LS95. C. Lynch and W. Snyder. Redundancy criteria for constrained completion. Theoritical Compluter Science, volume 142, pages 141-177, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....simplifying a constrained formula (F k c) takes into account all the schematized formulas. Some of these instances that are not reducible are recorded in the rest. It should be noted that solving constraints with negation is needed in this definition. This general form of simplification is used in [34]. Example 7 Let us consider the simplification of (a y = z k y z = AC d b) using (a b = b k T) and the substitution oe = fy 7 b; z 7 dg. Then the simplification produces two new constrained equalities: b = z k y = AC b z = AC d) and (a y = z k (y z = AC d b) y 6= ....

C. Lynch and W. Snyder. Redundancy criteria for constrained completion. In C. Kirchner, editor, Proceedings 5th Conference on Rewriting Techniques and Applications, Montreal (Canada), volume 690 of Lecture Notes in Computer Science, pages 2--16. Springer-Verlag, 1993.

....given congruence (usually syntactic equality of terms) that depend on the context. Paramodulation based theorem proving 9 In [Nieuwenhuis and Rubio 1992b] it is shown that by inheriting as well the ordering constraints one can restrict the search space even further without losing completeness. In [Lynch and Snyder 1993] equality, disequality and irreducibility constraints are applied for obtaining more powerful redundancy methods in basic equational completion. Finally, in [Nieuwenhuis and Rubio 1995] the use of constraints in theorem proving procedures is put in a more general framework based on the notion of ....

Lynch C. and Snyder W. [1993], Redundancy criteria for constrained completion, in C. Kirchner, ed., `5th International Conference on Rewriting Techniques and Applications (RTA)', LNCS 690, Springer-Verlag, Montreal, Canada, pp. 2--16.

....is more modular and better controls can be designed by delaying complex problem solving and pruning some parts of the search tree. Constraints also schematize (infinitely) many objects, especially substitutions or ground instances of equalities. Recent work involves irreducibility constraints [7] and deduction processes with AC constraints [12, 13] However introducing equational and ordering constraints in completion processes needs a cautious analysis. For efficiency reasons, simplification is essential in completion but more difficult in the context of constrained equalities. As ....

C. Lynch and W. Snyder. Redundancy criteria for constrained completion. In C. Kirchner, editor, Proceedings 5th Conference on Rewriting Techniques and Applications, Montreal (Canada), volume 690 of Lecture Notes in Computer Science, pages 2--16. Springer-Verlag, 1993.

.... with equality [4, 26, 27] The same idea was used in implementations of ordered completion described in [24, 29] and completion modulo associativity, commutativity and identity [6, 18] Completion with membership constraints is studied in [9] More recent work involves irreducibility constraints [23] and deduction processes with AC constraints [28, 33] There are several advantages in using constraints in automated deduction. They provide a way to make explicit every symbolic computation step, especially unification, orientation and typing problems to check while applying an inference rule. ....

....equalities, one can prove that, if a constrained equality of the form (l = r k oe) is RE1 reducible in the range of oe, it is redundant. More work is needed to obtain satisfactory criteria for elimination of redundancies, but this problem is not addressed here. Further hints can be found in [4, 26, 27, 23, 21]. Definition 4 A derivation from a set of constrained equalities E 0 is a sequence E 0 ; E 1 ; of sets of constrained equalities obtained by successive applications of superposition and eliminations of redundant constrained equalities. Formally: E i = E i Gamma1 [ f(l = r k c)g if (l = r ....

C. Lynch and W. Snyder. Redundancy criteria for constrained completion. In C. Kirchner, editor, Proceedings 5th Conference on Rewriting Techniques and Applications, Montreal (Canada), volume 690 of Lecture Notes in Computer Science, pages 2--16. Springer-Verlag, 1993.

....et al. 1992) have independently developed a comprehensive framework for the basic strategy in combination with techniques for simplification and restrictions based e.g. on term selection rules and redex orderings, using closure substitutions which play the role of our equality constraints. Lynch and Snyder (1993) apply equality, disequality and irreducibility constraints to obtain more powerful redundancy criteria in equational completion. The constraint paradigm has also been applied to theorem proving in (Huet, 1972) and (Peterson, 1990) Basic narrowing was introduced in (Hullot, 1980) All ....

Lynch, C., Snyder, W. (1993). Redundancy criteria for constrained completion. In C. Kirchner, editor, 5th International Conference on Rewriting Techniques and Applications, LNCS 690, pages 2--16, Montreal, Canada. Springer-Verlag.

....constraint or (2) denoting the false reducibility constraint or (3) of the form r 1 rn , where r i is of the form ( W j Red(t j ; e j ) or :Red(t j ; e j ) or where t j 2 T and e j 2 Gr(E) f g. First instances of reducibility constraints can be found in [Pet94] and in [LS95]. A ground reducibility constraint is a reducibility constraint such that the rst parameter of the predicate Red is a ground term. Let r be a ground reducibility constraint, and R be a ground rewrite system. Then r is satis able in R, if and only (1) r = or (2) r = Red(t; and t is ....

C. Lynch and W. Snyder. Redundancy criteria for constrained completion. Theoritical Computer Science, volume 142, pages 141-177, 1995.

.... Delta Delta rn , where r i is of the form ( W j Red(t j ) or :Red(t) or where t; t j 2 T (where T is the set of terms built on a particular signature) The syntax of the Red predicate is extended in [LS97] First instances of reducibility constraints can be found in [Pet94] and in [LS95]. A ground reducibility constraint is a reducibility constraint such that the parameter of the predicate Red is a ground term. Let r be a ground reducibility constraint, and R be a ground rewrite system. Then r is satisfiable in R, if and only if one of the following conditions is true: ....

Christopher Lynch and Wayne Snyder. Redundancy criteria for constrained completion. In Theoretical Computer Science, volume 142, pages 141--177, 1995.

....or denoting the false reducibility constraint or of the form r 1 Delta Delta Delta rn , where r i is of the form ( W j Red(t j ; e j ) or :Red(t j ; e j ) or where t j 2 T and e j 2 Gr(E) f g. First instances of reducibility constraints can be found in [Pet94] and in [LS95]. A ground reducibility constraint is a reducibility constraint such that the rst parameter of the predicate Red is a ground term. Let r be a ground reducibility constraint, and R be a ground rewrite system. Then r is satisable in R, if and only if one of the following conditions is true: 3 ....

Christopher Lynch and Wayne Snyder. Redundancy criteria for constrained completion. In Theoretical Computer Science, volume 142, pages 141177, 1995.

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C. Lynch, and W. Snyder. Redundancy Criteria for Constrained Completion. Theoretical Computer Science Vol. 142, No. 2 (1995) 141177.

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