Mizar formalization of pp. 105–108 of [10] which continues [27]. We found a simplification for the proof of Corollary 1.15, in the last case, see the proof in the Mizar article for details. One can prove the following propositions: (1) Let X be a set and F be a finite family of subsets of X. Then there exists a finite family G of subsets of X such that G ⊆ F and G = F and for every subset g of ...

(1) Let L be a non empty reflexive transitive relational structure and x, y be elements of L. If x ≤ y, then compactbelow(x)⊆ compactbelow(y). (2) For every non empty reflexive relational structure L and for every element x of L holds compactbelow(x) is a subset of CompactSublatt(L). (3) For every relational structure L and for every relational substructure S of L holds every subset of S is a s...

(1) For every sup-semilattice L and for all elements x, y of L holds d−eL(↑x∩↑y) = xt y. (2) For every semilattice L and for all elements x, y of L holds ⊔ L(↓x∩↓y) = xu y. (3) Let L be a non empty relational structure and x, y be elements of L. If x is maximal in (the carrier of L)\↑y, then ↑x\{x}= ↑x∩↑y. (4) Let L be a non empty relational structure and x, y be elements of L. If x is minimal ...

This research-in-progress attempts to investigate how the relational elements in SLAs may potentially boost the success of sourcing relationships. The study provides insight into the development of relational governance through contractual governance over the course of a sourcing engagement, drawing upon relational exchange theory (RET). In particular, we wish to develop a set of possible guide...

With respect to multiple attribute decision making (MADM) problems in which the attribute values take the form of hesitant fuzzy elements, the traditional grey relational projection (GRP) method is extended to solve multiple attribute decision making problems under hesitant fuzzy environment. Based on the hesitant fuzzy decision matrix provided by decision makers, all feasible alternatives are ...

Extensible markup language (XML), a simplified version of standard generalized markup language (SGML), is designed to enable electronic text interchange in the Internet. XML documents have a rigorously described structure that may be analyzed by computers and easily understood by humans. Most current approaches store XML documents in file systems or in relational database systems. However, the ...

The market trends indicate that the next generation database technology will be dominated by object-relational systems. This shift to the new technology calls for visual modeling techniques to facilitate the design of object-relational database systems. Even though Unified Modeling Language (UML) is not currently equiped to manage this task, it can be extended for it.The paper defines design co...

Numerous researchers have proposed to use relational databases to store and query XML documents. In these systems, the elements selected by an XML query are returned to an application either by select mode or by reconstruct mode. For the reconstruct mode, the XML subtrees that are rooted at the selected elements need to be extracted and reconstructed from the relational storage of XML documents...

The need for interoperation and data exchange through the Internet makes XML a dominant standard language. Much work has been done on translating relational data into XML documents and vice versa. However, there is not an integrated method to combine them together as one technology for mass information transmission on the Internet. Furthermore, most XMLenabled database management systems can on...