G.Coletti. Coherent numerical and ordinal probabilistic assessments, IEEE Trans. on Systems, Man, and Cybernetics, 24(12) (1994), 1747-1754.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....consequence, and computing tight logically entailed intervals. Another important approach to probabilistic reasoning with conditional constraints, which has been extensively explored in the area of statistics, is based on the coherence principle of de Finetti and suitable generalizations of it [8, 12, 13, 14, 15, 27, 28, 29, 50], or on similar principles that have been adopted for lower and upper probabilities [49, 54] Two important aspects of dealing with uncertainty in this framework are (i) checking the consistency of a probabilistic assessment, and (ii) the propagation of a given assessment to further uncertain ....

G. Coletti. Coherent numerical and ordinal probabilistic assessments. IEEE Trans. Syst. Man Cybern., 24(12):1747--1754, 1994.

....the family of uncertain quantities at hand has often no particular algebraic structure. In such cases, a general approach is obtained by using (conditional and or unconditional) probabilistic constraints, based on the coherence principle of de Finetti and suitable generalizations of it [BIA 00, COL 94, COL 96, COL 99a, COL 99b, GIL 95b, GIL 02, GIL 94, SCO 96] or on similar principles that have been adopted for lower and upper probabilities [PEL 98, WAL 91] Two important aspects in dealing with uncertainty are: i) checking the consistency of a probabilistic assessment, and (ii) the ....

....of a set of logical constraints and a mapping an interval M e F6 EG kw PI y is g coherent iff there exists a coherent PI yh yhj E #QSy E . We recall a characterization of g coherence due to Gilio [GIL 95b] equivalent results have been obtained by Coletti [COL 94] Given a set of logical constraints and a set of conditional events zXJ 2b2 E L z the set of all mappings that assign each JN H QYz a member of P ij H: Q z is satisfiable, and 4 Dij TJK Q Gc E E : ....

COLETTI G., "Coherent numerical and ordinal probabilistic assessments", IEEE Trans. Syst. Man Cybern., vol. 24, num. 12, 1994, p. 1747--1754. Journal of Applied Non-Classical Logics. Volume X - n

....quantities at hand has often no particular algebraic structure. In such cases, a general approach is obtained by using (conditional and or unconditional) probabilistic constraints, based on the coherence principle of de Finetti and suitable generalizations of it (Biazzo and Gilio [2] Coletti [10], Coletti and Scozzafava [11, 14, 13] Gilio [22, 23] Gilio and Scozzafava [24] and Scozzafava [34] or on similar principles which have been adopted for lower and upper probabilities (Pelessoni and Vicig [33] Vicig [35] and Walley [36] Two important aspects in dealing with uncertainty are: ....

....solvable: # ### ### ### # # ### # ### ### ### # # ### ### # # # (1) are defined by # ### # # are defined as follows for ### ####### ### # # # # ## # ## # # . 2) Equivalent results have been obtained by Coletti [10]. Let # # be a g coherent imprecise probability assessment on a set of conditional events . The imprecise probability on a conditional event is called a g coherent consequence of # for every g coherent precise probability assessment tight g coherent ....

G. Coletti. Coherent numerical and ordinal probabilistic assessments. IEEE Transactions on Systems, Man, and Cybernetics, 24(12):1747--1754, 1994.

.... Probabilistic reasoning under coherence is an approach to reasoning with conditional constraints, which has been extensively explored especially in the field of statistics, and which is based on the coherence principle of de Finetti and suitable generalizations of it (Biazzo and Gilio [8] Coletti [13], Coletti and Scozzafava [14, 16, 15] Gilio [31, 32] Gilio and Scozzafava [33] and Scozzafava [57] or on similar principles that have been adopted for lower and upper probabilities (Pelessoni and Vicig [56] Vicig [60] and Walley [61] Indeed, in probabilistic logic under coherence, ....

....assessment consists of a set of logical an interval 4 6 7 8j 4 with 6: is g coherent iff a coherent precise probability assessment k 9 for 92 . We recall a characterization of g coherence due to Gilio [31] equivalent results have been obtained by Coletti [13]. Given a set of logical constraints and a set of conditional events G Q Q X the set of all mappings that associate with each ( a member of G ) such that (i) qb Z L1 93 is satisfiable, and (ii) s ) ....

G. Coletti. Coherent numerical and ordinal probabilistic assessments. IEEE Trans. Syst. Man Cybern., 24(12):1747--1754, 1994.

....that both birds and ostriches have legs, and that birds (resp. ostriches) fly with a probability of at least 0.95 (resp. at most 0. 05) Another important approach to probabilistic reasoning with conditional constraints is based on the coherence principle of de Finetti and generalizations of it [7, 11, 12, 13, 14, 27, 28, 29, 54], or on similar principles that have been adopted for lower and upper probabilities [51, 57] The main tasks in this framework are checking the consistency of a probabilistic assessment, and the propagation of a given assessment to further conditional events. In coherence based probabilistic ....

G. Coletti. Coherent numerical and ordinal probabilistic assessments. IEEE Trans. Syst. Man Cybern., 24(12):1747--1754, 1994.

.... of these schemes build on quantitative information such as belief networks [Pearl, 1988] and undirected graphical models [Whittaker, 1990] others build on partial numerical specifi cations, allowing for interval rather than point prob abilities [Breese and Fertig, 1991; Coletti et al. 1991; Coletti, 1994; van der Gaag, 1991] or for order of magnitude estimates [Goldszmidt and Pearl, 1992] Yet other schemes are purely qualitative in nature, such as qualitative probabilistic networks [Wellman, 1990] Also non probabilistic schemes have been proposed, each addressing a specific type of uncertainty, ....

Giulianella Coletti. Coherent numer- ical and ordinal probabilistic assessments. IEEE Transactions on Systems, Man, and Cybernetics, 24(12):1747-1754, December 1994.

....Moreover, the family of uncertain quantities at hand has often no particular algebraic structure. In such cases, a general approach is obtained by using (conditional and or unconditional) probabilistic constraints, based on the coherence principle of de Finetti and suitable generalizations of it [5, 8, 9, 10, 11, 20, 21, 22, 37], or on similar principles that have been adopted for lower and upper probabilities [36, 41] Two important aspects in dealing with uncertainty are: i) checking the consistency of a probabilistic assessment, and (ii) the propagation of a given assessment to further uncertain quantities. Another ....

.... and a mapping that assigns each QO an interval : z E . We say is g coherent iff there exists a coherent precise probability assessment = We recall a characterization of g coherence due to Gilio [20] equivalent results have been obtained by Coletti [8]. Given a set of logical constraints and a set of conditional events TH 1 c 1 C the set of all mappings that assign each HT GY QO a member of 8 ]NP k 8mn eG Q ] is satisfiable, and 3 ]mn UHI Q F L . For such ....

G. Coletti. Coherent numerical and ordinal probabilistic assessments. IEEE Trans. Syst. Man Cybern., 24(12):1747--1754, 1994.

....consequence, and computing tight logically entailed intervals. Another important approach to probabilistic reasoning with conditional constraints, which has been extensively explored in the area of statistics, is based on the coherence principle of de Finetti and suitable generalizations of it [8, 12, 13, 14, 15, 27, 28, 29, 49], or on similar principles that have been adopted for lower and upper probabilities [48, 53] Two important aspects of dealing with uncertainty in this framework are (i) checking the consistency of a probabilistic assessment, and (ii) the propagation of a given assessment to further uncertain ....

G. Coletti. Coherent numerical and ordinal probabilistic assessments. IEEE Trans. Syst. Man Cybern., 24(12):1747--1754, 1994.

....Moreover, the family of uncertain quantities at hand has often no particular algebraic structure. In such cases, a general approach is obtained by using (conditional and or unconditional) probabilistic constraints, based on the coherence principle of de Finetti and suitable generalizations of it [5, 8, 9, 10, 11, 19, 20, 21, 33], or on similar principles that have been adopted for lower and upper probabilities [32, 37] Two important aspects in dealing with uncertainty are: i) checking the consistency of a probabilistic assessment, and (ii) the propagation of a given assessment to further uncertain quantities. Another ....

....1] with l u. We say (L; A) INFSYS RR 1843 01 03 5 is g coherent iff there exists a coherent precise probability assessment (L; A ) on E such that A ( 2A( for all 2 E . We recall a characterization of g coherence due to Gilio [19] equivalent results have been obtained by Coletti [8]. Given a set of logical constraints L and a set of conditional events E = f 1 ; n g, denote by RL (E) the set of all mappings r that assign each i = i j i 2E a member of f i i ; i i ; i g such that (i) L [ fr( i ) j i 2 Eg is satisfiable, and (ii) r( i ) 6= i ....

G. Coletti. Coherent numerical and ordinal probabilistic assessments. IEEE Trans. Syst. Man Cybern., 24(12):1747--1754, 1994. INFSYS RR 1843-01-03 19

.... into approaches that use the model theoretic notion of logical entailment [20, 25, 3, 45, 76, 24, 29, 43, 65, 62, 59] which can be traced back to Boole [14] and those that are based on entailment under de Finetti s notion of coherence and its generalizations (see especially the work by Coletti [18] and Gilio [36] However, we will see that neither logical entailment nor the weaker notion of entailment under coherence show the behavior that is desired in reference class reasoning. A more promising idea takes inspiration from the similarity between the behavior of reference class reasoning ....

....K K S D = N Oo rQ 0 . Roughly speaking, we simply draw our conclusion from the union of S and . 4.2. ENTAILMENT UNDER COHERENCE We now describe entailment under de Finetti s notion of coherence, which has been recently generalized to imprecise probability assessments by Coletti [18] and Gilio [36] We first define entailment under coherence for conditional constraints. We then introduce its conditioning and its constraining variant for probabilistic default theories and knowledge bases. 4.2.1. Conditional Constraints In the sequel, we identify hji4kol f and acbsdgf with ....

Coletti, G.: 1994, `Coherent numerical and ordinal probabilistic assessments'. IEEE Trans. Syst. Man Cybern. 24(12), 1747--1754.

....quantities at hand has often no particular algebraic structure. In such cases, a general approach is obtained by using (conditional and or unconditional) probabilistic constraints, based on the coherence principle of de Finetti and suitable generalizations of it (Biazzo and Gilio [2] Coletti [10], Coletti and Scozzafava [11, 14, 13] Gilio [22, 23] Gilio and Scozzafava [24] and Scozzafava [34] or on similar principles which have been adopted for lower and upper probabilities (Pelessoni and Vicig [33] Vicig [35] and Walley [36] Two important aspects in dealing with uncertainty are: ....

....i j i ) l i ; u i ] for all i 2 f1; ng, and p ri and q ri are defined as follows for all r 2R and i 2 f1; ng: p ri (resp. q ri ) 8 : 1; if r j= i i 0; if r j= i i l i (resp. u i ) if r j= i . 2) Equivalent results have been obtained by Coletti [10]. Let (L; A) be a g coherent imprecise probability assessment on a set of conditional events E . The imprecise probability assessment [l; u] on a conditional event is called a g coherent consequence of (L; A) iff A ( 2 [l; u] for every g coherent precise probability assessment A on E ....

G. Coletti. Coherent numerical and ordinal probabilistic assessments. IEEE Transactions on Systems, Man, and Cybernetics, 24(12):1747--1754, 1994.

....quantities at hand has often no particular algebraic structure. In such cases, a general approach is obtained by using (conditional and or unconditional) probabilistic constraints, based on the coherence principle of de Finetti and suitable generalizations of it (Biazzo and Gilio [2] Coletti [9], Coletti and Scozzafava [10, 13, 12] Gilio [21, 22] Gilio and Scozzafava [23] and Scozzafava [33] or on similar principles which have been adopted for lower and upper probabilities (Pelessoni and Vicig [32] Vicig [34] and Walley [35] Two important aspects in dealing with uncertainty are: ....

....A( i j i ) l i ; u i ] for all i 2 f1; ng, and p ri and q ri are defined as follows for all r 2R and i 2 f1; ng: p ri (resp. q ri ) 8 : 1; if r j= i i 0; if r j= i i l i (resp. u i ) if r j= i . 2) Equivalent results have been obtained by Coletti [9]. Let (L; A) be a g coherent imprecise probability assessment on a set of conditional events E . The imprecise probability assessment [l; u] on a conditional event is called a g coherent consequence of (L; A) iff A ( 2 [l; u] for every g coherent precise probability assessment A on E ....

G. Coletti. Coherent numerical and ordinal probabilistic assessments. IEEE Transactions on Systems, Man, and Cybernetics, 24(12):1747--1754, 1994.

....Moreover, the family of uncertain quantities at hand has often no particular algebraic structure. In such cases, a general approach is obtained by using (conditional and or unconditional) probabilistic constraints, based on the coherence principle of de Finetti and suitable generalizations of it [5, 8, 9, 10, 11, 18, 19, 20, 31], or on similar principles which have been adopted for lower and upper probabilities [30, 35] Two important aspects in dealing with uncertainty are: i) checking the consistency of a probabilistic assessment; and (ii) the propagation of a given assessment to further uncertain quantities. Another ....

....by A( i j i ) l i ; u i ] for all i 2 f1; ng, and p ri and q ri are defined as follows for all r 2R and i 2 f1; ng: p ri (resp. q ri ) 8 : 1; if r j= i i 0; if r j= i i l i (resp. u i ) if r j= i . Equivalent results have been obtained by Coletti [8]. Let (L; A) be a g coherent imprecise probability assessment on a set of conditional events E . The imprecise probability assessment [l; u] on a conditional event is called a g coherent consequence of (L; A) iff A ( 2 [l; u] for every g coherent precise probability assessment A on E ....

G. Coletti. Coherent numerical and ordinal probabilistic assessments. IEEE Transactions on Systems, Man, and Cybernetics, 24(12):1747--1754, 1994.

.... approach based on linear programming, see also [14] 15] Boole s problem and its dual version, in the sense of linear programming, came up already in de Finetti work [5] in a more general setting, as a basic notion for the subjective probabilistic approach under the bet interpretation (see [4] [11] for recent developments) Given events E 1 ; Em with the relations that they satisfy, denote by v 1 ; v s , where s 2 n , all possible outcomes of such events, in other words all possible truth assignement v j : fX 1 ; Xn g f0; 1g which are compatible with the ....

Coletti G. (1994) Coherent Numerical and Ordinal Probabilistic Assessments. IEEE Trans. on Systems, Man, and Cybernetics, 24(12): 1747-1754.

....to check the consistency of (1) or to nd out its solutions. These techniques start from the well known result that, if (1) is consistent then there is some solution with at most n 1 non zero components. Also de Finetti s approach has been developed by many authors (see for example [4] 6] [7], 13] 20] 22] 23] 24] but they focused mainly on the probabilistic aspects and on its applications instead of the complexity problem. A rst attempt in this direction is in [2] where assessment on particular sets of events are investigated and characterized without the generation of ....

....b are real constants. Finally observe that our approach allows to symbolically manipulate the numerical values of the assessment p 1 ; pn (like in Example 62) This feature can be useful to deal with coherence problems for qualitative or mixed probability (see for example [3] 4] 5] [7]) This situation arises when the user is not able (or he she does not want) to represent his her uncertainty only by numerical values but also just assessing if he she believes one event more or less probable of some other ones. To give just an idea of this more general framework (for an ....

Coletti G (1994) Coherent Numerical and Ordinal Probabilistic Assessments. IEEE Trans. on Systems, Man, and Cybernetics, 24(12): 1747-1754.

....the end a particularized description of an actual implementation is given. 1 Introduction Probabilistic models based on partial assessments play a central role for the treatment of partial knowledge and they have a wide relevance in both unconditional and conditional frameworks (see for example [3, 4, 5, 6, 7, 11, 17, 19]) The approaches, in line with de Finetti s thought [9] require to assess the probabilistic assessment explicitly and directly on the relevant set of propositions events that can be equipped with logical constraints. Moreover, such assessments can be extended computing the lower and upper bounds ....

G.Coletti (1994) Coherent Numerical and Ordinal Probabilistic Assessments. IEEE Trans. on Systems, Man, and Cybernetics, 24(12), 1747-1754.

.... can be roughly divided into approaches that use the model theoretic notion of logical entailment [16, 21, 2, 40, 39, 20, 25, 38, 60, 59, 56] which can be traced back to Boole [11] and those that are based on entailment under de Finetti s notion of coherence (see especially the work by Coletti [14] and Gilio [31] However, we will see that neither logical entailment nor the weaker notion of entailment under coherence show the behavior that INFSYS RR 1843 00 02 3 is desired in reference class reasoning. A more promising idea takes inspiration from the similarity between the behavior of ....

....draw our conclusion from the union of KB and T . 4. 2 Entailment under Coherence We now focus on entailment under de Finetti s notion of coherence, which has been recently generalized to imprecise probability assessments (that is, essentially sets of strict conditional constraints) by Coletti [14] and Gilio [31] see also [9] After defining the notion of entailment under de Finetti s coherence for conditional constraints, we generalize to probabilistic default theories and knowledge bases. 4.2.1 Conditional Constraints In the sequel, we identify false and true with the real numbers 0 ....

G. Coletti. Coherent numerical and ordinal probabilistic assessments. IEEE Trans. Syst. Man Cybern., 24(12):1747--1754, 1994.

....a joint nitely additive probability, P , on the subsets of X T , such that its conditional previsions P (h(x; j ) and P (h(x; j x) represent respectively the two given families of conditional comparisons. Via coherence conditions, Coletti, Gilio and Scozzafava (1993 [10] Coletti (1994 [9]) and Vicig (1995 [58] treat the problem of consistency of a comparative conditional probability on an arbitrary set of pairs of events: the relation is represented by de Finetti s coherent conditional probability and allows conditioning on events 10 GIULIANA REGOLI which may have probability 0. ....

G. Coletti. Coherent numerical and ordinal probabilistic assessments. IEEE Transactions on Systems, Man and Cybernetics, 12:1747-1754, 1994.

....the sum of all Pr(A) with A 2 A B and A ) G. Pr is extended to conditional constraints by: Pr j= HjG) u 1 ; u 2 ] iff u 1 Delta Pr(G) Pr(GH ) u 2 Delta Pr(G) Note that conditional constraints characterize conditional probabilities of events, rather than probabilities of conditional events (Coletti, 1994; Gilio Scozzafava, 1994) Note also that Pr(G) 0 always entails Pr j= HjG) u 1 ; u 2 ] This semantics of conditional probability statements is also assumed by Halpern (1990) and by Frisch and Haddawy (1994) The notions of models, satisfiability, and logical consequence for conditional ....

Coletti, G. (1994). Coherent numerical and ordinal probabilistic assessments. IEEE Transactions on Systems, Man, and Cybernetics, 24 (12), 1747--1754.

....the sum of all Pr(A) with A 2 A B and A ) G. Pr is extended to conditional constraints by: Pr j= HjG) u 1 ; u 2 ] iff u 1 Delta Pr(G) Pr(GH ) u 2 Delta Pr(G) Note that conditional constraints characterize conditional probabilities of events, rather than probabilities of conditional events (Coletti, 1994; Gilio Scozzafava, 1994) Note also that Pr(G) 0 always entails Pr j= HjG) u 1 ; u 2 ] This semantics of conditional probability statements is also assumed by Halpern (1990) and by Frisch and Haddawy (1994) The notions of models, satisfiability, and logical consequence for conditional ....

Coletti, G. (1994). Coherent numerical and ordinal probabilistic assessments. IEEE Transactions on Systems, Man, and Cybernetics, 24 (12), 1747--1754.

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G.Coletti. Coherent numerical and ordinal probabilistic assessments, IEEE Trans. on Systems, Man, and Cybernetics, 24(12) (1994), 1747-1754.

No context found.

G. Coletti. Coherent numerical and ordinal probabilistic assessments. IEEE Trans. on Systems, Man, and Cybernetics, 24(12):1747-1754, 1994.

No context found.

Coletti, G.: 1994, `Coherent numerical and ordinal probabilistic assessments'. IEEE Trans. Syst. Man Cybern. 24(12), 1747--1754.

No context found.

Coletti G (1994) Coherent Numerical and Ordinal Probabilistic Assessments. IEEE Trans. on Systems, Man, and Cybernetics, 24(12): 1747-1754.

No context found.

G.Coletti (1994) Coherent Numerical and Ordinal Probabilistic Assessments. IEEE Trans. on Systems, Man, and Cybernetics, 24(12), 1747-1754.

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