Relational-product architectures for information processing

Abstract This paper outlines the motivation for and the basic concepts on which relational-product architectures are built. The examples of relational expressions given here were chosen rather to demonstrate the great power of unification of relational representations across the seemingly unrelated branches of information processing, than to give technical details, which can be found elsewhere. Because the relational products can also capture the classical, probabilistic, and fuzzy inference in a unified form, the architectures are particularly suitable for implementation of intelligent knowledge based and expert systems. Relational is used here in the sense of mathematical crisp and fuzzy relations. Codd's relational forms used in data-base design can be viewed as rather special subspecies of mathematical relations; their properties and construction can be also expressed by relational products. However, they are only very special instances of relational structures, and our approach presents a much wider repertory of structures and algorithms for their manipulation.