Order Sorted Quotient Algebra
نویسنده
چکیده
Let R be a non empty poset. One can verify that there exists an order sorted set of R which is binary relation yielding. Let R be a non empty poset, let A, B be many sorted sets indexed by the carrier of R, and let I1 be a many sorted relation between A and B. We say that I1 is os-compatible if and only if the condition (Def. 1) is satisfied. (Def. 1) Let s1, s2 be elements of the carrier of R. Suppose s1 ¬ s2. Let x, y be sets. If x ∈ A(s1) and y ∈ B(s1), then 〈x, y〉 ∈ I1(s1) iff 〈x, y〉 ∈ I1(s2). Let R be a non empty poset and let A, B be many sorted sets indexed by the carrier of R. A many sorted relation between A and B is said to be an order sorted relation of A, B if: (Def. 2) It is os-compatible. The following proposition is true (1) Let R be a non empty poset, A, B be many sorted sets indexed by the carrier of R, and O1 be a many sorted relation between A and B. If O1 is os-compatible, then O1 is an order sorted set of R. This work was done during author’s research visit in Bialystok, funded by the CALCULEMUS grant HPRN-CT-2000-00102.
منابع مشابه
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Let R be a non empty poset and let A, B be many sorted sets indexed by R. One can check that every many sorted relation between A and B which is os-compatible is also order-sorted. Let R be a non empty poset and let A be a many sorted set indexed by the carrier of R. An order sorted relation of A is an order sorted relation of A, A. Let S be an order sorted signature and let U1 be an order sort...
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