| A Representation Theorem for Relation Algebras: Concepts of Scalar Relations and Point Relations (1997) | |||||||||||||||
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| This paper provides a proof of a representation theorem for homogeneous relation algebras by using concepts of scalar relations and point relations. Keywords : L-relations, relation algebras, scalar relations, point relations, representation theorem. 1 Introduction Just after Zadeh's work on fuzzy sets in 1965, Goguen [1] generalized the concepts of fuzzy sets and relations to taking values on arbitrary lattices, and also stressed the importance of relations as follows: The importance of relations is almost self-evident. Science is, in a sense, the discovery of relations between observables. Zadeh has shown the study of relations to be equivalent to the general study of systems (a system is a relation between an input space and an output space). The modern algebraic study of (binary) relations, namely relational calculus, was begun by Tarski; see [12] for details of the history of the study of Boolean relation algebras. In [10] Tarski proposed a formalisation of Boolean relation ... | |||||||||||||||
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