Characterizing downwards closed, strongly first order, relativizable dependencies

In Team Semantics, a dependency notion is strongly first order if every sentence of the logic obtained by adding the corresponding atoms to First Order Logic is equivalent to some first order sentence. In this work it is shown that all nontrivial dependency atoms that are strongly first order, downwards closed, and relativizable (in the sense that the relativizations of the corresponding atoms with respect to some unary predicate are expressible in terms of them) are definable in terms of constancy atoms. Additionally, it is shown that any strongly first order dependency is safe for any family of downwards closed dependencies, in the sense that every sentence of the logic obtained by adding to First Order Logic both the strongly first order dependency and the downwards closed dependencies is equivalent to some sentence of the logic obtained by adding only the downwards closed dependencies

Prioritized Repairing and Consistent Query Answering in Relational Databases

A consistent query answer in an inconsistent database is an answer obtained in every (minimal) repair. The repairs are obtained by resolving all conflicts in all possible ways. Often, however, the user is able to provide a preference on how conflicts should be resolved. We investigate here the framework of preferred consistent query answers, in which user preferences are used to narrow down the set of repairs to a set of preferred repairs. We axiomatize desirable properties of preferred repairs. We present three different families of preferred repairs and study their mutual relationships. Finally, we investigate the complexity of preferred repairing and computing preferred consistent query answers.Comment: Accepted to the special SUM'08 issue of AMA

On the equivalent descriptions of family of functional dependencies in the relational data model

The family of functional dependencies (FDs) was introduced by E.F. Codd. Equivalent descriptions of family of FDs play essential rules in the design and implementation of the relation datamodel. It is known [1,3,4,5,7,8,12,13,15] that closure operations, meet-semilattices, families of members which are not intersections of two other members give the equivalent descriptions of family of FDs. i.e. they and family of  FDs determine each other uniquely. These equivalent description were  successfully applied to find many desirable properties of  functional dependency. This paper introduces the concept of maximal family of attributes. We prove that this family is an equivalent description of family of FDs. The concept of nonredundant family of attributes is also introduced in this paper. We present some characterizations and desirable properties of these families

Zipf and Heaps laws from dependency structures in component systems

Complex natural and technological systems can be considered, on a coarse-grained level, as assemblies of elementary components: for example, genomes as sets of genes, or texts as sets of words. On one hand, the joint occurrence of components emerges from architectural and specific constraints in such systems. On the other hand, general regularities may unify different systems, such as the broadly studied Zipf and Heaps laws, respectively concerning the distribution of component frequencies and their number as a function of system size. Dependency structures (i.e., directed networks encoding the dependency relations between the components in a system) were proposed recently as a possible organizing principles underlying some of the regularities observed. However, the consequences of this assumption were explored only in binary component systems, where solely the presence or absence of components is considered, and multiple copies of the same component are not allowed. Here, we consider a simple model that generates, from a given ensemble of dependency structures, a statistical ensemble of sets of components, allowing for components to appear with any multiplicity. Our model is a minimal extension that is memoryless, and therefore accessible to analytical calculations. A mean-field analytical approach (analogous to the "Zipfian ensemble" in the linguistics literature) captures the relevant laws describing the component statistics as we show by comparison with numerical computations. In particular, we recover a power-law Zipf rank plot, with a set of core components, and a Heaps law displaying three consecutive regimes (linear, sub-linear and saturating) that we characterize quantitatively

Supporting 'design for reuse' with modular design

Engineering design reuse refers to the utilization of any knowledge gained from the design activity to support future design. As such, engineering design reuse approaches are concerned with the support, exploration, and enhancement of design knowledge prior, during, and after a design activity. Modular design is a product structuring principle whereby products are developed with distinct modules for rapid product development, efficient upgrades, and possible reuse (of the physical modules). The benefits of modular design center on a greater capacity for structuring component parts to better manage the relation between market requirements and the designed product. This study explores the capabilities of modular design principles to provide improved support for the engineering design reuse concept. The correlations between modular design and 'reuse' are highlighted, with the aim of identifying its potential to aid the little-supported process of design for reuse. In fulfilment of this objective the authors not only identify the requirements of design for reuse, but also propose how modular design principles can be extended to support design for reuse

Family-specific scaling laws in bacterial genomes

Among several quantitative invariants found in evolutionary genomics, one of the most striking is the scaling of the overall abundance of proteins, or protein domains, sharing a specific functional annotation across genomes of given size. The size of these functional categories change, on average, as power-laws in the total number of protein-coding genes. Here, we show that such regularities are not restricted to the overall behavior of high-level functional categories, but also exist systematically at the level of single evolutionary families of protein domains. Specifically, the number of proteins within each family follows family-specific scaling laws with genome size. Functionally similar sets of families tend to follow similar scaling laws, but this is not always the case. To understand this systematically, we provide a comprehensive classification of families based on their scaling properties. Additionally, we develop a quantitative score for the heterogeneity of the scaling of families belonging to a given category or predefined group. Under the common reasonable assumption that selection is driven solely or mainly by biological function, these findings point to fine-tuned and interdependent functional roles of specific protein domains, beyond our current functional annotations. This analysis provides a deeper view on the links between evolutionary expansion of protein families and the functional constraints shaping the gene repertoire of bacterial genomes.Comment: 41 pages, 16 figure

Polygraphs for termination of left-linear term rewriting systems

We present a methodology for proving termination of left-linear term rewriting systems (TRSs) by using Albert Burroni's polygraphs, a kind of rewriting systems on algebraic circuits. We translate the considered TRS into a polygraph of minimal size whose termination is proven with a polygraphic interpretation, then we get back the property on the TRS. We recall Yves Lafont's general translation of TRSs into polygraphs and known links between their termination properties. We give several conditions on the original TRS, including being a first-order functional program, that ensure that we can reduce the size of the polygraphic translation. We also prove sufficient conditions on the polygraphic interpretations of a minimal translation to imply termination of the original TRS. Examples are given to compare this method with usual polynomial interpretations.Comment: 15 page