The Wikipedia is a collaborative encyclopedia: anyone can contribute to its articles simply by clicking on an "edit" button. The open nature of the Wikipedia has been key to its success, but has also created a challenge: how can readers develop an informed opinion on its reliability? We propose a system that computes quantitative values of trust for the text in Wikipedia articles; these trust values provide an indication of text reliability.The system uses as input the revision history of each article, as well as information about the reputation of the contributing authors, as provided by a reputation system. The trust of a word in an article is computed on the basis of the reputation of the original author of the word, as well as the reputation of all authors who edited text near the word. The algorithm computes word trust values that vary smoothly across the text; the trust values can be visualized using varying text-background colors. The algorithm ensures that all changes to an article's text are reflected in the trust values, preventing surreptitious content changes.We have implemented the proposed system, and we have used it to compute and display the trust of the text of thousands of articles of the English Wikipedia. To validate our trust-computation algorithms, we show that text labeled as low-trust has a significantly higher probability of being edited in the future than text labeled as high-trust.
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We extend the classical system relations of trace inclusion, trace equivalence, simulation, and bisimulation to a quantitative setting in which propositions are interpreted not as boolean values, but as elements of arbitrary metric spaces. Trace inclusion and equivalence give rise to asymmetrical and symmetrical linear distances, while simulation and bisimulation give rise to asymmetrical and symmetrical branching distances. We study the relationships among these distances, and we provide a full logical characterization of the distances in terms of quantitative versions of LTL and mu-calculus. We show that, while trace inclusion (resp. equivalence) coincides with simulation (resp. bisimulation) for deterministic boolean transition systems, linear and branching distances do not coincide for deterministic metric transition systems. Finally, we provide algorithms for computing the distances over finite systems, together with a matching lower complexity bound
Nonmonotonic inferences are not yet supported by Description Logic technology, although their potential usefulness is widely recognized. Lack of support to nonmonotonic reasoning is due to a number of issues related to expressiveness, computational complexity, and optimizations. This work contributes to the practical support of nonmono-tonic reasoning in description logics by introducing a new semantics designed to address knowledge engineering needs. The formalism is validated through extensive comparison with the other non-monotonic DLs, and systematic scalability tests.
We extend the basic system relations of trace inclusion, trace equivalence, simulation, and bisimulation to a quantitative setting in which propositions are interpreted not as boolean values, but as real values in the interval [0, 1]. Trace inclusion and equivalence give rise to asymmetrical and symmetrical linear distances, while simulation and bisimulation give rise to asymmetrical and symmetrical branching distances. We study the relationships among these distances, and we provide a full logical characterization of the distances in terms of quantitative versions of Ltl and µ-calculus. We show that, while trace inclusion (resp. equivalence) coincides with simulation (resp. bisimulation) for deterministic boolean transition systems, linear and branching distances do not coincide for deterministic quantitative transition systems. Finally, we provide algorithms for computing the distances, together with matching lower and upper complexity bounds.
Temporal logic is two-valued: formulas are interpreted as either true or false. When applied to the analysis of stochastic systems, or systems with imprecise formal models, temporal logic is therefore fragile: even small changes in the model can lead to opposite truth values for a specification. We present a generalization of the branching-time logic CTL which achieves robustness with respect to model perturbations by giving a quantitative interpretation to predicates and logical operators, and by discounting the importance of events according to how late they occur. In every state, the value of a formula is a real number in the interval [0,1], where 1 corresponds to truth and 0 to falsehood. The boolean operators and and or are replaced by min and max, the path quantifiers ∃ and ∀ determine sup and inf over all paths from a given state, and the temporal operators ✸ and specify sup and inf over a given path; a new operator averages all values along a path. Furthermore, all path operators are discounted by a parameter that can be chosen to give more weight to states that are closer to the beginning of the path.We interpret the resulting logic DCTL over transition systems, Markov chains, and Markov decision processes. We present two semantics for DCTL: a path semantics, inspired by the standard interpretation of state and path formulas in CTL, and a fixpoint semantics, inspired by the -calculus evaluation ଁ Updated and extended text of paper to appear in Theoretical Computer Science, Elsevier. 140 L. de Alfaro et al. / Theoretical Computer Science 345 (2005) 139 -170 of CTL formulas. We show that, while these semantics coincide for CTL, they differ for DCTL, and we provide model-checking algorithms for both semantics.
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