### Table 1: Axiomatic Notation of Schema Changes

2001

"... In PAGE 4: ... To capture this notion of association, we use the referential relationship ( !) that speci es when one type refers to another type; and a bi-directional relationship ( !) that speci es a referential relationship and its inverse. Table1 presents some of the notation and functions for querying the system dictionary as used in the paper. Table 2 lists the basic schema evolution operations that are supported by most OODBs [35, 48].... In PAGE 15: ... The SERF framework is based on the ODMG object model (Section 2) [13]. Hence, the theorem prover must be provided with a formal de nition of the ODMG object model, its invariants and the functionality of each of the system dictionary functions as described in Table1 . This model of computation is part of the setup of the theorem prover system and thus would be created once a-priori for the SERF system.... In PAGE 16: ... System Functions. Table1 describes some helper functions which are a part of the system de - nition. For the theorem prover, the behavior of each of these functions must be precisely de ned in a set language.... ..."

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### Table 1. The axiomatization APAL

2006

"... In PAGE 7: ... DEFINITION 8. The axiomatization APAL is given in Table1 . A formula is a theorem if it belongs to the least set of formulae containing all axioms and closed under the rules.... ..."

Cited by 1

### Table 1. The axiomatization APAL

2006

"... In PAGE 7: ... DEFINITION 8. The axiomatization APAL is given in Table1 . A formula is a theorem if it belongs to the least set of formulas containing all axioms and closed under the rules.... ..."

### Table 2. Axiomatic model

"... In PAGE 3: ... The interface I(t) of the tag t is the set of all its attributes (the union of N(t) and H(t)). Table2 shows how the sets described above can be represented in terms of Pe(t) and Ne(t), which are spec- ified by the author of the schema. All modifications of the schema can be also described in terms of these sets.... In PAGE 4: ...f applied to H5120 apos;. Table2 presents nine axioms that describe the schema in terms of Pe and Ne. The validity of these axi- oms implies that changes to the database schema are automatically supported (it is sufficient to make proper modifications to the sets Pe and Ne).... ..."

### Table 2: Analysis of the Fuzzy Rule Set

"... In PAGE 4: ... Table 1: Financial ratios used as evaluation characteristics (criteria) Codification Financial Ratios a 1 Net income/Gross profit a 2 Gross profit/Total assets a 3 Net income/Total assets a 4 Net income/Net worth a 5 Current assets/Current liabilities a 6 Quick assets/Current liabilities a 7 (Long term debt+current liabilities)/Total assets a 8 Net worth/(net worth+long term debt a 9 Net worth/Net fixed assets a 10 Inventories/Working capital a 11 Current liabilities/Total assets a 12 Working capital/Net worth RESULTS As already mentioned in the corporate bankruptcy prediction application, the most recent year is used to apply the knowledge-based fuzzy rule generator and develop the classifier that assigns the firms into the considered classes. The fuzzy rule generator produced the fuzzy rule base presented in Table2 . The rating index denotes the probability of the correctness of a rule.... ..."

### Table 2: Complete axiomatizations for the equivalences

2001

"... In PAGE 5: ... The results obtained for the equivalences are extended to the associated preorders as well. Acknowledgment My thanks to Tony Hoare for suggesting that the axioms of Table2 could be... In PAGE 61: ...61 17.2 Axiomatizing the equivalences In Table2 , complete axiomatizations can be found for twelve of the fteen semantic equivalences of this paper that di er on BCCSP. Axioms for singleton-failures, 2-nested simulation and possible- futures semantics are more cumbersome, and the corresponding testing notions are less plausible.... In PAGE 61: ... I is a unary operator that calculates the set of initial actions of a process expression, coded as a process expression again. Theorem 8 For each of the semantics O 2 fT; S; CT; CS; F; R; F T; RT; P W; RS; Bg two process expressions p; q 2 T(BCCSP) are O-equivalent i they can be proved equal from the axioms marked with \+ quot; in the column for O in Table2 . The axioms marked with \v quot; or \! quot; are valid in O-semantics but not needed for the proof.... In PAGE 62: ... So assume p vO q and (3) has been proven for all pairs of smaller expres- sions p0; q0 2 T(BCCSP). Provided TO contains at least the rst four axioms of Table2 , one has TO ` q = q + p i TO ` q = q + ap0 for every summand ap0 of p. Take O = B, so p vB q.... In PAGE 63: ... This law falls outside conditional equational logic, but it can be reformulated equationally by considering the two cases I(x) = 0 = I(y) and I(x) 6 = 0 6 = I(y). In the rst case it must be that TB ` x = 0 = y and hence the law follows from the third and fourth axiom of Table2 . In the second, observe that I(p) 6 = 0 i p has the form bq +r with b 2 Act.... In PAGE 65: ...2 gives TB ` == nnhnn == = == nnU(h)nn == for h 2 IH. 2 In Theorem 8 the fth and seventh axioms of Table2 may be replayed by a n X i=1 (bixi + biyi) = a n X i=1 (bixi + biyi) + a n X i=1 biyi and a n X i=1 bixi + a n X i=1 biyi = a n X i=1 (bixi + biyi): These laws derive the same closed substitution instances. Thus none of the axiomatizations require the operator I, or conditional equations.... In PAGE 66: ...The linear time { branching time spectrum I from the axioms marked with `+ apos; or `! apos; in the column for O in Table2 . It follows that the axioms marked with `v apos; are derivable.... In PAGE 66: ... 17.3 Axiomatizing the preorders In Table 3, complete axiomatizations can be found for the eleven preorders corresponding to the equivalences axiomatized in Table2 (there is no preorder for tree semantics (U)). This time prov- ability is de ned according to the standards of either rst-order logic with inequality or conditional inequational logic, i.... In PAGE 66: ... In the latter case, the axioms of Table 3 also constitute complete axiomatizations of the equivalences. The three axioms in Table 3 in which the inequality is written \v quot; represent strengthenings of the corresponding axioms in Table2 . The axioms in which the inequality is written \w quot; are merely slick reformulations of the corresponding axioms in Table 2, and could be replaced by them.... In PAGE 66: ... The three axioms in Table 3 in which the inequality is written \v quot; represent strengthenings of the corresponding axioms in Table 2. The axioms in which the inequality is written \w quot; are merely slick reformulations of the corresponding axioms in Table2 , and could be replaced by them. Unlike in Table 2, the characteristic axiom for the readiness preorder (the ninth) is now a substitution instance of the characteristic axiom for the failures preorder (the tenth).... In PAGE 66: ... The axioms in which the inequality is written \w quot; are merely slick reformulations of the corresponding axioms in Table 2, and could be replaced by them. Unlike in Table2 , the characteristic axiom for the readiness preorder (the ninth) is now a substitution instance of the characteristic axiom for the failures preorder (the tenth). Note that the characteristic axiom for the ready simulation preorder (the fth) derives all closed instances of I(x) = I(y) ) ax v a(x + y), which gives the fth axiom of Table 2.... In PAGE 66: ... Unlike in Table 2, the characteristic axiom for the readiness preorder (the ninth) is now a substitution instance of the characteristic axiom for the failures preorder (the tenth). Note that the characteristic axiom for the ready simulation preorder (the fth) derives all closed instances of I(x) = I(y) ) ax v a(x + y), which gives the fth axiom of Table2 . Hence all closed instances of the characteristic axiom for the ready trace preorder (the seventh) are derivable from the fth and eighth axioms.... In PAGE 68: ... Thus requirements 1 and 2(a) are ful lled. As (the closed instances of) the axioms for the respective equivalences from Table2 are easily derivable from the ones for the corresponding preorders from Table 3, requirement 2(b) is ful lled as well. Requirement 3, which used to follow from Theorem 6 and Propositions 16.... In PAGE 71: ...1 and the soundness of the axioms for BCCSP. \First ) quot; (completeness of the axioms for the equivalences): Let T 0 O be the set of axioms marked with \+ quot; in the column for O in Table2 , but using a Pn i=1 bixi + a Pn i=1 biyi = a Pn i=1(bixi + biyi) and a Pn i=1(bixi + biyi) = a Pn i=1(bixi + biyi) + a Pn i=1 biyi instead of the axioms involving the operator I. As Theorem 8 establishes completeness for closed terms only, it holds for T 0 O as well.... In PAGE 71: ... As Theorem 8 establishes completeness for closed terms only, it holds for T 0 O as well. Claim: If T 0 O ` p = Pm j=1 aqj for p; qj 2 T(BCCSP), then, modulo applications of the rst three axioms of Table2 , p has the form p = Pn i=1 api. Proof of the claim: As all axioms in T 0 O are equations, I may use induction on the proof of p = Pm j=1 aqj in equational logic.... In PAGE 78: ... Furthermore, the predicate p T(BCCSP quot;) is generated by the rules of Table 6. Now the complete axiomatizations of Table2 apply to BCCSP quot; p( quot;) p(p) p(p + q) p(q) p(p + q) Table 6: Rules for the termination predicate as well, provided that the occurrences of 0 are changed into , an axiom I( quot;) = quot; is added, and the characteristic axioms for CS and CT also get variants in which by + z resp. cy + v is replaced by quot;.... ..."

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### Table 1: Positions developed within the framework of different food sovereignty visions

2006

"... In PAGE 6: ...6 List of tables Table1 : Positions developed within the framework of different food sovereignty visions.... ..."

### Table 1 Meta-analysis framework of elements, guidelines and principles relevant to IMCoP development

"... In PAGE 6: ... Sustenance of the community begins the day it opens. Table1 offers the end process of the aggregation, analysis and synthesis of the elements of the six sets of guidelines offered by the literature. The guidelines were aggregated and categorised firstly into the areas of influence and action (design, implement, sustain) in which it was hypothesised they should be initiated.... In PAGE 6: ... The elements were then banded within each category about each of the shared definitional concepts of community (Hillery, 1955) they appeared most relevant to. These appear in descending order on Table1 as common ties, people, social interaction and place or area. Table 1 Meta-analysis framework of elements, guidelines and principles relevant to IMCoP development ... In PAGE 7: ... Decisions about further synthesis and reduction were passed over to the next phase, the IMCoP case study research where the elements can be reviewed under empirical conditions. It is conspicuous, when examining the distribution of elements in Table1 , that the existing guidelines focus more attention on the development rather than sustenance of the community. When examining the elements in each wave, it can be seen that each does offer influence and action for community developers and managers, but that the weight of attention appears to have been on design and implementation.... In PAGE 7: ... Through cross case analysis the research will determine the conditions sufficient for IMCoP development and the aspects of those conditions that community developers can influence. Rich text data has been gathered from various sources (interview, artifacts, Web site audit and publications) for each case and is being coded with the elements in Table1 , synthesized from the literature, to research the cases and interpret, evaluate and build on the framework. The case study research program will report its findings in July 2004 and will be available online at http://www.... ..."

### Table 5. Number of Solutions within x percent near optimal for 1000 Tasks Sets.

"... In PAGE 6: ... For each experiment, a workload of 10 tasks has been generated with an overload (120% utilization for each task set). Results shown in Table5 indicate the number of solutions within a certain per- cent close to optimal. For the two optimality criteria a near optimal solution (more than 91%) is obtained using AP(2).... In PAGE 7: ... Figure 4 shows that the complexity of the algorithm is relatively low even with a high degree of quality ( = 0:02). From the results shown in Table5 it can be concluded that for values of k 2, 92.5% and 100% of the solutions are 95%-close to optimal when the criterion is to maximize criti- cality and utilization, respectively.... ..."