Intransitivity and Vagueness

There are many examples in the literature that suggest that indistinguishability is intransitive, despite the fact that the indistinguishability relation is typically taken to be an equivalence relation (and thus transitive). It is shown that if the uncertainty perception and the question of when an agent reports that two things are indistinguishable are both carefully modeled, the problems disappear, and indistinguishability can indeed be taken to be an equivalence relation. Moreover, this model also suggests a logic of vagueness that seems to solve many of the problems related to vagueness discussed in the philosophical literature. In particular, it is shown here how the logic can handle the sorites paradox.Comment: A preliminary version of this paper appears in Principles of Knowledge Representation and Reasoning: Proceedings of the Ninth International Conference (KR 2004

Weighted logics for artificial intelligence : an introductory discussion

International audienceBefore presenting the contents of the special issue, we propose a structured introductory overview of a landscape of the weighted logics (in a general sense) that can be found in the Artificial Intelligence literature, highlighting their fundamental differences and their application areas

Representing archaeological uncertainty in cultural informatics

This thesis sets out to explore, describe, quantify, and visualise uncertainty in a cultural informatics context, with a focus on archaeological reconstructions. For quite some time, archaeologists and heritage experts have been criticising the often toorealistic appearance of three-dimensional reconstructions. They have been highlighting one of the unique features of archaeology: the information we have on our heritage will always be incomplete. This incompleteness should be reflected in digitised reconstructions of the past. This criticism is the driving force behind this thesis. The research examines archaeological theory and inferential process and provides insight into computer visualisation. It describes how these two areas, of archaeology and computer graphics, have formed a useful, but often tumultuous, relationship through the years. By examining the uncertainty background of disciplines such as GIS, medicine, and law, the thesis postulates that archaeological visualisation, in order to mature, must move towards archaeological knowledge visualisation. Three sequential areas are proposed through this thesis for the initial exploration of archaeological uncertainty: identification, quantification and modelling. The main contributions of the thesis lie in those three areas. Firstly, through the innovative design, distribution, and analysis of a questionnaire, the thesis identifies the importance of uncertainty in archaeological interpretation and discovers potential preferences among different evidence types. Secondly, the thesis uniquely analyses and evaluates, in relation to archaeological uncertainty, three different belief quantification models. The varying ways that these mathematical models work, are also evaluated through simulated experiments. Comparison of results indicates significant convergence between the models. Thirdly, a novel approach to archaeological uncertainty and evidence conflict visualisation is presented, influenced by information visualisation schemes. Lastly, suggestions for future semantic extensions to this research are presented through the design and development of new plugins to a search engine

On the reliability of multistate systems with imprecise probabilities

Розглядається обчислення надійності в складних системах за наявності випадкового набору оцінок працездатності елементів. Виявлено, що підхід Демпстер-Шефера є відповідним математичним інструментом, який відповідає поставленим задачам. Для випадку, коли взаємозалежності елементів невідомі, наведено також оцінки ефективності системи переконань і правдоподібність функції.Рассматривается вычисления надежности в сложных системах при наличии случайного набора оце- нок работоспособности элементов. Выявлено, что подход Демпстер-Шефера является соответствующим математическим инструментом, который соответствует поставленным задачам. Для случая, когда взаимозависимости элементов неизвестны, приведены также оценки эффективности системы убеждений и правдоподобность функции.We consider the computation of multistate systems reliabilities in the presence of random set estimations for the elements' working abilities. It turns out that the Dempster-Shafer approach is a suitable mathematical tool. For the case that the interdependence of the elements is unknown, bounds for the system's performance belief and plausibility functions are given as well

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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Uncertainty reasoning and representation: A Comparison of several alternative approaches

Much of the research done in Artificial Intelligence involves investigating and developing methods of incorporating uncertainty reasoning and representation into expert systems. Several methods have been proposed and attempted for handling uncertainty in problem solving situations. The theories range from numerical approaches based on strict probabilistic reasoning to non-numeric approaches based on logical reasoning. This study investigates a number of these approaches including Bayesian Probability, Mycin Certainty Factors, Dempster-Shafer Theory of Evidence, Fuzzy Set Theory, Possibility Theory and non monotonic logic. Each of these theories and their underlying formalisms are explored by means of examples. The discussion concentrates on a comparison of the different approaches, noting the type of uncertainty that they best represent

Imprecise probabilistic evaluation of sewer flooding in urban drainage systems using random set theory

publication-status: Publishedtypes: ArticleCopyright © 2011 American Geophysical UnionUncertainty analysis is widely applied in water system modeling to quantify prediction uncertainty from models and data. Conventional methods typically handle various kinds of uncertainty using a single characterizing approach, be it probability theory or fuzzy set theory. However, using a single approach may not be appropriate, particularly when uncertainties are of different types. For example, in sewer flood estimation problems, random rainfall variables are used as model inputs and imprecise or subjective information is used to define model parameters. This paper presents a general framework for sewer flood estimation that enables simultaneous consideration of two types of uncertainty: randomness from rainfall data represented using imprecise probabilities and imprecision from model parameters represented by fuzzy numbers. These two types of uncertainties are combined using random set theory and then propagated through a hydrodynamic urban drainage model. Two propagation methods, i.e., discretization and Monte Carlo based methods, are presented and compared, with the latter shown to be much more computationally efficient and hence recommended for high-dimensional problems. The model output (flood depth) is generated in the form of lower and upper cumulative probabilities, which are best estimates given the various stochastic and epistemic uncertainties considered and which embrace the unknown true cumulative probability. The distance between the cumulative probabilities represents the extent of imprecise, incomplete, or conflicting information and can be reduced only when more knowledge is available. The proposed methodology has a more complete and thus more accurate representation of uncertainty in data and models and can effectively handle different uncertainty characterizations in a single, integrated framework for sewer flood estimation

Irrationality and human reasoning

In his account of intentional interpretation, Donald Davidson assumes that people are mostly rational. Several psychological experiments though, reveal that human beings deviate drastically from the normative standards of rationality. Therefore, some psychologists arrive to the conclusion that humans are mostly irrational. In this thesis, I raise some objections to both points of view. On the one hand, ascribing rationality to humans in an a priori manner seems a suspicious position to adopt, considering the empirical data that show otherwise. On the other hand, the validity of the experiments and what exactly they test can also be put in question, since the position that humans are in general irrational is also unacceptable intuitively. In this thesis, I suggest that the discrepancy is due to the notion of rationality we adopt, which I bring into question. I do not find convincing reasons that humans should be thought a priori as rational and I do not also see why humans should be called irrational just because they fail certain tests. Many of the alleged irrationalities in the tests can be explained if we adopt different styles of reasoning than the traditional ones. Hence, humans can count as rational in another way. But, is this what Davidson thinks of rational, or does he think of rationality in the traditional sense? I think the type of rationality that Davidson endorses relies on Classic Logical conditions, which makes it inflexible. A type of rationality that relies on Fuzzy Logical conditions, as I claim, is more appropriate to describe human rationality