## An Algebraic Framework For The Definition Of Compositional Semantics Of Normal Logic Programs (1994)

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### BibTeX

@MISC{Lucio94analgebraic,

author = {Paqui Lucio and Fernando Orejas and Elvira Pino and Elvira},

title = {An Algebraic Framework For The Definition Of Compositional Semantics Of Normal Logic Programs},

year = {1994}

}

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### Abstract

ion) Given two normal programs P1 and P2, the following three facts are equivalent: (i) Sem(P 1) = Sem(P 2) (ii) For every program P , Sem(P [ P 1) = Sem(P [ P 2) (iii) For every program P , MP[P1 = MP[P2 . Proof. It is enough to prove that (iii) implies (i), because the other implications are direct consequences of lemma 3.1 and theorem 5.1. Let us suppose that there exists a model A in Mod(; ;) such that F 1(A) 6= F 2(A), where F1 = Sem(P 1) and F2 = Sem(P 2). Then, we will show that there exists a program P such that MP[P1 6= MP[P2 . Let j 2 IN be the least layer such that F 1(A) + j 6= F 2(A) + j or F 1(A) j 6= F 2(A) j . Then we can consider two cases. First, if there exists the given level k 2 IN , and F 1(A) + j 6= F 2(A) + j , for some j < k, then F 1(B) 6= F 2(B) for all models B 2 Mod(; ;) such that A + j = B + i and A j 1 = B i 1 for some layer i. This is the case for the model B such that, for all i 2 IN : B + i = A + j B i = A j 1 In any other cas...