### Table 1. Additivity of uncertainty measures for credal sets under the concepts of strong independence and mass independence.

2005

Cited by 1

### Table 1: Extension of the Item relation

"... In PAGE 2: ... The domain of Type is a5 Eatable , Non- Eatable a6 . Table1 shows an extension of the Item relation. Query 1 What are the items whose weight is more than 50 and whose price is less than 50? .... In PAGE 8: ...0 WITH SUBSETS Shop sid CONSTRAINED BY sum(Distance) gt;30 and sum(Distance) lt;40 APPLY UNARY INTERSECTION sid Tuple 1 a45 a24 sid Tuple 1 a45 a9 1 a45 a9 1 a45 a25 a125a127a126 a60 a79 a123 a80a135a137 a60 a79 a80a135a138 a60 a49 a60a105a143a73a144a149a145a147a146a148a56a13a56a22a56a13a56 a129 a126 a60 a79 a123 a80a150a137 a60 a79 a80a150a138 a60 a49 a60 a45 a144a81a145a147a146a116a56a13a56a22a56a13a56 CA: sum(Distance)a113 30a141 sum(Distance)a110 40 CN: Ratinga113 4.0 Table1 0: Subset queries using Unary Union and Unary Intersection a)(SELECT * FROM Shop WHERE Rating gt;3.5 and Rating lt;4.... In PAGE 8: ...5a141 Ratinga110 4.7 CN2: Distancea113 14a141 Distancea110 19 Table1 1: Subset queries using Cross Union and Cross Intersection subset in the set of subsets. Examples 7 and 8 show example group by and having queries.... In PAGE 9: ...5 a141 sum(Rating)a110 7.0 CA2: sum(Weight)a113 60 a141 sum(Weight)a110 90 CN2: Pricea110 30 Table1 2: Subset query using cross cartesian product SELECT * FROM Item, Shop, Available WHERE Price lt;30 WITH SUBSETS Item sid,Shop sid CONSTRAINED BY Item.ItemId = Available.... In PAGE 9: ...5 a141 sum(Rating)a110 7.0 CA2: sum(Weight)a113 60 a141 sum(Weight)a110 90 CN2: Pricea110 30 Table1 3: The Available relation and the Subset Query using Cross Join Maximal and minimal subsets: There will be some applications which require maximal or min- imal subsets (in terms of cardinality) that sat- isfy a given set of constraints. For specifying maximal(minimal) subset constraint, the relational algebra operator a128 a49 ( a154 a49 ) is used.... In PAGE 10: ...FROM Item WHERE Pricea155 40 and Pricea156 70 WITH SUBSETS Item sid CONSTRAINED BY sum(Weight) gt;500 GROUP BY Type sid Type sum(Price) min(Weight) 1 Non-Eatable 120 150 1 Eatable 105 35 2 Non-Eatable 120 150 2 Eatable 150 20 a87a89a123a116a142 a137 a60 a114a55a123a116a157a116a158a103a159a20a160 a60 a79a124a123 a80a150a137 a60 a79 a80a150a138 a60 a49 a60a161a139 a36a10a140a8a53 a56a22a56a13a56a13a56a22a56 PA: sid,Type,sum(Price),min(Weight) CA: sum(Weight)a113 500 CN: Pricea155 40 a141 Pricea156 70 Table1 4: Subset Query using Group By SELECT sid,Type,sum(Price),min(Weight) FROM Item WHERE Pricea155 40 and Pricea156 70 WITH SUBSETS Item sid CONSTRAINED BY sum(Weight) gt;500 GROUP BY Type Having sum(Price) lt;110 sid Type sum(Price) min(Weight) 1 Eatable 105 35 a87 a123a148a142 a137 a60 a114 a123a148a157a81a158a103a159a20a160a103a162 a163 a80 a60 a79 a123 a80a135a137 a60 a79 a80a135a138 a60 a49 a60a86a139 a36a10a140a8a53 a56a13a56a13a56a22a56a13a56 PA: sid,Type,sum(Price),min(Weight) HC: sum(Price)a110 110 CA: sum(Weight)a113 500 CN: Pricea155 40 a141 Pricea156 70 Table 15: Subset Query using Group By and Having SELECT a31a32a31a32a31 FROM a31a32a31a32a31 WHERE a31a32a31a32a31 WITH SUBSETS lt;table gt; lt;sid gt;,a31a32a31a32a31 , lt;table gt; lt;sid gt; [CONSTRAINED BY lt;cond gt;,a31a32a31a20a31 , lt;cond gt;] [[UNARY UNION]| [UNARY INTERSECTION]] [[GROUP BY a31a20a31a32a31 ] [HAVING a31a20a31a32a31 ]] SQ(CROSS UNION| CROSS INTERSECTION)SQ (where SQ is a subset SQL query). personalized queries [6, 4, 39, 30, 36, 33, 10, 16], developing the relational algebra and SQL for user preferences [32, 17, 2, 21, 35, 29, 26, 27, 9, 8, 42, 41, 20, 28, 43], processing queries on set- oriented attributes in object relational databases [38, 37], nding top-K results when multiple pref- erence functions are provided [12, 14, 13, 15, 5], joining multiple ranked inputs [34, 23] and nd- ing top-K results of joins on multiple inputs [24] are some of the efforts the authors are aware of in this direction.... In PAGE 10: ...FROM Item WHERE Pricea155 40 and Pricea156 70 WITH SUBSETS Item sid CONSTRAINED BY sum(Weight) gt;500 GROUP BY Type sid Type sum(Price) min(Weight) 1 Non-Eatable 120 150 1 Eatable 105 35 2 Non-Eatable 120 150 2 Eatable 150 20 a87a89a123a116a142 a137 a60 a114a55a123a116a157a116a158a103a159a20a160 a60 a79a124a123 a80a150a137 a60 a79 a80a150a138 a60 a49 a60a161a139 a36a10a140a8a53 a56a22a56a13a56a13a56a22a56 PA: sid,Type,sum(Price),min(Weight) CA: sum(Weight)a113 500 CN: Pricea155 40 a141 Pricea156 70 Table 14: Subset Query using Group By SELECT sid,Type,sum(Price),min(Weight) FROM Item WHERE Pricea155 40 and Pricea156 70 WITH SUBSETS Item sid CONSTRAINED BY sum(Weight) gt;500 GROUP BY Type Having sum(Price) lt;110 sid Type sum(Price) min(Weight) 1 Eatable 105 35 a87 a123a148a142 a137 a60 a114 a123a148a157a81a158a103a159a20a160a103a162 a163 a80 a60 a79 a123 a80a135a137 a60 a79 a80a135a138 a60 a49 a60a86a139 a36a10a140a8a53 a56a13a56a13a56a22a56a13a56 PA: sid,Type,sum(Price),min(Weight) HC: sum(Price)a110 110 CA: sum(Weight)a113 500 CN: Pricea155 40 a141 Pricea156 70 Table1 5: Subset Query using Group By and Having SELECT a31a32a31a32a31 FROM a31a32a31a32a31 WHERE a31a32a31a32a31 WITH SUBSETS lt;table gt; lt;sid gt;,a31a32a31a32a31 , lt;table gt; lt;sid gt; [CONSTRAINED BY lt;cond gt;,a31a32a31a20a31 , lt;cond gt;] [[UNARY UNION]| [UNARY INTERSECTION]] [[GROUP BY a31a20a31a32a31 ] [HAVING a31a20a31a32a31 ]] SQ(CROSS UNION| CROSS INTERSECTION)SQ (where SQ is a subset SQL query). personalized queries [6, 4, 39, 30, 36, 33, 10, 16], developing the relational algebra and SQL for user preferences [32, 17, 2, 21, 35, 29, 26, 27, 9, 8, 42, 41, 20, 28, 43], processing queries on set- oriented attributes in object relational databases [38, 37], nding top-K results when multiple pref- erence functions are provided [12, 14, 13, 15, 5], joining multiple ranked inputs [34, 23] and nd- ing top-K results of joins on multiple inputs [24] are some of the efforts the authors are aware of in this direction.... In PAGE 11: ...a80a135a137 a60 a79 a80a135a138 a60 a49 a60a86a139 a36a10a140a8a53 a56a13a56a22a56 CA: count(sid)a155 4a141 count(sid)a156 5a141 sum(Weight)a113 190 CN: Type= Eatable SELECT * FROM Item WHERE Type= quot;Eatable quot; WITH SUBSETS Item sid CONSTRAINED BY sum(Weight) gt;190 and count(sid) gt;=4 and count(sid) lt;=5 Table1 6: Subset query using cardinality constraint a79a124a123 a80a135a137 a60 a128 a49 a60 a79 a80a150a138 a60a86a139 a36a10a140a8a53 a56a13a56a22a56 CA: sum(Weight)a113 175a141 sum(Weight)a110 200 CA: Type= Eatable SELECT * FROM Item WHERE Type= quot;Eatable quot; WITH SUBSETS Item sid MAXIMAL CONSTRAINED BY sum(Weight) gt;175 and sum(Weight) lt;200 Table 17: Subset query using maximal set constraint eral model for complex values and languages for it. The main result of the [1] is that the domain- independent calculus, the safe calculus, the alge- bra and the logic-programming oriented language have the equivalent expressive power.... In PAGE 11: ...a80a135a137 a60 a79 a80a135a138 a60 a49 a60a86a139 a36a10a140a8a53 a56a13a56a22a56 CA: count(sid)a155 4a141 count(sid)a156 5a141 sum(Weight)a113 190 CN: Type= Eatable SELECT * FROM Item WHERE Type= quot;Eatable quot; WITH SUBSETS Item sid CONSTRAINED BY sum(Weight) gt;190 and count(sid) gt;=4 and count(sid) lt;=5 Table 16: Subset query using cardinality constraint a79a124a123 a80a135a137 a60 a128 a49 a60 a79 a80a150a138 a60a86a139 a36a10a140a8a53 a56a13a56a22a56 CA: sum(Weight)a113 175a141 sum(Weight)a110 200 CA: Type= Eatable SELECT * FROM Item WHERE Type= quot;Eatable quot; WITH SUBSETS Item sid MAXIMAL CONSTRAINED BY sum(Weight) gt;175 and sum(Weight) lt;200 Table1 7: Subset query using maximal set constraint eral model for complex values and languages for it. The main result of the [1] is that the domain- independent calculus, the safe calculus, the alge- bra and the logic-programming oriented language have the equivalent expressive power.... ..."

### Table 9. Tests of Common Consequence Independence Type 3 (Internet D)

"... In PAGE 17: ...1, also in the direction previously observed in the literature (Wu amp; Gonzalez, 1998). Choices 6 and 14 of Table9 create the Type 3 (Table 4) common consequence condition, created by shifting the common branch from the lowest to the highest consequence (.8 to win $0 is changed to .... In PAGE 24: ...1. Choices 14 and 10 in Table9 provide a test of upper cumulative independence (Birnbaum amp; Navarrete, 1998). Gambles S and T have been created from a and b by changing a common branch of .... In PAGE 27: ...49 upper tail independence in Internet E. This model predicts a reversal between 14 and 10 in Table9 , violating upper cumulative independence in Internet D. Although the percentages in Choices 19 and 10 do not fall below 50% as predicted by TAX with prior parameters, these shifts in choice percentages in Tables 8 and 9 are significant and in the direction predicted.... ..."

### Table 8. Tests of Common Consequence Independence Type 2 (Internet D)

"... In PAGE 17: ...39 middle consequence, is consistent with the findings of Wu and Gonzalez (1996; 1998). In Choices 11 and 13 of Table8 , probability is shifted from a middle consequence to a higher consequence, labeled Type 2 in Table 4. The difference in choice percentages between Choices 11 and 13 is statistically significant, z = 12.... In PAGE 24: ... These results thus leave few descriptive decision theories standing. Choices 13 and 19 in Table8 create a test of upper tail independence, a property tested by Wu (1994). Upper tail independence is a combination of comonotonic branch independence, coalescing, and transitivity.... In PAGE 26: ... Both predict reversals between 7 and 18 and between 18 and 12 in Table 7. Both predict the reversal between Choices 11 and 13 in Table8 , and both predict the reversal between Choices 6 and 14 in Table 9. The TAX model predicts violations of stochastic dominance, coalescing, upper cumulative independence, and upper tail independence.... In PAGE 26: ... The TAX model predicts violations of stochastic dominance, coalescing, upper cumulative independence, and upper tail independence. The TAX model (based on median parameters estimated in Internet A) predicts a reversal of preference between Choices 13 and 19 in Table8 , violating Table 13. Test of Upper Tail Independence (Internet E) Choice No.... ..."

### Table 13: Independence of Own Past Choices Hypothesis Tests

1996

"... In PAGE 24: ... The next step of the hypothesis testing exercise is to examine speci c types of serial correlation: namely, the dependence of a player apos;s action upon his own previous action and on that of his opponent. Table13 presents the results of hypothesis tests of the dependency of players apos; choices on their own previous choice. A speci cation that incorporates the independence of one apos;s choice and his own previous choice can be made by eliminating the terms of equation (4) that capture the interaction of a choice and its lagged value.... ..."

Cited by 4

### Table 13. Test of Upper Tail Independence (Internet E)

"... In PAGE 25: ...333), predicts a reversal of preference in this case, consistent with the majority choice. Table13 shows results from Internet E of another test of Upper Tail Independence, similar to a test by Wu (1994). According to RDU, a person should prefer T f S if and only if f f e.... In PAGE 27: ... The TAX model correctly predicts violations of stochastic dominance and reversals of preference due to event-splitting (as in Table 11) observed in Internet A and B. It also correctly predicts the reversals of preference in Table 12 produced by event splitting (and contrary to monotonicity) and it correctly predicts the violation of upper tail independence in Table13 in Internet E. Thus, the configural weight, TAX model accounts for effects observed that violate any form of RDU model.... ..."

### Table-1 It is worthy noting here that we are just considering system networks as a simple language for describing certain types of choices that are available in the construction/specification of a complex (linguistic) object. Thus, we are deliberately ignoring the linguistic motivations and components required in a full Systemic Grammar. For instance, the so called realization rules, will only be alluded to in the Section 3 as a way for possible extensions of this specification language. In other words, we are stressing the logical semantics of these constructs.

### Table 10. Attributes and levels used in the choice modelling surveys

in Contents

2000

"... In PAGE 38: ... Selection of attribute levels was constrained by the biophysical attributes of the two study areas and management possibilities for RNV, and informed by feedback from focus group and pre- test participants. The attributes and levels used in the CM surveys are shown in Table10 . Each choice set comprised three options.... ..."

### Table 1: Logic functions which can be implemented by a logic module.

"... In PAGE 5: ... the structure for this logic module. A large number of logic functions can be implemented by using an appropriate subset of the inputs and tying the remaining inputs of a logic module high or low as shown in Table1 . Each logic module of DLB can be used independently for random logic implemen- tation.... ..."