J. S. Sheperdson. SLDNF--Resolution with Equality. Journal of Automated Reasoning, 8:297--306, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....investigated in [18] as a negative literal occurs in the body of a clause. On the other hand, it also does not belong to the class of programs investigated in e.g. 2] as our program contains the equational theory AC1. Thus, our program falls into a class which has recently been investigated in [28]. Section 4 focuses on models which assign to operators which can be used to build up multisets. Section 5 introduces SLDENF resolution as SLDNF resolution extended by a unification algorithm for an equational theory. Section 6 shows how SLDENF resolution can be used as a sound and ....

....algorithm is known [13, 29] The programs are carefully specified such that the need for AC1 unification is localized within calls to subgoals of the form s = AC1 t or s AC1 t , whereas all other subgoals can be solved by applying the usual unification procedure. Following the ideas of [28], SLDENF resolution is like SLDNF resolution [6] if the selected literal is not of the form s = AC1 t or s AC1 t . If the selected literal is of the form s = AC1 t and s and t are AC1 terms, then the AC1 unification algorithm in [13, 29] is called, which either returns a minimal complete ....

[Article contains additional citation context not shown here]

J. S. Sheperdson. SLDNF--Resolution with Equality. Journal of Automated Reasoning, 8:297--306, 1992.

....theorem proving with equality [18] They generalize the notions of a unifier and a most general unifier, respectively, for the case of built in equational theories. In logic programming, E unifiers were introduced in [13] The complete sets of unifiers in logic programming have been considered in [9, 6, 7, 11, 19, 20]. All these papers except [6, 7] considered restricted classes of logic programs with equality. Despite different formulations, these restricted programs can be characterized as pairs (P ; E) where E is an equational theory (a set of equations) and P is a logic program where equality can only ....

J.C. Sheperdson. SLDNF-resolution with equality. Journal of Automated Reasoning, 8:297--306, 1992. 11

....the rest of axioms does not contain positive occurrences of equality. Equational logic programs are defined by this restriction as a pair hP; Ei, where P is a logic program without positive occurrences of equality, and E is a set of equality facts in [JLM 84, GM 86] or facts and rules [Hol 89, She 92] Jaffar et al. defined SLDE resolution as the procedural interpretation of such a program. An extension of SLD resolution called SLDE resolution has been proposed in [GR 86, GR 89] Completeness of SLDE resolution was only proved for well behaved programs, which are exactly equational ....

J.C. Sheperdson. SLDNF-resolution with equality. Journal of Automated Reasoning, 8:297--306, 1992.

....theorem proving with equality [17] They generalize the notions of a unifier and a most general unifier, respectively, for the case of built in equational theories. In logic programming, E unifiers were introduced in [12] The complete sets of unifiers in logic programming have been considered in [8, 5, 6, 10, 18, 19]. All these papers except [5, 6] considered restricted classes of logic programs with equality. Despite different formulations, these restricted programs can be characterized as pairs (P; E) where E is an equational theory (a set of equations) and P is a logic program where equality can only ....

J.C. Sheperdson. SLDNF-resolution with equality. Journal of Automated Reasoning, 8:297-- 306, 1992.

....investigated in [18] as a negative literal occurs in the body of a clause. On the other hand, it also does not belong to the class of programs investigated in e.g. 2] as our program contains the equational theory AC1. Thus, our program falls into a class which has recently been investigated in [28]. Section 4 focuses on models which assign to ffi and ; operators which can be used to build up multisets. Section 5 introduces SLDENF resolution as SLDNF resolution extended by a unification algorithm for an equational theory. Section 6 shows how SLDENF resolution can be used as a sound and ....

....algorithm is known [13, 29] The programs are carefully specified such that the need for AC1 unification is localized within calls to subgoals of the form s = AC1 t or s 6= AC1 t , whereas all other subgoals can be solved by applying the usual unification procedure. Following the ideas of [28], SLDENF resolution is like SLDNF resolution [6] if the selected literal is not of the form s = AC1 t or s 6= AC1 t . If the selected literal is of the form s = AC1 t and s and t are AC1 terms, then the AC1 unification algorithm in [13, 29] is called, which either returns a minimal complete ....

[Article contains additional citation context not shown here]

J. S. Sheperdson. SLDNF--Resolution with Equality. Journal of Automated Reasoning, 8:297--306, 1992.

....means that the rest of axioms does not contain positive occurrences of equality. Equational logic programs are defined by this restriction as a pair hP; Ei, where P is a logic program without positive occurrences of equality, and E is a set of equality facts in [30, 22] or facts and rules [27, 47]. Jaffar et al. defined SLDE resolution as the procedural interpretation of such a program. An extension of SLD resolution called SLDE resolution has been proposed in [18, 19] Completeness of SLDE resolution was only proved for well behaved programs, which are exactly equational logic ....

J.C. Sheperdson. SLDNF-resolution with equality. Journal of Automated Reasoning, 8:297--306, 1992.

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