Consensus in the Presence of Multiple Opinion Leaders: Effect of Bounded Confidence

The problem of analyzing the performance of networked agents exchanging evidence in a dynamic network has recently grown in importance. This problem has relevance in signal and data fusion network applications and in studying opinion and consensus dynamics in social networks. Due to its capability of handling a wider variety of uncertainties and ambiguities associated with evidence, we use the framework of Dempster-Shafer (DS) theory to capture the opinion of an agent. We then examine the consensus among agents in dynamic networks in which an agent can utilize either a cautious or receptive updating strategy. In particular, we examine the case of bounded confidence updating where an agent exchanges its opinion only with neighboring nodes possessing 'similar' evidence. In a fusion network, this captures the case in which nodes only update their state based on evidence consistent with the node's own evidence. In opinion dynamics, this captures the notions of Social Judgment Theory (SJT) in which agents update their opinions only with other agents possessing opinions closer to their own. Focusing on the two special DS theoretic cases where an agent state is modeled as a Dirichlet body of evidence and a probability mass function (p.m.f.), we utilize results from matrix theory, graph theory, and networks to prove the existence of consensus agent states in several time-varying network cases of interest. For example, we show the existence of a consensus in which a subset of network nodes achieves a consensus that is adopted by follower network nodes. Of particular interest is the case of multiple opinion leaders, where we show that the agents do not reach a consensus in general, but rather converge to 'opinion clusters'. Simulation results are provided to illustrate the main results.Comment: IEEE Transactions on Signal and Information Processing Over Networks, to appea

Partial observable update for subjective logic and its application for trust estimation

Subjective Logic (SL) is a type of probabilistic logic, which is suitable for reasoning about situations with uncertainty and incomplete knowledge. In recent years, SL has drawn a significant amount of attention from the multi-agent systems community as it connects beliefs and uncertainty in propositions to a rigorous statistical characterization via Dirichlet distributions. However, one serious limitation of SL is that the belief updates are done only based on completely observable evidence. This work extends SL to incorporate belief updates from partially observable evidence. Normally, the belief updates in SL presume that the current evidence for a proposition points to only one of its mutually exclusive attribute states. Instead, this work considers that the current attribute state may not be completely observable, and instead, one is only able to obtain a measurement that is statistically related to this state. In other words, the SL belief is updated based upon the likelihood that one of the attributes was observed. The paper then illustrates properties of the partial observable updates as a function of the state likelihood and illustrates the use of these likelihoods for a trust estimation application. Finally, the utility of the partial observable updates is demonstrated via various simulations including the trust estimation case.U.S. Army Research Laboratory ; U.K. Ministry of Defence ; TÜBİTAKpre-prin

Intensional Cyberforensics

This work focuses on the application of intensional logic to cyberforensic analysis and its benefits and difficulties are compared with the finite-state-automata approach. This work extends the use of the intensional programming paradigm to the modeling and implementation of a cyberforensics investigation process with backtracing of event reconstruction, in which evidence is modeled by multidimensional hierarchical contexts, and proofs or disproofs of claims are undertaken in an eductive manner of evaluation. This approach is a practical, context-aware improvement over the finite state automata (FSA) approach we have seen in previous work. As a base implementation language model, we use in this approach a new dialect of the Lucid programming language, called Forensic Lucid, and we focus on defining hierarchical contexts based on intensional logic for the distributed evaluation of cyberforensic expressions. We also augment the work with credibility factors surrounding digital evidence and witness accounts, which have not been previously modeled. The Forensic Lucid programming language, used for this intensional cyberforensic analysis, formally presented through its syntax and operational semantics. In large part, the language is based on its predecessor and codecessor Lucid dialects, such as GIPL, Indexical Lucid, Lucx, Objective Lucid, and JOOIP bound by the underlying intensional programming paradigm.Comment: 412 pages, 94 figures, 18 tables, 19 algorithms and listings; PhD thesis; v2 corrects some typos and refs; also available on Spectrum at http://spectrum.library.concordia.ca/977460

Intensional Cyberforensics

This work focuses on the application of intensional logic to cyberforensic analysis and its benefits and difficulties are compared with the finite-state-automata approach. This work extends the use of the intensional programming paradigm to the modeling and implementation of a cyberforensics investigation process with backtracing of event reconstruction, in which evidence is modeled by multidimensional hierarchical contexts, and proofs or disproofs of claims are undertaken in an eductive manner of evaluation. This approach is a practical, context-aware improvement over the finite state automata (FSA) approach we have seen in previous work. As a base implementation language model, we use in this approach a new dialect of the Lucid programming language, called Forensic Lucid, and we focus on defining hierarchical contexts based on intensional logic for the distributed evaluation of cyberforensic expressions. We also augment the work with credibility factors surrounding digital evidence and witness accounts, which have not been previously modeled. The Forensic Lucid programming language, used for this intensional cyberforensic analysis, formally presented through its syntax and operational semantics. In large part, the language is based on its predecessor and codecessor Lucid dialects, such as GIPL, Indexical Lucid, Lucx, Objective Lucid, MARFL, and JOOIP bound by the underlying intensional programming paradigm

Cumulative and Averaging Fusion of Beliefs

International audienceThe problem of fusing beliefs in the Dempster-Shafer belief theory has attracted consid-erable attention over the last two decades. The classical Dempster's Rule has often been criticised, and many alternative rules for belief combination have been proposed in the lit-erature. We show that it is crucial to consider the nature of the situation at hand and to select the appropriate fusion operator as a function thereof. In this paper we present the cu-mulative rule and the averaging rule of belief fusion, which represent generalisations of the subjective logic consensus operator for independent and dependent opinions respectively. The generalised operators are applicable to the combination of general basic belief assign-ments (bbas). These rules, which can be directly derived from classical statistical theory, produce results that correspond well with human intuition