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# Topic: Possibility theory

 Possibility theory - Wikipedia, the free encyclopedia Possibility theory is a mathematical theory for dealing with certain types of uncertainty and is an alternative to probability theory. Whereas probability theory uses a single number, the probability, to describe how likely an event is to occur, possibility theory uses two concepts, the possibility and the necessity of the event. The operators of possibility theory can be seen as a hyper-cautious version of the operators of the transferable belief model, a modern development of the theory of evidence. en.wikipedia.org /wiki/Possibility_theory   (754 words)

 Probability theory - Wikipedia, the free encyclopedia Probability theory is the mathematical study of probability. Two crucial concepts in the theory of probability are those of a random variable and of the probability distribution of a random variable; see those articles for more information. Mathematicians usually take probability theory to be the study of probability spaces and random variables — an approach introduced by Kolmogorov in the 1930s. en.wikipedia.org /wiki/Probability_theory   (838 words)

 Logical possibility - Wikipedia, the free encyclopedia Philosophers generally consider logical possibility to be the broadest sort of subjunctive possibility in modal logic. While it is logically possible for the sky to be green, it is not logically possible for the sky to be both green and not green at the same time and in the same respect. For example, it may be logically possible for the laws of nature to be different from what they actually are. en.wikipedia.org /wiki/Logical_possibility   (311 words)

 RPDMP/RLIAQQ Uncertainty in possibility theory is represented by a pair of dual "measures" of possibility and necessity, usually graded on the unit interval (although any pseudo-complemented lattice structure could be used in its place). Possibility measures are max-decomposable for the union of events, in contrast with probability measures which are additive, while necessity measures are min-decomposable for the intersection of events. Possibility and necessity measures can be usually defined from a possibility distribution which assigns a level of plausibility to each element of the referential or universe of discourse. www.irit.fr /recherches/RPDMP/RLIAQQ.frame-eng.shtml   (729 words)

 Possibility theory   (Site not responding. Last check: 2007-11-05) Whereas probability theory uses a single number, the probability, to describe how likely an event is to occur Possibility theory uses two numbers, the possibility of the event and the necessity of the event. The Possibility is a non-additive set measure (mathematics) when it is applied to the membership function of a set. Possibility measure can be seen as a consonant plausibility measure in Dempster-Shafer theory of evidence (when the focal sets are nested Like Russian dolls). possibility-theory.area51.ipupdater.com   (485 words)

 Book review of Didier Dubois   (Site not responding. Last check: 2007-11-05) Possibility theory (formulated by Zadeh in 1977) developed as a branch of the theory of fuzzy sets to deal with the lexical elasticity of ordinary language (i.e., the fuzziness of words such as "small" and "many"), and other forms of uncertainty which are not probabilistic in nature. Possibility theory is both a theory of imprecision (represented by fuzzy sets) and a theory of uncertainty. Possibility logic (a logic of partial ignorance) extends modal logic by assigning a degree of possibility and a degree of necessity to each axiom. www.thymos.com /mind/dubois.html   (360 words)

 Possibility theory: Facts and details from Encyclopedia Topic   (Site not responding. Last check: 2007-11-05) Possibility theory is a mathematical theory for dealing with certain types of uncertainty uncertainty quick summary: Bayes theorem is a result in probability theory, which gives the conditional probability distribution of a random variable a given b in terms of... The dempster-shafer theory is a mathematical theory of evidence that was introduced in the late 1970s by glenn shafer.... www.absoluteastronomy.com /encyclopedia/p/po/possibility_theory.htm   (765 words)

 FAQ: Fuzzy Logic and Fuzzy Expert Systems 1/1 [Monthly posting] - [12] What is possibility theory?   (Site not responding. Last check: 2007-11-05) Date: 15-APR-93 Possibility theory is a new form of information theory which is related to but independent of both fuzzy sets and probability theory. Technically, a possibility distribution is a normal fuzzy set (at least one membership grade equals 1). Possibility theory has a methodological advantage over probability theory as a representation of nondeterminism in systems, because the PLUS/TIMES calculus does not validly generalize nondeterministic processes, while MAX/MIN and MAX/TIMES do. www-2.cs.cmu.edu /Groups/AI/html/faqs/ai/fuzzy/part1/faq-doc-12.html   (241 words)

 Time and Timelessness in the Philosophy of A. N. Whitehead As in the case of the different possible ways of explaining a particular color perception, or of different possible ways of gaining access to a universally valid explanation of it, there is also a uniform method of explanation for the different relationships to the perception of time. Whitehead’s theory of becoming is in fact noteworthy in the way it takes for granted that the coming-to-be is not only a coming-to-be of something, but beyond that, is a coming-to-be of something absolutely determinate. These possibilities, of which our wishes and our hopes are the subjective counterpart, never finally reach actuality, and in the all-inclusive realm of the actual, a place must be found for them distinct from that of actualized possibilities. www.religion-online.org /showarticle.asp?title=2381   (13052 words)

 Abstracts in Imprecise Probabilities   (Site not responding. Last check: 2007-11-05) Possibility measures and conditional possibility measures are given a behavioural interpretation as marginal betting rates against events. The measures are additive probabilities (used in the Bayesian theory), coherent lower (or upper) previsions, belief functions (used in the Dempster-Shafer theory) and possibility measures (fuzzy logic). Special emphasis is given to the theory of coherent lower previsions, in which upper and lower probabilities, expectations and conditional probabilities are constructed from initial assessments through a technique of natural extension. ippserv.rug.ac.be /abstracts/abstracts.html   (3649 words)

 Possibilistic Processes
for Complex Systems Modeling
Although possibility theory is logically independent of probability theory, they are related: both arise in Dempster-Shafer evidence theory as fuzzy measures defined on random sets; and their distributions are both fuzzy sets. While possibility theory is logically independent of probability theory, they are related: both arise in Dempster-Shafer evidence theory as fuzzy measures defined on random sets; and their distributions are both fuzzy sets. The purpose of this dissertation is to extend interpretations and applications of possibility theory beyond those of fuzzy sets; in particular, to develop a natural semantics of possibility for the purposes of qualitative modeling of complex physical systems. www.c3.lanl.gov /~joslyn/thesis.html   (443 words)

 math lessons - Possibility theory Possibility theory is a mathematical theory for dealing with certain types of uncertainty. Zadeh first introduced possibility theory in 1978 in the context of fuzzy sets. It can be used to analyze evidence, etc.: the Dempster-Shafer theory is a possibility theory for dealing with evidence. www.mathdaily.com /lessons/Possibility_theory   (202 words)

 [No title] Since possibility and necessity measures are, respectively, special plausibility and belief measures, the counterpart of (3) in possibility theory is the equation  EMBED Equation.2  (11) and the counterpart of (4) in possibility theory is the inequality Pos(A) (Nec(A). The amount is expressed by the difference between the maximum possible uncertainty associated with the set of alternatives postulated in the situation and the actual uncertainty of the model. Classical formalisms for describing uncertainty (probability theory and crisp possibility theory), notwithstanding their useful role in inductive modeling, are not adequate to capture uncertainty inherent in some applications. www.acims.arizona.edu /CONFERENCES/ais2000/InvitedPapers/GKlir.doc   (6995 words)

 Possibility Theory with Applications to Data Analysis   (Site not responding. Last check: 2007-11-05) Their application to real-world problems induces various types of uncertainty related to the observation of processes, the measurement of signals and the mismatch between mathematical models and reality in general. The illustration of the application of possibility theory to data analysis in process and supervisory control systems with examples taken from the area of condition monitoring. Possibility Theory - Extension Principle, Algebraic Operations with Fuzzy Quantities, Fuzzy Events, Assessing Fuzzy Sets, Confidence Measures, Probability - Possibility Transformations, Upper and Lower Distribution Functions, Ranking Fuzzy Quantities, Mean Value of a Fuzzy Number, Fuzzy Measures. www.csc.umist.ac.uk /publications/cscseries5.htm   (288 words)

 UAI-2000 Tutorials This talk is an introduction to possibility theory, a theory of uncertainty closely related to fuzzy set theory, but similar to probability theory although following different operating rules. Contrary to probability, a possibility measure is maxitive and not self-dual. In the first (numerical) case, there are several possible clear connections between possibility and probability theory, in terms of upper probabilities, belief functions,confidence intervals, likelihood functions and infinitesimal probabilities. www.cs.toronto.edu /~cebly/uai2000/tutorials.html   (745 words)

 Ephilosopher :: View topic - TLP Propositions 1 - 2.063 The existence of objects is entailed by the possibility of propositions. Consider, e.g., that prior to quantum theory or even atomic theory or basic biology, we could still speak of humans and ducks and whatnot in a determinate sense. Certainly, the concept of possibility is vital to the TLP (for reasons I’ve started to unpack in the “pictures and thoughts” thread) and W characteristically talks of “possibility” in terms of form (again, see 2.033 and 2.15). www.ephilosopher.com /index.php?name=PNphpBB2&file=viewtopic&p=72&POSTNUKESID=2e0b7b714c9bf6e3a30491da467827b5#72   (4572 words)

 WordNet Search - 2.1   (Site not responding. Last check: 2007-11-05) S: (n) theory (a well-substantiated explanation of some aspect of the natural world; an organized system of accepted knowledge that applies in a variety of circumstances to explain a specific set of phenomena) "theories can incorporate facts and laws and tested hypotheses"; "true in fact and theory" S: (n) hypothesis, possibility, theory (a tentative theory about the natural world; a concept that is not yet verified but that if true would explain certain facts or phenomena) "a scientific hypothesis that survives experimental testing becomes a scientific theory"; "he proposed a fresh theory of alkalis that later was accepted in chemical practices" S: (n) theory (a belief that can guide behavior) "the architect has a theory that more is less"; "they killed him on the theory that dead men tell no tales" wordnet.princeton.edu /perl/webwn?s=theory   (144 words)

 » The math behind Sudoku: Graph Theory - Possibility And Probability This really got my attention because graph theory is an important field of mathematics that has a number of applications (network traffic flows for example), and it is something that I’m always interested to learn more about. Since there are 81 cells and 9 possible numbers per cell that means there are 9^81 possible answers (in plain english this means 19 followed by 76 zeros) give or take a few depending how many numbers were already filled in for you. Possibility And Probability is proudly powered by WordPress ♦ Entries (RSS) and Comments (RSS). ironboundsoftware.com /blog/2006/01/15/the-math-behind-sudoku-graph-theory   (755 words)

 Possibility Theory III: Possibilistic Independence (ResearchIndex)   (Site not responding. Last check: 2007-11-05) My tools will be the measureand integral-theoretic treatment of possibility theory, developed in parts I and II of this series. 1.1: Possibility Theory I - The Measure- And Integral-Theoretic.. Possibility Theory I - The Measure- And Integral-Theoretic.. citeseer.ist.psu.edu /23723.html   (356 words)

 Trust Theory of Environmental Protection, and Some Dark Thoughts on the Possibility of Law Reform Sax's public trust theory won rapid and widespread acceptance during a time of considerable agitation when new theories and approaches to environmental protection were being explored. I believe it is possible to generalize from society's experience with Sax's public trust theory of environmental protection. The public trust theory, although deeply compromised, solidified the partial revolution in social thought on the issue of environmental protection. www.bepress.com /ils/iss4/art4   (336 words)

 Distinct possibility Theory of Evolution is not a theory anymore - ShopForum   (Site not responding. Last check: 2007-11-05) Distinct possibility Theory of Evolution is not a theory anymore - ShopForum Distinct possibility Theory of Evolution is not a theory anymore That theory teeters on the edge of Lamarkian theory of evolution. www.mercedesshop.com /shopforum/showthread.php3?t=97703   (1298 words)

 Possibility Theory It is the only way to deal, within the same framework, with knowledge numerically provided by measuring devices, and knowledge symbolically expressed by a human observer for instance. But these two types of imperfection in knowledge are closely linked, if only because, in many cases, the more accuracy is required for the terms of an assertion, the less certain becomes the assertion. a means of assessing to what extent the occurrence of an event is possible and to what extent we are certain of its occurrence, without, however, knowing the evaluation of the probability of this occurrence. www.survey.ntua.gr /main/labs/rsens/DeCETI/IRIT/MSI-FUSION/node93.html   (255 words)

 Journal of Logic and Computation, Volume 9, Issue 6, pp. 873-895: Abstract.   (Site not responding. Last check: 2007-11-05) In previous works, the authors have cast this view in the framework of comparative possibility theory, showing that a set of default rules is equivalent to a set of comparative possibility distributions, each encoding an epistemic state. This paper offers a detailed analysis of the structure of comparative possibility distributions representing default knowledge, by laying bare two different relations between epistemic states: the specificity ordering and the informativeness ordering. They correspond to all the possible completions of the default knowledge by means of a so-called completion rule of inference. www.mi.sanu.ac.yu /~uros.m/logcom/hdb/Volume_09/Issue_06/090873.sgm.abs.html   (281 words)

 Exception-tolerant reasoning and decision under uncertainty using qualitative possibility theory   (Site not responding. Last check: 2007-11-05) Logic and decision belong to two different traditions; logic is concerned with consistency and is oriented towards symbolic inference, while decision deals with trade-offs (possibly involving uncertainty), and decision theory is often developed in numerical terms. Among weighted logics, possibilistic logic, based on the conjoint use of classical logic and qualitative possibility theory (Dubois and Prade, 1998) offers a framework at the meeting point of the two traditions. This short paper merely provides a brief overview of the use of possibility theory and possibilistic logic both in default reasoning and in decision under uncertainty. www.kuenstliche-intelligenz.de /Artikel/Exception-tolerantreasoninganddecisionun.htm   (179 words)

 Detailed Product page   (Site not responding. Last check: 2007-11-05) This report summarizes techniques that use possibility theory to estimate the risk of terrorist acts. LED captures the uncertainty due to vagueness and imprecision that is inherent in the fidelity of the information available for terrorist acts; probability theory cannot capture these uncertainties. The numerical technique uses traditional possibility theory applied to crisp sets, while the linguistic technique applies possibility theory to fuzzy sets. www.ntis.gov /search/product.asp?ABBR=DE2005836683   (394 words)

 Possibility theory : - A Key Topic in Science, Technology, and Knowledge Management -- Resources and References for ...   (Site not responding. Last check: 2007-11-05) Possibility theory : - A Key Topic in Science, Technology, and Knowledge Management -- Resources and References for academic and corporate research and development. Foundation and Applications of Possibility Theory : Proceedings of Fapt '95 : Ghent, Beigium 13-15 December 1995 (Advances in Fuzzy Systems. A theory of possibility : a constructivistic and conceptualistic account of possible individuals and possible worlds www.research.oxydex.com /Possibility_theory.html   (524 words)

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