### Table 1: Summary of the existing information theories. General Probabilistic Possibilistic

### Table 1. Comparison of observed compositions with both possibilistic, extended possibilistic and probabilistic models (all ps lt;.0005).

"... In PAGE 3: ...ramework (e.g., negative predicted values). In order to reinforce the case against Possibility Theory, those measures were withdrawn from computation of the agreement between data and the probabilistic model. Results show that the probabilistic and possibilistic models both fitted the data ( Table1... ..."

### Table 1: Examples of static probabilistic combination strategies

"... In PAGE 10: ...resp., D4BD A8C3BUBC D4BE, D4BD A9C3BUBC D4BE), where C3BUBC is obtained from C3BU by replacing CP (resp., CQ) by CTBD (resp., CTBE). The static probabilistic combination strategies for the dependence informations in Figure 1 are shown in Table1... In PAGE 12: ... Recently, the prob- abilistic conjunction and disjunction strategies for ignorance, independence, positive correlation, negative correlation, and mutual exclusion have especially been discussed in [18] and [17]. To our knowledge, the strategies for the remaining dependence informations in Table1 have not been considered so far. 2.... In PAGE 12: ... For associative static or dynamic probabilistic disjunction strategies A8 and probabilistic pairs D4BDBN BM BM BM BN D4CZ with CZ AL BD, we write C4CXBECJBDBMCZCL D4CX to denote D4BD A8 A1 A1 A1 A8 D4CZ. The following proposition identifies some static probabilistic conjunction and disjunction strategies in Table1 that are commutative, associative, and distributive. Proposition 2.... In PAGE 29: ...INFSYS RR 1843-00-04 Table1 0: ProbView postulates for probabilistic combination strategies BOTTOMLINE D4BD AA D4BE AK D4BD AAD4CR D4BE D4BD A8 D4BE AL D4BD A8D4CR D4BE IGNORANCE D4BD AA D4BE AI D4BD AACXCV D4BE D4BD A8 D4BE AI D4BD A8CXCV D4BE IDENTITY D4BD AA D4BE AH D4BD, if CJD0BEBN D9BECL BP CJBDBN BDCL and CTBD CM CTBE is consistent D4BD A8 D4BE AH D4BD, if CJD0BEBN D9BECL BP CJBCBN BCCL ANNIHILATOR D4BD AA D4BE AH BR, if CJD0BEBN D9BECL BP CJBCBN BCCL D4BD A8 D4BE AH BQ, if CJD0BEBN D9BECL BP CJBDBN BDCL COMMUTATIVITY D4BD AA D4BE AH D4BE AA D4BD D4BD A8 D4BE AH D4BE A8 D4BD ASSOCIATIVITY B4D4BD AA D4BEB5 AA D4BF AH D4BD AA B4D4BE AA D4BFB5 B4D4BD A8 D4BEB5 A8 D4BF AH D4BD A8 B4D4BE A8 D4BFB5 MONOTONICITY D4BD AA D4BE AK D4BR BD AA D4BE, if CJD0BDBN D9BDCL AK CJD0BR BDBN D9BR BDCL D4BD A8 D4BE AK D4BR BD A8 D4BE, if CJD0BDBN D9BDCL AK CJD0BR BDBN D9BR BDCL In summary, these observations show that ProbView assumes a number of postulates that do not have any justification in probability theory. Moreover, as ProbView is missing a rigorous probabilistic background, it also ignores the important fact that there are combinations of probabilistic pairs D4BD BP B4CTBDBN CJD0BDBN D9BDCLB5 and D4BE BP B4CTBEBN CJD0BEBN D9BECLB5 with dependence information C3BU AI C3BUBRB4CTBDBN CTBEB5 that are unsatisfiable.... In PAGE 30: ...27 Table1 1: Comparison with ProbView Our Approach ProbView D4BD AAD0CX D4BE BP B4CTBD CM CTBEBN CJBMBHBN BMBICLB5 D4BD AAD4CR D4BE BP B4CTBD CM CTBEBN CJBMBEBN BMBICLB5 D4BD A8D0CX D4BE BP B4CTBD CN CTBEBN CJBMBHBN BMBJCLB5 D4BD A8D4CR D4BE BP B4CTBD CN CTBEBN CJBMBHBN BMBJCLB5 D4BD A9D0CX D4BE BP B4CTBD CM BMCTBEBN CJBCBN BMBECLB5 D4BD A9 D4BE BP B4CTBDBN CJBMBEBN BMBJCLB5 AACXCV B4BMCTBEBN CJBMBGBN BMBHCLB5 BP B4CTBD CM BMCTBEBN CJBCBN BMBHCLB5 which imprecise attributes are modeled as probability distributions over finite sets of values. Their approach assumes that key attributes are deterministic (have probability 1) and that non-key attributes in different relations are independent.... In PAGE 34: ...10 (sketch). The statements can be easily verified along the static probabilistic combination strategies shown in Table1 (see Proposition 2.9).... In PAGE 36: ...33 The claim is immediate for C3BU BP CUC1D2CSB4CPBN CQB5CV, since the static probabilistic combination strategies for independence are clearly computable in time C7B4BDB5 (see Table1 ; in fact, this holds for every C3BU there). Assume now C3BU BI BP CUC1D2CSB4CPBN CQB5CV.... ..."

### Table 10: ProbView postulates for probabilistic combination strategies

"... In PAGE 28: ...n [17], a probabilistic conjunction (resp., disjunction) strategy is defined as a function AA (resp., A8) that assigns any two probabilistic pairs D4BD BP B4CTBDBN CJD0BDBN D9BDCLB5 and D4BE BP B4CTBEBN CJD0BEBN D9BECLB5 a probabilistic pair B4CTBDCMCTBEBN CJD0BN D9CLB5 (resp., B4CTBD CN CTBEBN CJD0BN D9CLB5) such that the postulates BOTTOMLINE, IGNORANCE, IDENTITY, ANNIHILATOR, COMMUTATIVITY, ASSOCIATIVITY, and MONOTONICITY shown in Table10 hold for all probabilistic pairs D4BD BP B4CTBDBN CJD0BDBN D9BDCLB5, D4BR BD BP B4CTBDBN CJD0BR BDBN D9BR BDCLB5, D4BE BP B4CTBEBN CJD0BEBN D9BECLB5, and D4BF BP B4CTBFBN CJD0BFBN D9BFCLB5. Our rigorous foundation on probability theory now allows us to verify this axiomatic approach of Prob- View.... ..."

### Table 5: Dataset For Experiment 2a

"... In PAGE 23: ... The embedded theory is edge(X,Y), edge(Y,X), and each example has six other random facts. The dataset is shown in Table5 and Figure 4 shows the results of five different runs of LPMEME on the above dataset with 40 EM iterations each. The vertical axis shows the log of the likelihood of the probabilistic theory; the higher a value (less negative), the better the theory.... ..."

### Table 1. Three Families of Accounts of Inductive Inference Each of the three families will be discussed in turn in the three sections to follow and the entries in this table explicated.2 While most accounts of inductive inference fit into one of these three families, some span across two families. Achinstein apos;s (2001) theory of evidence, for example, draws on ideas from both hypothetical induction and probabilistic induction, in so far as it invokes both explanatory power and probabilististic notions. Demonstrative induction, listed here under inductive generalization, can also be thought of as an extension of hypothetical induction.

2003

"... In PAGE 3: ... As a result, it is possible to group virtually all accounts of induction into three families. This system is summarized in Table1 below. Each family is governed by a principle upon which every account in each family depends.... ..."

### Tables 3,4, and 5, respectively. Figures 7, 8, and 9 depict the intervals and the basic probability assignments graphically with a generalized cumulative distribution function (gcdf). This is the probabilistic concept of cumulative distribution function generalized to Dempster-Shafer structures where the focal elements (intervals) are represented on the x-axis and the cumulative basic probability assignments on the y-axis. A discussion of the generalization of some of the ideas from the theory of random variable to the Dempster-Shafer environment is discussed in [Yager, 1986].

2002

Cited by 18

### Table 1. Probabilistic techniques.

1994

Cited by 192

### Table 1: Probabilistic Approaches

"... In PAGE 2: ...3 Word-based, Probabilistic Approaches The third category assumes at most whitespace and punctuation knowledge and attempts to infer MWUs using word combination probabilities. Table1 (see next page) shows nine commonly-used probabilistic MWU-induction approaches. In the table, f and P signify frequency and probability XX of a word X.... ..."