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A file is relational if it stores a relation as defined by E. F. Codd [4]. Each tuple of a relational file represents a record. Each attribute of a relation is called an attribute of the relational file. File segmentation aims to minimize the average or the maximum number of segment accesses necessary to execute a query of a certain class. Most segmentation schemes deal with the class of equiselection queries. An equiselection query with a quantification condition A = V requests records with the value v as the value of the attribute A.

For A = C(T), the most significant bit is used to select either L(T) or R(T). Hence, in this case, we have Cavg(T,A) = ( l / 2 ) m { E v e { 0 j l } m _ 1 n a c c e ^ ( L ( T ) , ^ , v) + ^ve{o,i}m-inaccess(R(T), A, v)}. (12) Let vov' denote the concatenation oft; and v'. Since L(T) has no node a satisfying p{A(aj) > m, we obtain naccess{L{T),A,v) = naccess(L(T), Α,υ ο 0) naccess(L(T), A, v) = naccess(L(T), Α,νο 1). (13) Therefore, we have (l/2) m E i ; € { 0 j l } m-i naccess(L(T), A, v) = (l/2) m E vG{ o 5l} m-i(l/2){naccess{L(T), A, v o 0) + naccess(L(T), Α,υο 1)} = (l/2) m + 1 E v € { 0 ,i } m nacce^(L(T), A, v) (14) = {l/2)Cavg(L(T),A).

However, there are substantial differences in the treatment of negations: 1. In Miller's language, there is no way to retract an assertion once it has been added. The theory of the language is monotonie with respect to addition of modules. Uranus has denials to override assertions. Advances in Software Science and Technology 1, 1989 26 2. Miller's language can state exclusive facts by explicitly introducing contradiction. When the user asserts: contradiction :- p,q. p and q are mutually exclusive.

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