligible probability, so that they are available if future information makes them more plausible. Multistate top revision satisfies a slightly modified version of the set of basic and supplementary AGM postulates, except the inclusion and success postulates. This result shows that hyperreal probabilities can provide us with efficient tools for overcoming the well known difficulties in combining dichotomous and probabilistic models of belief change.

scholarly journals Epistemic-entrenchment Characterization of Parikh’s Axiom

2017 ◽  
Author(s):  
Theofanis Aravanis ◽  
Pavlos Peppas ◽  
Mary-Anne Williams
Keyword(s):  
Belief Revision ◽  
Weak Version ◽  
Epistemic Entrenchment ◽  
New Information ◽  
Additional Constraints ◽  
Belief Set

In this article, we provide the epistemic-entrenchment characterization of the weak version of Parikh’s relevance-sensitive axiom for belief revision — known as axiom (P) — for the general case of incomplete theories. Loosely speaking, axiom (P) states that, if a belief set K can be divided into two disjoint compartments, and the new information φ relates only to the first compartment, then the second compartment should not be affected by the revision of K by φ. The above-mentioned characterization, essentially, constitutes additional constraints on epistemic-entrenchment preorders, that induce AGM revision functions, satisfying the weak version of Parikh’s axiom (P).

Characterization of the Uncertainties in the Inspection Results of Ultrasonic Intelligent Pigs

2013 ◽  
Author(s):  
Mamdouh M. Salama ◽  
Bruce J. Nestleroth ◽  
Marc A. Maes ◽  
Chris Dash
Keyword(s):  
Probabilistic Models ◽  
Service Providers ◽  
Quantitative Risk Assessment ◽  
Life Extension ◽  
Internal Corrosion ◽  
Integrity Assessment ◽  
Diameter Pipe ◽  
Length Width ◽  
Pull Through

In-Line Inspections using magnetic flux leakage (MFL) and the Ultrasonic (UT) intelligent pigs are the most common tools used to assess the integrity of pipelines. But, both MFL and UT inspection results are subject to various sources of uncertainties which must be quantified and accounted for in the integrity assessment of the inspected pipeline. A series of pull-through tests (PTT) of seven MFL tools and two UT tools from five service providers was performed on a 12-inch diameter pipe containing pre-existing internal corrosion defects of various length, width, and depth, and located in a variety of circumferential and longitudinal positions. The results of these tests are used to quantify the detectability statistics and the sizing uncertainties of the different tools for future use in developing calibrated probabilistic models for reliability based inspection, quantitative risk assessment and life extension studies for pipelines. The results of the MFL tools were presented in 2012 OMAE conference and this paper presents the results of the two UT tools.

(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 Revising Probabilities and Full Beliefs

2020 ◽  
Vol 49 (5) ◽  
pp. 1005-1039 ◽  
Author(s):  
Sven Ove Hansson
Keyword(s):  
Formal Model ◽  
Belief Change ◽  
Learning From Experience ◽  
Epistemic Agent ◽  
Set Operations ◽  
Proposed Model ◽  
Formal Properties ◽  
Belief States ◽  
Do So ◽  
Belief Set

Abstract A new formal model of belief dynamics is proposed, in which the epistemic agent has both probabilistic beliefs and full beliefs. The agent has full belief in a proposition if and only if she considers the probability that it is false to be so close to zero that she chooses to disregard that probability. She treats such a proposition as having the probability 1, but, importantly, she is still willing and able to revise that probability assignment if she receives information that gives her sufficient reasons to do so. Such a proposition is (presently) undoubted, but not undoubtable (incorrigible). In the formal model it is assigned a probability 1 − δ, where δ is an infinitesimal number. The proposed model employs probabilistic belief states that contain several underlying probability functions representing alternative probabilistic states of the world. Furthermore, a distinction is made between update and revision, in the same way as in the literature on (dichotomous) belief change. The formal properties of the model are investigated, including properties relevant for learning from experience. The set of propositions whose probabilities are infinitesimally close to 1 forms a (logically closed) belief set. Operations that change the probabilistic belief state give rise to changes in this belief set, which have much in common with traditional operations of belief change.

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.

scholarly journals Digital Trees and Memoryless Sources: from Arithmetics to Analysis

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Philippe Flajolet ◽  
Mathieu Roux ◽  
Brigitte Vallée
Keyword(s):  
Probabilistic Models ◽  
Asymptotic Form ◽  
Leader Election ◽  
Text Compression ◽  
Digital Trees ◽  
Arithmetic Properties ◽  
International Audience ◽  
Error Terms ◽  
Dynamic Hashing

International audience Digital trees, also known as $\textit{"tries''}$, are fundamental to a number of algorithmic schemes, including radix-based searching and sorting, lossless text compression, dynamic hashing algorithms, communication protocols of the tree or stack type, distributed leader election, and so on. This extended abstract develops the asymptotic form of expectations of the main parameters of interest, such as tree size and path length. The analysis is conducted under the simplest of all probabilistic models; namely, the $\textit{memoryless source}$, under which letters that data items are comprised of are drawn independently from a fixed (finite) probability distribution. The precise asymptotic structure of the parameters' expectations is shown to depend on fine singular properties in the complex plane of a ubiquitous $\textit{Dirichlet series}$. Consequences include the characterization of a broad range of asymptotic regimes for error terms associated with trie parameters, as well as a classification that depends on specific $\textit{arithmetic properties}$, especially irrationality measures, of the sources under consideration.

An axiomatic characterization of temporalised belief revision in the law

2019 ◽  
Vol 27 (4) ◽  
pp. 347-367 ◽  
Author(s):  
Luciano H. Tamargo ◽  
Diego C. Martinez ◽  
Antonino Rotolo ◽  
Guido Governatori
Keyword(s):  
Belief Revision ◽  
Axiomatic Characterization ◽  
The Law

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.

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