scholarly journals Kernel Contraction and Base Dependence

2017 ◽  
Vol 60 ◽  
pp. 97-148
Author(s):  
Mehrdad Oveisi ◽  
James P. Delgrande ◽  
Francis Jeffry Pelletier ◽  
Fred Popowich
Keyword(s):  
Belief Change ◽  
Dependence Relation ◽  
Specific Criterion ◽  
Strong Base ◽  
Belief Base ◽  
Dependence Relations ◽  
Kernel Contraction ◽  
Approximate Dependence ◽  
Information Finding ◽  
Belief Set

The AGM paradigm of belief change studies the dynamics of belief states in light of new information. Finding, or even approximating, those beliefs that are dependent on or relevant to a change is valuable because, for example, it can narrow the set of beliefs considered during belief change operations. A strong intuition in this area is captured by Gärdenfors’s preservation criterion (GPC), which suggests that formulas independent of a belief change should remain intact. GPC thus allows one to build dependence relations that are linked with belief change. Such dependence relations can in turn be used as a theoretical benchmark against which to evaluate other approximate dependence or relevance relations. Fariñas and Herzig axiomatize a dependence relation with respect to a belief set, and, based on GPC, they characterize the correspondence between AGM contraction functions and dependence relations. In this paper, we introduce base dependence as a relation between formulas with respect to a belief base, and prove a more general characterization that shows the correspondence between kernel contraction and base dependence. At this level of generalization, different types of base dependence emerge, which we show to be a result of possible redundancy in the belief base. We further show that one of these relations that emerge, strong base dependence, is parallel to saturated kernel contraction. We then prove that our latter characterization is a reversible generalization of Fariñas and Herzig’s characterization. That is, in the special case when the underlying belief base is deductively closed (i.e., it is a belief set), strong base dependence reduces to dependence, and so do their respective characterizations. Finally, an intriguing feature of Fariñas and Herzig’s formalism is that it meets other criteria for dependence, namely, Keynes’s conjunction criterion for dependence (CCD) and Gärdenfors’s conjunction criterion for independence (CCI). We prove that our base dependence formalism also meets these criteria. Even more interestingly, we offer a more specific criterion that implies both CCD and CCI, and show our base dependence formalism also meets this new criterion.

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.

scholarly journals Selection Strategies for Inductive Reasoning From Conditional Belief Bases and for Belief Change Respecting the Principle of Conditional Preservation

2021 ◽  
Vol 34 (1) ◽  
Author(s):  
Christoph Beierle ◽  
Gabriele Kern-Isberner
Keyword(s):  
Belief Change ◽  
Inductive Reasoning ◽  
Conditional Belief ◽  
Belief Base ◽  
Belief Bases ◽  
Selection Strategies ◽  
Ranking Model

Given a belief base ∆ consisting of a set of conditionals,there are many different ways an agent may inductivelycomplete the knowledge represented by ∆ to a completeepistemic state; two well-known approaches are given by systemP and system Z, and also each ranking model of ∆ induces afull inference relation. C-representations are special rankingmodels that obey the principle of conditional indifference.Inductive reasoning using c-representations can be done withrespect to all c-representations, with respect to a subclass of,e.g., minimal c-representations, or with respect to singlec-representations. In this paper, we present and investigateselection strategies for determining single c-representations tobe used for inductive reasoning from belief bases. We developaxioms for specifying characteristics of selection strategies.We illustrate which desirable properties, like syntaxsplitting, are ensured by the axioms, and develop constructionsfor obtaining selection strategies satisfying the axioms.Furthermore, we also present and study the extension of selectionstrategies to c-revisions that follow the principle ofconditional preservation and that have been employed successfullyin various belief change settings.

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.

Theory contraction and base contraction unified

1993 ◽  
Vol 58 (2) ◽  
pp. 602-625 ◽  
Author(s):  
Sven Ove Hansson
Keyword(s):  
Contraction Operator ◽  
Partial Meet Contraction ◽  
Belief Base ◽  
Theory Contraction ◽  
Axiomatic Characterizations ◽  
Base Contraction ◽  
Belief Set

AbstractOne way to construct a contraction operator for a theory (belief set) is to assign to it a base (belief base) and an operator of partial meet contraction for that base. Axiomatic characterizations are given of the theory contractions that are generated in this way by (various types of) partial meet base contractions.

scholarly journals Degree-free bounds for dependence relations

1981 ◽  
Vol 31 (4) ◽  
pp. 496-507
Author(s):  
A. Bijlsma ◽  
P. L. Cijsouw
Keyword(s):  
Dependence Relation ◽  
Integer Coefficients ◽  
Dependence Relations ◽  
The Absolute

AbstractLet α1,…, αn be non-zero albegraic numbers and let l1(α1),…ln(αn) denote arbitrary fixed values of the logarithms of α1,…n, respectively Given that l1(α1),…ln(αn) are linearly dependent over Q, the existence of non-trival dependence relation between these numbers with integer coefficients of low absolute values can be proved. Existing results of this kind give bounds for the absolute values of the coefficients which are expressions in the degree D = [Q(α1…αn): Q], the heights of α1,…αn and the magnitudes of the logarithms involved.

scholarly journals Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 885 ◽  
Author(s):  
Irina Cristea ◽  
Juš Kocijan ◽  
Michal Novák
Keyword(s):  
Point Of View ◽  
The Other ◽  
Dependence Relation ◽  
Algebraic Point ◽  
Dependence Relations ◽  
New Interpretation ◽  
Atmospheric Variables ◽  
Algebraic Hyperstructure

The aim of this paper is to study, from an algebraic point of view, the properties of interdependencies between sets of elements (i.e., pieces of secrets, atmospheric variables, etc.) that appear in various natural models, by using the algebraic hyperstructure theory. Starting from specific examples, we first define the relation of dependence and study its properties, and then, we construct various hyperoperations based on this relation. We prove that two of the associated hypergroupoids are H v -groups, while the other two are, in some particular cases, only partial hypergroupoids. Besides, the extensivity and idempotence property are studied and related to the cyclicity. The second goal of our paper is to provide a new interpretation of the dependence relation by using elements of the theory of algebraic hyperstructures.

Kernel contraction

1994 ◽  
Vol 59 (3) ◽  
pp. 845-859 ◽  
Author(s):  
Sven Ove Hansson
Keyword(s):  
Belief Change ◽  
Partial Meet Contraction ◽  
Kernel Contraction

AbstractKernel contraction is a natural nonrelational generalization of safe contraction. All partial meet contractions are kernel contractions, but the converse relationship does not hold. Kernel contraction is axiomatically characterized. It is shown to be better suited than partial meet contraction for formal treatments of iterated belief change.

56. Proficiency at the end of practice predicts retention of a technical clinical skills

2007 ◽  
Vol 30 (4) ◽  
pp. 59
Author(s):  
H. Carnahan ◽  
E. Hagemann ◽  
A. Dubrowski
Keyword(s):  
Virtual Reality ◽  
Clinical Skills ◽  
Clinical Skill ◽  
Technical Skills ◽  
Skills Training ◽  
Retention Performance ◽  
Specific Criterion ◽  
Practice Trials ◽  
Practice Time ◽  
Criterion Time

A debate is emerging regarding the efficacy of proficiency based versus duration based training of technical skills. It is not clear whether the performance level attained at the end of practice (i.e., proficiency criteria), or the overall amount of practice performed during learning will best predict the retention of a technical clinical skill. The skill learned was the single-handed double square-knot. Forty two trainees learned the skill through video-based instruction and were divided into three groups (14 participants per group) each with a specific criterion time to tie the knot (10, 15, and 20 seconds). Practice continued until participants completed the knot within their criterion time. The total number of trials, and the overall practice time required to obtain each respective criterion were recorded during practice. Participants returned one-week later for a timed retention test consisting of one trial of the knot tying skill with no video instruction. A multiple regression analysis tested whether the amount of practice, the total practice time, or the criterion reached at the end of practice was the best predictor of the time taken to perform the skill during retention. This analysis showed that the number of practice trials was highly correlated with total practice time (r = .82, p = .01), therefore total practice time was withdrawn as a predictor variable from the subsequent analysis. The regression showed that the only significant predictor of retention performance was the criterion reached at the end of practice (p = .03). The number of practice trials was not found to significantly predict the retention performance (p = .87). The results support the notion that proficiency based training results in better retention of a technical clinical skill in comparison to duration based approaches. This provides evidence for the introduction of proficiency based educational approaches in technical skills curricula. Jowett N, LeBlanc V, Xeroulis G, MacRae H, Dubrowski A. Surgical skill acquisition with self-directed practice using computer-based video training. Am J Surg. 2007; 193(2):237-42. Gallagher AG, Ritter EM, Champion H, Higgins G, Fried MP, Moses G, Smith CD, Satava RM. Virtual reality simulation for the operating room: proficiency-based training as a paradigm shift in surgical skills training. Ann Surg. 2005; 241(2):364-72. Van Sickle KR, Ritter EM, McClusky DA, Lederman A, Baghai M, Gallagher AG, Smith CD. Attempted establishment of proficiency levels for laparoscopic performance on a national scale using simulation: the results from the 2004 SAGES Minimally Invasive Surgical Trainer-Virtual Reality (MIST-VR) learning center study. Surg Endosc. 2007; 21(1):5-10.

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