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N-Tuple Algebra as a Generalized Theory of Relations
Abstract
In ITs, analysis of heterogeneous information often necessitates unification of presentation forms and processing procedures for such data. To solve this problem, one needs a universal structure, which allows reducing various data and knowledge models to a single mathematical model with unified analysis methods. Such a universal structure is the relation, which is mainly associated with relational algebra. However, relations can model as different, at first glance, mathematical objects as graphs, networks, artificial intelligence structures, predicates, logical formulas, etc. Representation and analysis of such structures and models requires for more expressive means and methods than relational algebra provides. So, with a view to developing a general theory of relations, the authors propose n-tuple algebra (NTA) that allows for formalizing a wide set of logical problems (deductive, abductive, and modified reasoning; modeling uncertainties; and so on). This paper considers matters of metrization and clustering for NTA objects with ordered domains of attributes.
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