Composition and Inversion of Schema Mappings

In the recent years, a lot of attention has been paid to the development of solid foundations for the composition and inversion of schema mappings. In this paper, we review the proposals for the semantics of these crucial operators. For each of these proposals, we concentrate on the three following problems: the definition of the semantics of the operator, the language needed to express the operator, and the algorithmic issues associated to the problem of computing the operator. It should be pointed out that we primarily consider the formalization of schema mappings introduced in the work on data exchange. In particular, when studying the problem of computing the composition and inverse of a schema mapping, we will be mostly interested in computing these operators for mappings specified by source-to-target tuple-generating dependencies

Generative sound art as poeitic poetry for an information society

This paper considers computer music in relation to broader society and asks what algorithmic composition can learn from the metaphysical shift which is happening in the so-called information societies. This is explored by taking the mapping problem inherent in the use of extra- musical models in generative composition and presenting a simple generative schema which prioritises sound, ex- ploiting the generative potential of digital audio. It is sug- gested that the exploration of such models has more than aesthetic relevance and that the interdisciplinary nature of digital sound art represents a microcosm of an emerging reality, thereby constituting a poietic playground for com- ing to terms with the implications and challenges of the information age

Reconciling Equational Heterogeneity within a Data Federation

Mappings in most federated databases are conceptualized and implemented as black-box transformations between source schemas and a federated schema. This approach does not allow specific mappings to be declared once and reused in other situations. We present an alternative approach, in which data-level mappings are represented independent of source and federated schemas as a network between “contexts”. This compendious representation expedites the data federation process via mapping reuse and automated mapping composition from simpler mappings. We illustrate the benefits of mapping reuse and composition by using an example that incorporates equational mappings and the application of symbolic equation solving techniques

Optimization Model of Fuzzy Rule Based Expert System Using Max-Min Composition and Schema Mapping Translation

Abstract— Fuzzy Decision Making involves a process of selecting one or more alternatives or solutions from a finite set of alternatives which suits a set of constraints. In the rule-based expert system, the terms following in the decision making is using knowledge based and the IF Statements of the rule are called the premises, while the THEN part of the rule is called conclusion. Membership function and knowledge based determines the performance of fuzzy rule based expert system. Membership function determines the performance of fuzzy logic as it relates to represent fuzzy set in a computer. Knowledge Based in the other side relates to capturing human cognitive and judgemental processes, such as thinking and reasoning. In this paper, we have proposed a method by using Max-Min Composition combined with Genetic Algorithm for determining membership function of Fuzzy Logic and Schema Mapping Translation for the rules assignment.Keywords— Fuzzy Decision Making, Rule-Based Expert System, Membership Function, Knowledge Based, Max-Min Composition, Schema Mapping Translatio

XML data exchange under expressive mappings

Data Exchange is the problem of transforming data in one format (the source schema) into data in another format (the target schema). Its core component is a schema mapping, which is a high level specification of how such transformation should be done. Relational data exchange has been extensively studied, but exchanging XML data have been paid much less attention. The goal of this thesis is to develop a theory of XML data exchange with expressive schema mappings, extending a previous work using restricted mappings. Our mapping language is based on tree patterns that can use horizontal navigation and data comparison in addition to downward navigation. First we look at static analysis problems concerning a single mapping. More specif- ically, we consider consistency problems with different flavours. One such problem, for instance, asks if any tree has a solution under the given mapping. Then we turn to analyse the complexity of mapping themselves, i.e., recognising pairs of trees such that the one is mapped to the other. For both problems, we provide classifications based on sets of features used in the mappings. Second we investigate the composition of XML schema mappings. Generally it is hard, or rather simply impossible, to achieve closure under composition in XML settings unlike in relational settings. Nevertheless we identify a class of XML schema mappings that is closed under composition. Lastly we consider the problem of query answering. It is important to exchange data so that we can feasibly answer queries while it often leads to intractability. We identify the dividing line between tractable and intractable cases: answering queries with extended features is always intractable while tractability of answering simple queries can be retained in extended mappings

Cendrarsiana

Schema mappings have been extensively studied in the context of data exchange and data integration, where they have turned out to be the right level of abstraction for formalizing data interoperability tasks. Up to now and for the most part, schema mappings have been studied as static objects, in the sense that each time the focus has been on a single schema mapping of interest or, in the case of composition, on a pair of schema mappings of interest. In this paper, we adopt a dynamic viewpoint and embark on a study of sequences of schema mappings and of the limiting behavior of such sequences. To this effect, we first introduce a natural notion of distance on sets of finite target instances that expresses how "Close" two sets of target instances are as regards the certain answers of conjunctive queries on these sets. Using this notion of distance, we investigate pointwise limits and uniform limits of sequences of schema mappings, as well as the companion notions of pointwise Cauchy and uniformly Cauchy sequences of schema mappings. We obtain a number of results about the limits of sequences of GAV schema mappings and the limits of sequences of LAV schema mappings that reveal striking differences between these two classes of schema mappings. We also consider the completion of the metric space of sets of target instances and obtain concrete representations of limits of sequences of schema mappings in terms of generalized schema mappings, that is, schema mappings with infinite target instances as solutions to (finite) source instances

Composition with Target Constraints

It is known that the composition of schema mappings, each specified by source-to-target tgds (st-tgds), can be specified by a second-order tgd (SO tgd). We consider the question of what happens when target constraints are allowed. Specifically, we consider the question of specifying the composition of standard schema mappings (those specified by st-tgds, target egds, and a weakly acyclic set of target tgds). We show that SO tgds, even with the assistance of arbitrary source constraints and target constraints, cannot specify in general the composition of two standard schema mappings. Therefore, we introduce source-to-target second-order dependencies (st-SO dependencies), which are similar to SO tgds, but allow equations in the conclusion. We show that st-SO dependencies (along with target egds and target tgds) are sufficient to express the composition of every finite sequence of standard schema mappings, and further, every st-SO dependency specifies such a composition. In addition to this expressive power, we show that st-SO dependencies enjoy other desirable properties. In particular, they have a polynomial-time chase that generates a universal solution. This universal solution can be used to find the certain answers to unions of conjunctive queries in polynomial time. It is easy to show that the composition of an arbitrary number of standard schema mappings is equivalent to the composition of only two standard schema mappings. We show that surprisingly, the analogous result holds also for schema mappings specified by just st-tgds (no target constraints). This is proven by showing that every SO tgd is equivalent to an unnested SO tgd (one where there is no nesting of function symbols). Similarly, we prove unnesting results for st-SO dependencies, with the same types of consequences.Comment: This paper is an extended version of: M. Arenas, R. Fagin, and A. Nash. Composition with Target Constraints. In 13th International Conference on Database Theory (ICDT), pages 129-142, 201

Conditions for interoperability

Interoperability for information systems remains a challenge both at the semantic and organisational levels. The original three-level architecture for local databases needs to be replaced by a categorical four-level one based on concepts, constructions, schema types and data together with the mappings between them. Such an architecture provides natural closure as further levels are superfluous even in a global environment. The architecture is traversed by means of the Godement calculus: arrows may be composed at any level as well as across levles. The necessary and sufficient conditions for interoperability are satisfied by composable (formal) diagrams both for intension and extension in categories that are cartesian closed and locally cartesian closed. Methods like partial categories and sketches in schema design can benefit from Freyd’s punctured diagrams to identify precisely type-forcing natural transformations. Closure is better achieved in standard full categories. Global interoperability of extension can be achieved through semantic annotation but only if applied at run time