Mathematical Foundations of Databases

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In this project the theoretical foundations of databases are being investigated through the use of discrete mathematics. Research is conducted toward two major subgoals, i.e. to: (1) Find conceptually simple set-theoretic and/or algebraic models of database issues and practices, especially those associated with the relational database model. Examples of such models are those for object histories, spreadsheets, sequential- data query languages, and nested relations. Such models are in contrast with the familiar logical and programming language models. (2) Use these models to address significant questions of database studies and possibly in other areas of computer science interest. Such questions are being suggested by either (a) the underlying database physical situation and design methodologies or (b) analytic considerations and the underlying mathematical formalism. Results of this research are expected to formulate a better understanding of current database concerns, as well as provide tools for examining and solving database management problems. For example, one line of activity is addressing the fundamental problem of data restructuring, i.e., what does it mean, how can it be accomplished, and what are the fundamental laws related to it.