Michael J. Maher. Equivalences of logic programs. In Jack Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 627--658. Morgan Kaufmann, Los Altos, CA, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....renaming is a substitution # for which there exists the inverse # 1 , such that ## 1 = # 1 # = #. A set equation E is unifiable, if there exists # such that, for all s = t in E, we have s# t#, and # is called a unifier of E. We let mgu(E) denote the most general unifier of the equation set E [41]. We write mgu( s 1 = t 1 , s n = t n , s # 1 = t # 1 , s # n = t # n ) to denote the most general unifier of the set of equations s 1 = s # 1 , t 1 = t # 1 , s n = s # n , t n = t # n . A conditional term rewriting system (CTRS for short) is a pair (#, is ....

M.J. Maher. Equivalences of Logic Programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 627--658. Morgan Kaufmann, Los Altos, Ca., 1988.

....symbols. Identity of syntactic objects is denoted by . A substitution is a mapping from the set of variables V to the set ( V ) By j s we denote the restriction of to the set of variables in the syntactic object s. Given a set of equations E, mgu(E) denotes the most general uni er of E [30]. A conditional term rewriting system (CTRS for short) is a pair ( R) where R is a nite set of reduction (or rewrite) rule schemes of the form ( C) 2 ( V ) 62 V and V ar( V ar( The condition C is a (possibly empty) sequence e 1 ; e n , n 0, of equations which ....

M.J. Maher. Equivalences of Logic Programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 627-658. Morgan Kaufmann, Los Altos, Ca., 1988.

....renaming is a substitution p for which there exists the inverse p l, such that pp 1 = p lp = e. A set equation E is unifiable, if there exists t9 such that, for all s = t in E, we have st9 tt9, and t9 is called a unifier of E. We let mgu(E) denote the most general unifier of the equation set E [40]. We write mgu( 1 = tl, n = tn , t , to denote the most general unifier of the set of equations t , n t 1 : t, n : n, tn : tin 81 81, A conditional term rewriting system (CTRS for short) is a pair (E, where T4 is a finite set of reduction (or rewrite) rule ....

M.J. Maher. Equivalences of Logic Programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 627-658. Morgan Kaufmann, Los Altos, Ca., 1988.

....a suitable notion of program equivalence serves as a correctness criterion for transformations between programs, e.g. in partial evaluation and deduction. Our concern is the problem of program equivalence in its generality, where the programs to be compared are independent from each other. [67] provides a systematic comparison of the relative strengths of various formulations of equivalence of logic programs. These formulations arise naturally from several formal semantics of logic programs. Maher does not study how to test for equivalence. The results may be extensible to constraint ....

M. J. Maher. Equivalences of logic programs. In Proceedings of Third International Conference on Logic Programming, Berlin, 1986. Springer.

....the operational predicates are facts. The (Completed) Resulting Set is thus MRS[CT=MRS. Given the above de nitions, the following proposition is easily proved: Proposition 3.1 The least Herbrand models of the two sets DT[TE and CRS[TE are equal. It is not possible to get a stronger equivalence [Ma86] of the two theories. Maps T P [Ll87] are in fact not equal for the two programs CRS[TE and DT[TE. Thus the subsumption equivalence does not hold, since the equality of maps T P is a prerequisite for that kind of equivalence. 4 Theory revision The standard application of EBG requires a complete, ....

Maher M.J. Equivalence of Logic Programs. Third Int. Conf. on Logic Programming, 1986.

....defined w.r.t. the language with the signature Sigma = fa=0; b=0g. Then M(P 1 ) M(P 2 ) fp(a) p(b)g, while C(P 1 ) fp(X) p(a) p(b)g and C(P 2 ) fp(a) p(b)g. 2 In case the signature contains infinitely many constants, the situation changes, as the following result due to Maher [9] shows. Theorem 4.3 Assume that Sigma contains infinitely many constants. Then C(P ) T rue(M(P ) Proof. We provide here an alternative, direct proof based on the theory of SLD resolution. The implication C(P ) T rue(M(P ) always holds, since M(P ) is a model of P . Take now A 2 T rue(M(P ....

M. J. Maher. Equivalences of Logic Programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 627--658. Morgan Kaufmann, Los Altos, Ca., 1988.

.... of logic programs the least Herbrand model semantics is not compositional wrt the union of programs (i.e. it is not OR compositional) If the observable is successful derivations, OR compositionality can be understood in logical terms since the set of all the (Herbrand) models is OR compositional [30] (and correct wrt successful derivations) The only OR compositional semantics correct wrt computed answers are described in [24, 9, 8] while all the other OR compositional semantics [26, 33, 31, 30, 23] are only correct wrt successful derivations. Clearly, compositionality wrt program ....

.... can be understood in logical terms since the set of all the (Herbrand) models is OR compositional [30] and correct wrt successful derivations) The only OR compositional semantics correct wrt computed answers are described in [24, 9, 8] while all the other OR compositional semantics [26, 33, 31, 30, 23] are only correct wrt successful derivations. Clearly, compositionality wrt program composition operators is a desirable property since it allows to define in a modular way and incrementally the semantics of structured programs. For example, a semantics compositional wrt a generalized composition ....

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M. J. Maher. Equivalences of Logic Programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 627--658. Morgan Kaufmann, Los Altos, Ca., 1988.

....as Failure. More detail (including proofs) may be found in [2] 5 Minimal Operational Equivalence As mentioned above, we may think of normal(P ) as a transformation of P which produces an equivalent program P 0 , in that every goal derivable from one is derivable from the other. Maher [9] has shown that there are several meaningful conceptions of equivalence between logic programs; one obvious such notion is to consider two programs P 1 and P 2 to be operationally equivalent if for every goal G, P 1 o G , P 2 o G. This may be thought of as treating the programs as two black ....

M.J. Maher, Equivalences of Logic Programs, in Foundations of Deductive Databases and Logic Programming 627-658, J. Minker (ed.), Morgan Kaufmann, 1988.

....and we have not included them here for the sake of clarity. More details of this extension (including proofs) may be found in [6] Note that the results above are expressed purely in terms of o , and so we think of the transformations given above as preserving operational equivalence. Maher [10] has shown that there are many natural notions of equivalence for logic programs, and in our context, another obvious notion of equivalence is equivalence with respect to I . Hence, a natural question to ask at this point is whether programs which are operationally equivalent are logically ....

M.J. Maher, Equivalences of Logic Programs, in Foundations of Deductive Databases and Logic Programming 627-658, J. Minker (ed.), Morgan Kaufmann, 1988.

....fine tuning is lost by our representation of logic programs by neural networks. However, passing to classes of programs with the same single step operator is something that is often done in the literature on semantics and in fact is exactly the notion of subsumption equivalence due to Maher, see [17]. Moreover, there exist uncountably many homeomorphisms : I P C; for example, every bijective mapping from BP to N gives rise to such a homeomorphism as observed in the paragraph preceeding Corollary 4.4. So there is a lot of flexibility in the choice of and therefore in how one embeds I P ....

Maher M: Equivalences of Logic Programs. In: Minker J (ed) Foundations of Deductive Databases and Logic Programming. Morgan Kaufmann Publ. Inc., Los Altos, 1988

.... property, it would be possible to show that P and Q are inequivalent in S 1 by showing that S 2 (P ) 6= S 2 (Q) For definite clause logic programs the translation property holds among the classical semantics, the Clark completion semantics and the least model semantics (see, for example, [15]) It was shown in [16] that if S 2 is the perfect model semantics, and under a certain condition on P and Q, the translation property holds. The property also holds between the classical semantics and the minimal model semantics. However, in general the translation property does not hold. One ....

M.J. Maher, Equivalences of Logic Programs, in: Foundations of Deductive Databases and Logic Programming, J. Minker (Ed), Morgan-Kaufmann, 627-658, 1988. 19

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M.J. Maher, Equivalences of Logic Programs, in: Foundations of Deductive Databases and Logic Programming, J. Minker (Ed), Morgan Kaufmann, 627--658, 1988.

....subsumption of facts. The next result follows quickly from the definitions. Proposition 4.8 If every rule of P 1 is subsumed by the rules of P 2 then T D P 1 T D P 2 . For logic programs there is the stronger result: T D P 1 T D P 2 iff every rule of P 1 is subsumed by some rule of P 2 [26]. However the link between this notion of subsumption and the ordering on functions T D P is not as direct for arbitrary constraint domains as it is for the Herbrand domain. The following example from [14] demonstrates the extra subtlety in other constraint domains. Example 4.9 Consider the ....

....of constraints by a constraint. This theorem provides one more property equivalent to the Independence of Negated Constraints. In contrast with the above containment problem, which needs Strong Compactness of the constraint domain to directly generalize the result for the Herbrand domain [26], expressiveness properties have no effect on the following result. Proposition 4.12 For every constraint domain (D; L) P 1 ] P 2 ] iff D j= P 1 P 2 Proof: For every program P we have: M is a model of P iff [ P ] M) M . Furthermore, every closure operator such as [ P ] is ....

M.J. Maher, Equivalences of Logic Programs, in: Foundations of Deductive Databases and Logic Programming, J. Minker (Ed), Morgan Kaufmann, 627-- 658, 1988.

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Michael J. Maher. Equivalences of logic programs. In Jack Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 627--658. Morgan Kaufmann, Los Altos, CA, 1988.

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M.J. Maher. Equivalences of logic programs. In J. Minker, editor, Deductive databases and logic programming, pages 627--658. Morgan Kaufmann, 1988.

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Maher, M.J. (1988). Equivalences of Logic Programs. In: Foundations of Deductive Databases and Logic Programming (J. Minker, Ed.). pp. 627-658. Morgan Kaufmann Publishers.

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M. Maher, Equivalences of logic programs, in Foundations of Deductive Databases and Logic Programming, Morgan Kaufman, pp.627-658, (1988).

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M. Maher, "Equivalences of logic programs", in: J. Minker (ed.) Foundations of deductive databases and logic programming, Morgan Kaufmann, pp.627-658, Los Altos, CA, 1988.

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M. J. Maher. Equivalences of logic programs. In Minker [21], pp. 627--658.

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M. J. Maher. Equivalences of Logic Programs. In Minker [15], pp. 627--658.

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Michael J. Maher. Equivalences of logic programs. In Jack Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 627-658. Morgan Kaufmann, Los Altos, CA, 1988.

No context found.

Michael J. Maher. Equivalences of logic programs. In Jack Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 627--658. Morgan Kaufmann, Los Altos, CA, 1988.

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M. J. Maher. Equivalences of logic programs. In Minker [21], pp. 627--658.

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M. J. Maher. Equivalences of logic programs. In Minker [17], pp. 627--658.

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M.J. Maher. Equivalences of Logic Programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 627--658. Morgan Kaufmann, Los Altos, Ca., 1988.

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