On the Use of F-transform on the Reduction of Concept Lattices

In this paper, we show that F-transform can be used to re- duce relational databases. Subsequently, we show that the respective concept lattice is reduced significantly as well. Moreover, we present a clarifying example of the procedure.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. The research was supported by the European Regional Development Fund by projects (CZ.1.05/1.1.00/02.0070) and (TIN12-39353- C04-04)

AsterixDB: A Scalable, Open Source BDMS

AsterixDB is a new, full-function BDMS (Big Data Management System) with a feature set that distinguishes it from other platforms in today's open source Big Data ecosystem. Its features make it well-suited to applications like web data warehousing, social data storage and analysis, and other use cases related to Big Data. AsterixDB has a flexible NoSQL style data model; a query language that supports a wide range of queries; a scalable runtime; partitioned, LSM-based data storage and indexing (including B+-tree, R-tree, and text indexes); support for external as well as natively stored data; a rich set of built-in types; support for fuzzy, spatial, and temporal types and queries; a built-in notion of data feeds for ingestion of data; and transaction support akin to that of a NoSQL store. Development of AsterixDB began in 2009 and led to a mid-2013 initial open source release. This paper is the first complete description of the resulting open source AsterixDB system. Covered herein are the system's data model, its query language, and its software architecture. Also included are a summary of the current status of the project and a first glimpse into how AsterixDB performs when compared to alternative technologies, including a parallel relational DBMS, a popular NoSQL store, and a popular Hadoop-based SQL data analytics platform, for things that both technologies can do. Also included is a brief description of some initial trials that the system has undergone and the lessons learned (and plans laid) based on those early "customer" engagements

Fuzzy inequational logic

We present a logic for reasoning about graded inequalities which generalizes the ordinary inequational logic used in universal algebra. The logic deals with atomic predicate formulas of the form of inequalities between terms and formalizes their semantic entailment and provability in graded setting which allows to draw partially true conclusions from partially true assumptions. We follow the Pavelka approach and define general degrees of semantic entailment and provability using complete residuated lattices as structures of truth degrees. We prove the logic is Pavelka-style complete. Furthermore, we present a logic for reasoning about graded if-then rules which is obtained as particular case of the general result