Smets,P., Belief functions, Non-Standard Logics for Automated Reasoning, ( Smets, Mamdani, Dubois and Prade Eds.), 253-286, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....others) So roughly speaking, when a HMM, possibly with unknown parameters, is well suited to the data considered and when the noise is not too strong, there is no serious difficulty in performing segmentation. The purpose of our work is to extend, using the theory of evidence [1] 15] 34] [37], these well known methods to some situations in which the use of classical HMFs poses difficulties. Of course, the use of theory of evidence in image processing is not new and has already given satisfactory results in various problems, like medical image classification [4] or SAR image ....

, "Belief functions (with discussion)," in Non-Standard Logics for Automated Reasoning, P. Smets, A. Mamdani, D. Dubois, and H. Prade, Eds. New York: Academic, 1988, pp. 252--286.

.... esponenziale dello spazio e del tempo di computazione sono all origine del limite di intrattabilita che si incontra in deduzione automatica (si veda [HU79] per una introduzione ai problemi di complessita 2 Per la descrizione di alcuni dimostratori automatici per logiche non standard si veda [SMDP88] 3 In questo articolo si suppone che il formalismo di rappresentazione sia la logica, nella maggior parte dei casi, del primo ordine. I risultati di Church e Turing hanno pero una portata assai piu generale, essendo validi per tutti i formalismi di potenza espressiva equivalente. 4 Il ....

P. Smets, E. H. Mandami, D. Dubois, and H. Prade. Non-Standard Logics for Automated Reasoning. academic press, 1988.

....only the given data, but also the associated uncertainty. The stochastic approach is a traditional way of dealing with uncertainty. However, it has been recognized that not all types of uncertainty can be dealt with within the stochastic framework. Various alternative approaches have been proposed (Smets, et al. 1988), fuzzy logic and set theory being one of them. Transparent (gray box) modeling and identification. Identification of dynamic systems from inputoutput measurements is an important topic of scientific research with a wide range of practical applications. Many real world systems are inherently ....

Smets, P., E.H. Mamdani, D. Dubois and H. Prade (Eds.) (1988). Non-Standard Logics for Automated Reasoning. Academic Press, London.

.... language of rst order predicate logic o ers sucient expressiveness for the representation of medical knowledge, although there is room for additional machinery, such 3 as meta level reasoning, Van Harmelen, 1991; Maes Nardi, 1988; Weyhrauch, 1980] and non standard logic, Lukaszewicz, 1990; Smets et al. 1988; Turner, 1984] From a medical point of view, there are several advantages linked with the logic engineering approach: Logic has a well de ned syntax and semantics, resulting in clearly de ned meanings of the represented medical knowledge in terms of the relationships among pieces of ....

Smets, P, Mamdani, A, Dubois, D and Prade, H (eds.), 1988. NonStandard Logics for Automated Reasoning, Academic Press, London.

.... His work remained hidden in the statistics literature until Glenn Shafer, one of Dempster s students, brought the material to a wider audience in his doctoral dissertation [11] The method has become popular, and the basic model has been extended in a number of directions in recent years [12], 13] 14] In this paper we propose another adaptation of the model. Our area of interest is reasoning under uncertainty when all the numerical information required by methods such as Dempster Shafer theory are not available, handling such a lack of information [8] 9] by using techniques from ....

....Section 8 concludes. 2. DEMPSTER SHAFER THEORY The basic idea of the theory is that numerical measures of uncertainty, termed basic probability masses, may be assigned to sets of hypotheses as well as individual hypotheses. Consider the following example, adapted from the work of Philippe Smets [12]. Mr Jones has been murdered. We know that the murderer was one of three Current address: Advanced Computation Laboratory, Imperial Cancer Research Fund, P.O. Box 123, Lincoln s Inn Fields, London, WC2A 3PX. Proceedings of the III Imacs International Workshop on Qualitative Reasoning and ....

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SMETS, Ph. - 'Belief functions', Non-standard logics for automated reasoning, Ed. Smets, Ph., Mamdani, E. H., Dubois, D. and Prade, H., Academic Press, London, 1988, p.253.

....in which the network entities were modeled as finite state machines. Today, the number of available approaches is much larger. Some of these approaches are probabilistic, others utilize traditional artificial intelligence paradigms and others apply principles defined in non conventional logics [Smets et al. 1988]. There are also approaches which adopt ad hoc methods to deal with the alarm correlation problem. 2.2.1 Rule Based Correlation Of the several approaches presented in the literature on alarm correlation in telecommunications systems, a significant part is constituted of variations around the ....

Philippe Smets, Abe Mamdani, Didier Dubois, and Henri Prade, editors. Non-Standard Logics for Automated Reasoning. Academic Press, London, England, 1988.

....Semantics, Spreadsheets, SLD resolution. 1 Introduction Extensions of classical logics such as temporal and modal logic have been successfully used as a formalism in many areas, including program specification and verification [22] temporal reasoning [33] and knowledge representation [34]. In temporal and modal logics, the meanings of formulas vary depending on an implicit context, and elements from different contexts can be combined through the use of contextual (temporal and modal) operators, not by explicit references to context (time, space or otherwise) Therefore these ....

P. Smets, A. Mamdani, D. Dubois, and H. Prade, editors. Non-Standard Logics for Automated Reasoning. Academic Press, 1988.

....u(A) jA Ug[f P a i 2U x i = 1g. See [9] for algorithms to determine redundant restrictions. If L u(A) is redundant, then the value u(A) may be calculated by linear programming from the nonredundant restrictions. A particular case of probability bounds are those used in the Theory of Evidence [20, 21]. A pair (Bel; P l) of belief plausibility intervals is a pair of mappings: Bel; P l : 2 U [0; 1] 13) such that there is a mapping m : 2 U [0; 1] the mass assignment) verifying, m( 0 X A U m(A) 1 (14) Bel(B) X A B m(A) P l(B) X A B 6= m(A) 15) A pair of ....

....to m given by: m(A) ffm 1 (A) 1 Gamma ff)m 2 (A) 8A U . 4 Discounting Experts Opinions In classical methods, the weights measuring experts realibility are used in the aggregation function. However, we shall take the approach of Dempster Shafer theory of evidence, acccording to which [21] the weights are used to transform expert opinions. If an expert is completely reliable, then his opinion is not changed. If an expert is not very reliable, then his opinion is transformed into a much less precise one. In general, we have a convex set of probabilities, H, and a measure of ....

[Article contains additional citation context not shown here]

Ph. Smets: Belief functions, Non-Standard Logics for Automated Reasoning, Ph. Smets, E.H. Mamdani, D. Dubois, H. Prade (eds.) Academic Press, London, 253286, 1988.

....We will show in section 5 how such a continuous valued rejection function such as confidence provides extra information about the agent s model, which can be used to compare and combine a number of agents. One may alternatively interpret confidence as an indication as to the amount of belief [20] that should be placed in the current approximation. Eqn. 6) states that reflection is the generation of an inner model of the reliability of the modeling process itself. It differs from the modeling processes described before in that there is no tuple (x; P (f ff (x) y) that is available from ....

....transformed into a posteriori probabilities p(kjx) that the class is k. Sets of classifiers can be combined using such probabilities [12, 5] but generally in a nonadaptive way. The parameters needed to be determined for the combination are fixed statistically or by using evidence [3] or belief [20]. In order that a team work, its constituting members should possess a minimum level of confidence reliability. Otherwise the areas where the answer from one agent should better be used than that of another will only rarely be found, and the desired synergy will not be attained. The objective of a ....

P. Smets, E. Mamdani, D. Dubois, and H. Prade, editors. Non-standard Logics for Automated Reasoning, chapter Belief Functions, pages 253--286. Academic Press, 1988.

....problem from a different perspective. An alternative approach to defining incidence functions from probability distributions is explored. The result gives a new way to check whether a numerical assignment on a set is a belief function and then calculate its mass functions when it is in DS theory [15, 16] and to construct probability spaces from inner measures (or lower bounds) of probabilities on the relevant propositional language sets [6] The paper is organized as follows. In section 2, a brief introduction to incidence calculus is given. The key features of incidence functions are discussed. ....

....last portion will only be contributed by its basic incidence set. 4 Extending the Result to DS Theory and Probability Spaces One of the meaningful extensions of this algorithm is to calculate the mass function in DS theory when A is the whole language set L(P ) and p is a belief function on it [15, 16] and, in particular, to recover the corresponding probability space when p is thought of as an inner measure (or a lower bound) on A in probability structures [6] One may suspect that bel is usually defined on a frame of discernment 2 in DS theory rather on a set of formulae. We will briefly ....

[Article contains additional citation context not shown here]

Smets,P., Belief functions, Non-Standard Logics for Automated Reasoning, ( Smets, Mamdani, Dubois and Prade Eds.), 253-286, 1988.

.... 32] and temporal databases [34, 95, 47] Or if we want to model knowledge and belief, why not use modal and or epistemic logics These logics have been extensively studied in philosophy and mathematics and applied in many problem domains (including those in artificial intelligence) with success [8, 57, 92, 93]. Therefore we advocate extending logic programming with temporal and modal logics (or with other non classical logics) whenever appropriate. Recently, several researchers have proposed extending logic programming with temporal logic, modal logic and other forms of intensional logic. There are a ....

P. Smets, A. Mamdani, D. Dubois, and H. Prade, editors. Non-Standard Logics for Automated Reasoning. Academic Press, 1988.

....from a different perspective. An alternative approach to defining incidence functions from probability distributions is explored. The result gives a new way to check whether an numerical assignment on a set is a belief function and then calculate its mass functions when it is true in DS theory [13, 14] and to construct probability spaces from inner measures (or lower bounds) of probabilities on the relevant propositional language sets [5] The paper is organized as follows. In section 2, a brief introduction to incidence calculus is given. The key features of incidence functions are discussed. ....

....by OE itself. Then the last portion will only be contributed by its basic incidence set. 4 Extending the Result to DS Theory One of the meaningful extensions of this algorithm is to calculate the mass function in DS theory when A is the whole language set L(P ) and p is a belief function on it [13, 14] and, in particular, to recover the corresponding probability space when p is thought of as an inner measure (or a lower bound) on A in probability structures [5] One may suspect that bel is usually defined on a frame of discernment 1 in DS theory rather on a set of formulae. We will briefly ....

[Article contains additional citation context not shown here]

Smets,P., Belief functions, Non-Standard Logics for Automated Reasoning, ( Smets, Mamdani, Dubois and Prade Eds.), 253-286, 1988.

....Teko alyss a on teorian merkitys ollut t arke a. T allaista merkityst a voidaan pit a a preskriptiivisen a, mik ali korostetaan sit a, miten asiat tulisi tehd a, tai deskriptiivisen a, mik ali kuvataan miten asiat on tehty. Ep astandardeja logiikoita voi tarkastella kummastakin n ak okulmasta (ks. [Smets et al. 1988, vii] Ep astandardit logiikat voidaan jakaa karkeasti numeerisiin ja ei numeerisiin eli symbolisiin formalismeihin. Symbolisia logiikoita ovat mm. modaalilogiikka, autoepisteeminen logiikka, intuitionistinen logiikka, temporaalilogiikka, dynaaminen 15 16 2. EP ASTANDARDIT LOGIIKAT TEKO ....

....muodostaa ainoastaan yl a ja alarajat. K ayt ann on tilanteissa huomioonotettava asia on my os informaation luotettavuus, joka kuvaa informaation virhemahdollisuutta. Virhemahdollisuus voi toisinaan olla per aisin ep aluotettavasta tietol ahteest a. Toinen numeerinen formalismi on uskomusfunktiot [Smets, 1988]. Teoria on kvantitatiivinen, ja se eroaa kahdella tavalla todenn ak oisyysteoriasta. Se koskee henkil okohtaisia, subjektiivisia uskomuksia, eik a todenn ak oisyysteorian objektiivisia todenn ak oisyyksi a. Toisaalta se kertoo enemm an ep at aydellisest a tiet amyksest a. Vastakohtana sek a ....

[Article contains additional citation context not shown here]

Smets, P., E. H. Mamdani, D. Dubois ja H. Prade (toim.): Non-standard logics for automated reasoning Academic press, London 1988.

....tree verifying this criterion will be declared as a leaf. The problems of overfitting and tree pruning are not considered in this paper. 3 Belief function theory 3.1 Basic concepts In the following, we shall briefly recall some of the basics of the belief function theory. Details can be found in [26, 33, 38]. Let # be a finite non empty set including all the elementary events related to a given problem. In the present context, # is a set of classes, and the elementary events are the possible classes. These events are assumed to be exhaustive and mutually exclusive. Such set # is classically called ....

....impact of the two pieces of evidence. This rule, denoted by # # , is defined by [39] m 1 # #m 2 ) A) X B,C##:B#C=A m 1 (B) m 2 (C) 14) The conjunctive rule can be seen as an unnormalized Dempster s rule of combination. This latter, denoted by #, deals with the closed world assumptions [33], and is defined as [26] m 1 #m 2 ) A) K. X B,C##:B#C=A m 1 (B) m 2 (C) 15) where K 1 = 1 X B,C##:B#C=# m 1 (B) m 2 (C) 16) and (m 1 #m 2 ) #) 0 (17) K is called the normalization factor. 2. The disjunctive rule: The dual of the conjunctive rule is the disjunctive rule of ....

P. Smets, Belief functions, Non Standard Logics for Automated Reasoning. Smets Ph., Mamdani A., Dubois D. and Prade H. (Editors) Academic Press, London pp 253-286, 1990.

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Smets,P., Belief functions, Non-Standard Logics for Automated Reasoning, ( Smets, Mamdani, Dubois and Prade Eds.), 253-286, 1988.

No context found.

P. Smets, E. H. Mamdani, D. Dubois and H. Prade, Non-Standard Logics for Automated Reasoning, Academic Press, 1988.

No context found.

Smets, Ph, Mamdani, E. H., Dubois, D. and Prade, H.Non-standard logics for automated reasoning, Academic Press, London, 1988.

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Smets, P., Mamdani, A., Dubois, D. and Prade, H., eds. (1988). NonStandard Logics for Automated Reasoning. Academic Press, London.

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