Y. Kawahara, Relational Set Theory, in Proceedings of Category Theory and Computer Science: 6th International Conference (CTCS 95), Lecture Notes in Computer Science, 953(1995) 44--58. Home/Search Document Details and Download
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A Representation Theorem for Relation Algebras: Concepts of.. - Furusawa (1997) (Correct)
....Tarski rule and a point axiom. Dedekind categories [2] or allegories [3] provide a categorical framework for relational calculus. In relational calculus one calculates with relations in an element free style, which makes relational calculus a very useful framework for the study of mathematics [7, 11] and theoretical computer science [8, 13] and also a useful tool for applications. Some element free formalisations of fuzzy relations and proofs of representation theorems were provided in [4, 5, 6] 1 2 Hitoshi Furusawa In this paper we consider relation algebras, which may not be Boolean, and ....
Y. Kawahara, Relational Set Theory, in Proceedings of Category Theory and Computer Science: 6th International Conference (CTCS 95), Lecture Notes in Computer Science, 953(1995) 44--58.
Algebraic Formalisations of Fuzzy Relations and Their.. - Furusawa (1998) (Correct)
.... BZ86, BM97, DOR94, DO96, HH86a, HH86b, HH87, Hut93, KM92, SS93] The relational calculus can be applied to not only the theory of programs but also databases [BDJM93, BBG 94, JOB94, OJB94] natural languages [Bot92a, Bot92b, Sup76, Sup79, Sup81] graphs [KM94, Miz93, MiK95, SS93] set theory [Kaw95, TG87] and so on. Orlowska described benefit from applying relational calculus to all sorts of scientific research areas in just one sentence in chapter 6 of [BKS97] so clearly: The main advantages of the relational formalisation are uniformity and modularity. Actually, once problems in these ....
....in the last proposition is called modular law in [FS90, BM97] in [Rig48, SS85, SS93] the Dedekind rule is given as QR S (Q SR [ R Q [ S) Since these formulae are equivalent, we use the name Dedekind formula for the shorter variant in this thesis. In relational calculus ( FS90, Kaw95, SS93] a function R : X Y is a univalent R [ R E Y and total EX RR [ relation. Note that R [ R E Y ( 8y; y 0 : R [ R(y; y 0 ) x2X (R [ y; x) R(x; y 0 ) E Y (y; y 0 ) 8x; y; y 0 : y 6= y 0 = R(x; y) R(x; y 0 ) 0 ; and EX RR [ 8x : R [ ....
Kawahara, Y.: Relational Set Theory, Lecture Notes in Comput. Sci., vol. 953, Springer, Berlin, 1995, pp. 44--58.
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