A Syntax-based approach to measuring the degree of inconsistency for belief bases

Measuring the degree of inconsistency of a belief base is an important issue in many real world applications. It has been increasingly recognized that deriving syntax sensitive inconsistency measures for a belief base from its minimal inconsistent subsets is a natural way forward. Most of the current proposals along this line do not take the impact of the size of each minimal inconsistent subset into account. However, as illustrated by the well-known Lottery Paradox, as the size of a minimal inconsistent subset increases, the degree of its inconsistency decreases. Another lack in current studies in this area is about the role of free formulas of a belief base in measuring the degree of inconsistency. This has not yet been characterized well. Adding free formulas to a belief base can enlarge the set of consistent subsets of that base. However, consistent subsets of a belief base also have an impact on the syntax sensitive normalized measures of the degree of inconsistency, the reason for this is that each consistent subset can be considered as a distinctive plausible perspective reflected by that belief base,whilst eachminimal inconsistent subset projects a distinctive viewof the inconsistency. To address these two issues,we propose a normalized framework formeasuring the degree of inconsistency of a belief base which unifies the impact of both consistent subsets and minimal inconsistent subsets. We also show that this normalized framework satisfies all the properties deemed necessary by common consent to characterize an intuitively satisfactory measure of the degree of inconsistency for belief bases. Finally, we use a simple but explanatory example in equirements engineering to illustrate the application of the normalized framework.

Children’s attributions of belief to humans and God: cross-cultural evidence

The capacity to attribute beliefs to others in order to understand action is one of the mainstays of human cognition. Yet it is debatable whether children attribute beliefs in the same way to all agents. In this paper, we present the results of a false-belief task concerning humans and God run with a sample of Maya children aged 4–7, and place them in the context of several psychological theories of cognitive development. Children were found to attribute beliefs in different ways to humans and God. The evidence also speaks to the debate concerning the universality and uniformity of the development of folk-psychological reasoning.

Acculturation and religion in schools: the views of young people from minority belief backgrounds

This paper aims to explore the relationship between religious identity, acculturation strategies and perceptions of acculturation orientation in the school context amongst young people from minority
belief backgrounds. Based on a qualitative study including interviews with 26 young people from religious minority belief backgrounds in Northern Ireland, it is argued that acculturation theory provides a useful lens for understanding how young people from religious minority belief backgrounds navigate majority religious school contexts. Using a qualitative approach to explore acculturation theory enables an in-depth understanding of the inter-relationship between minority belief youth’s acculturation strategies and their respective school contexts. Similar to previous research, integrationist attitudes generally prevailed amongst minority belief young people in this study. The findings highlight how young people negotiate their religious identities in a complex web of inter-relationships between their minority religious belief community and the mainstream school culture as represented through peer and staff attitudes, school ethos and practices and religious education. Young people demonstrated differentiated understandings of acculturation orientations within the school context, which they evaluated on the basis of complex perceptions of educational policy, interpersonal relationships and individuals’ motivations. Findings are discussed in view of acculturation tensions, which arose particularly in relation to the religious education curriculum and their implications for opt-out provision as stipulated by human rights law.

The Importance of Religious Displays for Belief Acquisition and Secularization

Both the sociology and the cognitive science of religion seek to explain the acquisition of religious beliefs. In this article, I offer an account of the acquisition and distribution of religious beliefs using the findings of both fields. In the process, I seek to illustrate the potential of interdisciplinary dialogue for improving our understanding of religion and its absence. More specifically, I present a prima facie case—based on existing work in the social and cognitive sciences, exploratory online surveys, and participant observation—that witnessing actions attesting to religious claims is one of the most crucial variables determining whether or not an individual will explicitly believe such claims. Further, I argue that the connection between action and belief can help produce an improved account of secularization and non-theism, defined here as the lack of explicit belief in the existence of non-physical agents.

Information aggregation and belief elicitation in experimental parimutuel betting markets

This paper studies the impact of belief elicitation on informational efficiency and individual behavior in experimental parimutuel betting markets. In one treatment, groups of eight participants, who possess a private signal about the eventual outcome, play a sequential betting game. The second treatment is identical, except that bettors are observed by eight other participants who submit incentivized beliefs about the winning probabilities of each outcome. In the third treatment, the same individuals make bets and assess the winning probabilities of the outcomes. Market probabilities more accurately reflect objective probabilities in the third than in the other two treatments. Submitting beliefs reduces the favorite-longshot bias and making bets improves the accuracy of elicited beliefs. A level-k framework provides some insights about why belief elicitation improves the capacity of betting markets to aggregate information. (C) 2012 Elsevier B.V. All rights reserved.

Logics for belief functions on MV-algebras

In this paper we present a generalization of belief functions over fuzzy events. In particular we focus on belief functions defined in the algebraic framework of finite MV-algebras of fuzzy sets. We introduce a fuzzy modal logic to formalize reasoning with belief functions on many-valued events. We prove, among other results, that several different notions of belief functions can be characterized in a quite uniform way, just by slightly modifying the complete axiomatization of one of the modal logics involved in the definition of our formalism. © 2012 Elsevier Inc. All rights reserved.

PROSTATIC INTRAEPITHELIAL NEOPLASIA (PIN) - PERFORMANCE OF BAYESIAN BELIEF NETWORK FOR DIAGNOSIS AND GRADING

Prostatic intraepithelial neoplasia (PIN) diagnosis and grading are affected by uncertainties which arise from the fact that almost all knowledge of PIN histopathology is expressed in concepts, descriptive linguistic terms, and words. A Bayesian belief network (BBN) was therefore used to reduce the problem of uncertainty in diagnostic clue assessment, while still considering the dependences between elements in the reasoning sequence. A shallow network was used with an open-tree topology, with eight first-level descendant nodes for the diagnostic clues (evidence nodes), each independently linked by a conditional probability matrix to a root node containing the diagnostic alternatives (decision node). One of the evidence nodes was based on the tissue architecture and the others were based on cell features. The system was designed to be interactive, in that the histopathologist entered evidence into the network in the form of likelihood ratios for outcomes at each evidence node. The efficiency of the network was tested on a series of 110 prostate specimens, subdivided as follows: 22 cases of non-neoplastic prostate or benign prostatic tissue (NP), 22 PINs of low grade (PINlow), 22 PINs of high grade (PINhigh), 22 prostatic adenocarcinomas with cribriform pattern (PACcri), and 22 prostatic adenocarcinomas with large acinar pattern (PAClgac). The results obtained in the benign and malignant categories showed that the belief for the diagnostic alternatives is very high, the values being in general more than 0.8 and often close to 1.0. When considering the PIN lesions, the network classified and graded most of the cases with high certainty. However, there were some cases which showed values less than 0.8 (13 cases out of 44), thus indicating that there are situations in which the feature changes are intermediate between contiguous categories or grades. Discrepancy between morphological grading and the BBN results was observed in four out of 44 PIN cases: one PINlow was classified as PINhigh and three PINhigh were classified as PINlow. In conclusion, the network can grade PlN lesions and differentiate them from other prostate lesions with certainty. In particular, it offers a descriptive classifier which is readily implemented and which allows the use of linguistic, fuzzy variables.

EXPERT-SYSTEM SUPPORT USING BAYESIAN BELIEF NETWORKS IN THE DIAGNOSIS OF FINE-NEEDLE ASPIRATION BIOPSY SPECIMENS OF THE BREAST

Aim-To develop an expert system model for the diagnosis of fine needle aspiration cytology (FNAC) of the breast.

Methods-Knowledge and uncertainty were represented in the form of a Bayesian belief network which permitted the combination of diagnostic evidence in a cumulative manner and provided a final probability for the possible diagnostic outcomes. The network comprised 10 cytological features (evidence nodes), each independently linked to the diagnosis (decision node) by a conditional probability matrix. The system was designed to be interactive in that the cytopathologist entered evidence into the network in the form of likelihood ratios for the outcomes at each evidence node.

Results-The efficiency of the network was tested on a series of 40 breast FNAC specimens. The highest diagnostic probability provided by the network agreed with the cytopathologists' diagnosis in 100% of cases for the assessment of discrete, benign, and malignant aspirates. A typical probably benign cases were given probabilities in favour of a benign diagnosis. Suspicious cases tended to have similar probabilities for both diagnostic outcomes and so, correctly, could not be assigned as benign or malignant. A closer examination of cumulative belief graphs for the diagnostic sequence of each case provided insight into the diagnostic process, and quantitative data which improved the identification of suspicious cases.

Conclusion-The further development of such a system will have three important roles in breast cytodiagnosis: (1) to aid the cytologist in making a more consistent and objective diagnosis; (2) to provide a teaching tool on breast cytological diagnosis for the non-expert; and (3) it is the first stage in the development of a system capable of automated diagnosis through the use of expert system machine vision.