Duda, R. O., Hart, P. E., and Nilsson, N. J., 1976. Subjective bayesian methods for rulebased inference systems, Proc. National Computer Conference, AFIPS Conference Proceedings Vol. 45, 1075-1082.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....have received considerable attention for more than a decade. Several numerical and symbolic methods have been proposed for handling uncertain information (see [3] 10] 11] for details) The traditional numerical method is Bayesian probability. The well known expert system Prospector ([5]) is a typical example of using this method. Bayesian updating rule provides this method with the ability to revise a result in the light of new evidence. Generally speaking, Bayesian probability (subjective and conditional) is powerful for a certain class of problems, but not suitable for all ....

R.O. Duda, P.E. Hart, N.J. Nisson. Subjective Bayesian methods for rule-based inference systems. Proc. of the 1976 National Computer Conference (AFIPS) 45, 1976, pp.1075-1082.

....From DES Final Solutions Add a new case Case Matching is fail. Fig. 2. The principle of the case based approach This strategy consists of a transformation module, a normalization module, a case matching module, a case base, and a matching rule set. The strategy works in the PROBABILITY [1] inexact reasoning model. The area of uncertainties should be in the range [0, 1] The following is a brief introduction to each module and a case base. a) Transformation module If the range of uncertainties of a proposition is not in the range [0,1] the uncertainties of the proposition are ....

....2. The principle of the case based approach This strategy consists of a transformation module, a normalization module, a case matching module, a case base, and a matching rule set. The strategy works in the PROBABILITY [1] inexact reasoning model. The area of uncertainties should be in the range [0, 1]. The following is a brief introduction to each module and a case base. a) Transformation module If the range of uncertainties of a proposition is not in the range [0,1] the uncertainties of the proposition are transformed from that range to the range of [0, 1] by using the heterogeneous ....

[Article contains additional citation context not shown here]

R. Duda, P. Hart and N. Nilsson (1976). Subjective Bayesian Method for Rulebased Inference System, AFIPS, Vol. 45, pp. 1075-1082.

....disease (h i ) from a set of possible diseases fh 1 ; hn g, given a set of recorded symptoms fe 1 ; e m g. There have been several adaptations of probability theory within the literature of artificial intelligence including the odds likelihood formulation used by Prospector [28], and the cautious approach adopted by Inferno [74] Another is i j i j i j i j i j i j ae ae ae ae= Z Z Z Z j j j j Z Z Z old battery good battery ok radio ok lights ok battery charging alternator ok Fig. 2. Part of a probabilistic ....

R. O. Duda, P. E. Hart, and N. J. Nilsson. Subjective Bayesian methods for a rule-based inference system. In Proceedings of the National Computer Conference, pages 1075--1082, 1976.

....on a set. These sets are di erent in di erent models. For example, the set is the interval [ 1; 1] in the certainty factor model [52, 80, 44] used in a seminal expert system MYCIN [78] for diagnosing bacterial infections, while the set is the interval [0; 1] in the subjective Bayesian method [10] used in another seminal expert system PROSPECTOR [11] for determining site potential for mineral exploration. So, to achieve cooperation among these expert systems, the rst step is to transform the uncertainty of a proposition from one uncertain reasoning model to another if they use di erent ....

....rst one to reformulate the certainty factor model to understand its derivation from probability theory. However, the relationship between the certainty factor model and probability theory is still not clear. In the following we will make it clearer. According to probability theory, Duda et al. [10] showed the following two lemmas: Lemma 4 If H and S are conditionally independent given E and :E, that is, P (H jE S) P (H jE) 13) P (Hj:E S) P (Hj:E) 14) then P (H jS) P (EjS) P (H jE) P (Hj:E) P (Hj:E) 15) Formula (15) actually is the sequential propagation formula of ....

R.O. Duda, P.E. Hart, and N.J. Nillson, Subjective Bayesian Methods for RuleBased Inference Systems, AFIPS Conference Proceedings, 45, AFIPS Press, pp. 1075-1082, 1976.

.... of CF (H; E) CF (H; E) and CF (E;S) into the values of P (HjE) P (Hj:E) and P (EjS) respectively; then we use the following formula (5) to nd the values of P (HjS) nally, by using (1) we turn the value of P (HjS) into the values of CF (H; S) According to probability theory, Duda et al. [7] showed: Lemma 3: If H and S are conditionally independent given E and P (HjS) P (EjS) P (HjE) P (Hj:E) P (Hj:E) 5) In the following theorem, we give an important property of sequential propagation based on probability theory. 1. If CF (H; E) 0, then CF (H; S) 0 , CF (E;S) ....

.... S 2 ) CF (H; S 1 )CF (H; S 2 ) if CF (H; S 1 ) 0; CF (H; S 2 ) 0 CF (H;S1) CF (H;S2 ) 1 minfjCF (H;S1 )j;jCF (H;S2 )jg if CF (H; S 1 ) CF (H; S 2 ) 0: 22) 5 from the de nition formula (1) of the certainty factor, and the below parallel propagation formula (which is shown by Duda [7] according to probability theory) O(H jS 1 S 2 ) O(H jS 1 )O(H jS 2 ) O(H) 23) O(x) P (x) 1 P (x) 24) or directly P (H jS 1 S 2 ) P (H jS 1 )P (H jS 2 )P (H) P ( H jS 1 ) H jS 2 )P (H) P (H jS 1 )P (H jS 2 )P ( H) 25) However, Adams did not think the EMYCIN formula ....

R.O. Duda, P.E. Hart and N.J. Nillson (1976), \Subjective Bayesian Methods for Rule-Based Inference Systems," AFIPS Conference Proceedings, vol. 45, pp.1075-1082, AFIPS Press.

....early rule based expert systems as developed in the 1980s, the representation and manipulation of uncertain knowledge was accomplished by various ad hoc schemes. Typical examples of such schemes are the certainty factor calculus of Shortli e and Buchanan [4, 20] and the subjective Bayesian method [7]. At the time in particular the certainty factor model enjoyed much popularity, possibly due to its mathematical and computational simplicity. After the introduction of more expressive, and mathematically sound, probabilistic methods for the representation and manipulation of uncertainty the ....

R.O. Duda, P.E. Hart and N.J. Nilsson. Subjective Bayesian methods for rule-based inference systems. In: AFIPS Conference Proceedings of the 1976 National Computer Conference, 45, 1075-82.

....is required. Some alternative approaches have already been proposed for reasoning under uncertainty in rule based expert systems. Two of the most wellknown models of uncertain reasoning in rule based expert systems are those employed in the EMYCIN system [19, 17] and in the PROSPECTOR system [8]. One of the important issues associated with these models is whether the prior probabilities of the nodes in an inference network need to be supplied with values. If so, this is a very arduous task for human experts, because the prior probabilities are rarely available, and are dif cult to ....

....follows: if the value of the uncertainty measure of E is C(E; S) then by the rule E H it is concluded that the value of the uncertainty measure of H is C(H;S) ILN 1 ILN ILS (ILS P (E) P ( E) 8) Proof. From formulae (3) 4) and (5) we can easily derive formula (8) 2 Duda et al. [8] showed Lemma 3 If H and S are conditionally independent P (H jS) P (H jE)P (EjS) P (Hj:E) 1 P (EjS) 11) By Theorems 1 and 3, and Lemmas 2 and 3, we easily prove the following theorems. Note that for the sake of convenience in these theorems, we put u = 12) v = u ILS (13) ....

[Article contains additional citation context not shown here]

Duda, R.O., Hart, P.E. and Nillson, N.J., \Subjective Bayesian Methods for Rule-Based Inference Systems", AFIPS Conference Proceedings, Vol.45, AFIPS Press, pp. 1075-1082, 1976.

....Such a structure corresponds to a model of uncertain reasonings in a rule based expert system, and exposes some of the laws of uncertainty assessments and propagation in an inference network. In turn, this is followed by two sections in which we prove that EMYCIN s [13, 12] and PROSPECTOR s [6] uncertain reasoning models correspond to good NT algebras, and the constructive existence of any nite NT algebra. Finally, Section 6 summarizes this paper. 2 The Concept of Near Degree Space In reality, the uncertainties of evidence or rules may be assessed in terms of numbers, intervals, ....

....: xm . 3.6 NT Algebra De nition 10 The 9 tuple (L; I ; U ; C ; S ; P ; L ; is called a near topological algebra on (L; NT algebra on L for short. In this section, our discussion mainly refers to uncertain reasoning models like those used by EMYCIN [13] and PROSPECTOR [6]. We have known that in a rule based knowledge base, every rule is in a form of IF E THEN H That is, E H where E is a Boolean combination of E 1 ; En , which can be obtained by three ways: AND;OR and NOT . The three operators I , U and C are the operations of combining assessments ....

[Article contains additional citation context not shown here]

R. O. Duda, P. E. Hart, N. J. Nillson. Subjective Bayesian methods for rule-based inference systems. In: AFIPS Conference Proceedings 45, AFIPS Press, 1976, pp. 1075-1082.

....Va [0,1] aG =a. 53) Here is called the unit element of the uninorm. Clearly, when = 1, a uninorm is a T norm; when = 0, a uninorm is a T conorm. For (0, 1) Klement, Mesiar and Pap [38] showed that the following parallel combination formula in the PROSPECTOR uncertain rea soning model [26,44,46,48,50] is a uninorm operator: 1 )aa2 a ( a2 (1 )aa2 q (1 a0(1 (54) where (0, 1) is the unit element. Further, Yager and Rybalov [80] introduced the weighted uninorm aggrega tion: Definition 11 A weighted uninorm aggregation (WUA) of dimension n is a mapping Fwtya: 0, 1] x [0, ....

R.O. Duda, P.E. Hart, N.J. Nilsson, R. Reboh, J. Slocum, and G. Sutherland. Subjective Bayesian methods for rule-based inference systems. In AFIPS Conference Proceedings, volume 45, pages 1075-1082, 1976.

....early rule based expert systems as developed in the 1980s, the representation and manipulation of uncertain knowledge was accomplished by various ad hoc schemes. Typical examples of such schemes are the certainty factor calculus of Shortliffe and Buchanan [4,20] and the subjective Bayesian method [7]. At the time in particular the certainty factor model enjoyed much popularity, possibly due to its mathematical and computational simplicity. However, after the introduction of more expressive, and mathematically sound, probabilistic methods for the representation and manipulation of uncertainty ....

R.O. Duda, P.E. Hart, N.J. Nilsson, Subjective Bayesian methods for rule-based inference systems, AFIPS Conference Proceedings of the 1976 National Computer Conference 45 (1976) 1075-1082.

....a = a: 53) Here is called the unit element of the uninorm. 2 Clearly, when = 1, a uninorm is a T norm; when = 0, a uninorm is a T conorm. For 2 (0; 1) Klement, Mesiar and Pap [38] showed that the following parallel combination formula in the PROSPECTOR uncertain reasoning model [26,44,46,48,50] is a uninorm operator: a 1 a 2 = 1 )a 1 a 2 (1 )a 1 a 2 (1 a 1 ) 1 a 2 ) 54) where 2 (0; 1) is the unit element. Further, Yager and Rybalov [80] introduced the weighted uninorm aggregation: De nition 11 A weighted uninorm aggregation (WUA) of dimension n is a mapping FWUA ....

R.O. Duda, P.E. Hart, N.J. Nilsson, R. Reboh, J. Slocum, and G. Sutherland. Subjective Bayesian methods for rule-based inference systems. In AFIPS Conference Proceedings, volume 45, pages 1075-1082, 1976.

....disease (h i ) from a set of possible diseases fh 1 ; hn g, given a set of recorded symptoms fe 1 ; e m g. There have been several adaptations of probability theory within the literature of arti cial intelligence including the odds likelihood formulation used by Prospector [28], and the cautious approach adopted by Inferno [74] Another is = Z Z Z Z Z Z Z Z battery old battery good battery ok radio ok lights ok battery charging alternator ok Fig. 2. Part of a ....

R. O. Duda, P. E. Hart, and N. J. Nilsson. Subjective Bayesian methods for a rule-based inference system. In Proceedings of the National Computer Conference, pages 1075-1082, 1976.

....information is lost, unless the quality of the intermediate objects is stored somehow and influences the further abstraction process. We have been investigating several ways to propagate these quality measures during the abstraction, including fuzzy theory methods ( 13] probabilistic methods ([5], 11] 9] methods based on the reliability theory ( 4] Dempster Shafer Theory of evidence ( 6] and some heuristic methods (e.g. MYCIN model, 2] The most promising approach is presented in the next chapter. 4.1 Fuzzy Theory Methods Definitions Fuzzy logic is a well known and widely ....

R. O. Duda et al. Subjective bayesian methods for rule-based inference systems. In Proceedings of the National Computer Conference, pages 1075--1082, 1976.

....of A in the other examples. This makes it possible to apply Bayesian classification rules to examples in the normalized space, which will be the subject of the next subsection. 2. 2 Bayesian Rules and Odds Multipliers A Short Review In general, our approach learns PROSPECTOR style rules [DU76] that have the form: syntax: If E then (to degree S,N) H In the above, S and N are odds multipliers, measuring the sufficiency and necessity of H for E. In general, PROSPECTOR rules work with odds instead of probabilities, using the following conversion from probabilities to odds O(H) P ....

Duda, R.; Hart,P; Nilsson,J.: "Subjective Bayesian Methods for Rule-based Inference Systems", in Proc. National Computer Conference, pp. 1075-1082, 1976.

....early rule based expert systems as developed in the 1980s, the representation and manipulation of uncertain knowledge was accomplished by various ad hoc schemes. Typical examples of such schemes are the certainty factor calculus of Shortli e and Buchanan [4, 20] and the subjective Bayesian method [7]. At the time in particular the certainty factor model enjoyed much popularity, possibly due to its mathematical and computational simplicity. However, after the introduction of more expressive, and mathematically sound, probabilistic methods for the representation and manipulation of uncertainty ....

R.O. Duda, P.E. Hart and N.J. Nilsson, Subjective Bayesian methods for rule-based inference systems, in: AFIPS Conference Proceedings of the 1976 National Computer Conference, Vol. 45, 1976, pp. 1075-82.

....probabilistic conjunctions and disjunctions. 8 Related Work In this section we summarize the related work. 8. 1 Uncertainty in Logic Programming Logic knowledge bases have been extended to handle fuzzy modes of uncertainty since the early 70 s with the advent of the MYCIN and Prospector systems [18]. Shapiro was one of the first to develop results in fuzzy logic programming [47] Baldwin [2] was one of the first to introduce evidential logic programming and a language called FRIL. Van Emden [54] was the first to provide formal semantical foundations for logic programs that was later extended ....

R. O. Duda, P. E. Hart and N. J. Nilsson. (1976) Subjective Bayesian Methods for Rule-based Inference Systems, Proceedings of National Computer Conference, pp 1075--1082.

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Duda, R. O., Hart, P. E., and Nilsson, N. J., 1976. Subjective bayesian methods for rulebased inference systems, Proc. National Computer Conference, AFIPS Conference Proceedings Vol. 45, 1075-1082.

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R. Duda, R. Hart, N. Nilsson, "Subjective Bayesian Methods for Rule Based Inference Systems", Proc. 1976.

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R. Duda, R. Hart, N. Nilsson, "Subjective Bayesian Methods for Rule Based Inference Systems", Proc. 1976 Nat. Computer Conference, AFIPS, Vol 45, 1976.

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Duda, R.O., Hart, P.E., & Nilsson, N.J. Subjective Bayesian Methods for RuleBased Inference Systems. Technical Note 124, Stanford Research Institute, Artificial Intelligence Center, Menlo Park, CA, January, 1976.

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R. O. Duda, P. E. Hart and N. J. Nillson, \Subjective Bayesian methods for rulebased inference systems", in AFIPS Conference Proceedings, 45, (AFIPS Press, 1976) pp. 1075-1082.

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Hart P.E. Nilsson N.J. Duda, R.O. Subjective bayesian methods for rule-based inference systems. In Proceedings of the AIFPS National Computer Conference, volume 45, pages 1075-1082, 1976.

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Duda, R.O., P.E. Hart, and N.J. Nilsson. "Subjective Bayesian Methods for Rule-Based Inference Systems." Proceedings of the 1976.

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R. O. Duda, P. E. Hart and N.J. Nillson, "Subjective Bayesian methods for rule- based inference systems", in AFIPS Conference Proceedings, 45, (AFIPS Press, 1976) pp. 1075-1082.

No context found.

R. O. Duda, P. E. Hart and N. J. Nilsson. (1976) Subjective Bayesian Methods for Rule-based Inference Systems, Proceedings of National Computer Conference, pp 1075--1082.

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