Claude March'e. Normalised Rewriting and Normalised Completion. In Ninth Annual IEEE Symposium on Logic in Computer Science, Paris, France, July 1994. IEEE Computer Society Press, Los Alamitos, CA, USA.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....under equational ordered paramodulation w.r.t. a west ordering extending a give reduction ordering r , and let R denote the (unique) canonical TRS for E and r . Then E 0 R. 4 Building in abelian groups Paramodulation with built in abelian groups (AG) has been investigated by many authors [Che86,Mar94,Mar96,GW96,Wal98,Wal99,Stu98]. This is not surprising since abelian groups are of course ubiquitous in many applications of (semi )automated reasoning. But building in AG is also attractive for at least two more reasons. On the one hand, due to the fact that diophantine equation solving is easier in the integers than in the ....

....restrict inferences to this maximal summand and to avoid the prolific inferences with extended equations that appear in the AC case. Symmetrization is also exploited in March e s framework for Knuth Bendix completion of unit equations with built in theories (ranging from AC to commutative rings) [Mar94,Mar96]. His completion procedure decides the ground word problem modulo AG by building a finite convergent rewrite system. However, his procedure is not refutation complete for equations with variables: in many cases it fails since it cannot handle symmetrization at the non ground level. 4.1 Recent ....

Claude March'e. Normalised Rewriting and Normalised Completion. In Ninth Annual IEEE Symposium on Logic in Computer Science, Paris, France, July 1994. IEEE Computer Society Press, Los Alamitos, CA, USA.

....specialized techniques to work efficiently with standard algebraic theories, since a nave handling of some axioms (like associativity and commutativity, AC) leads to an explosion of the search space. Paramodulation with built in abelian groups (AG) has been investigated by many authors [6, 23, 11, 12, 10, 21, 22, 18]. This is not surprising since abelian groups are of course ubiquitous in many applications of (semi )automated reasoning. But building in AG is also attractive for at least two more reasons. On the one hand, due to the fact that diophantine equation solving is easier in the integers than in the ....

....to restrict inferences to this maximal summand and to avoid the prolific inferences with extended equations that appear in the AC case. Symmetrisation is also exploited in Marche s framework for Knuth Bendixcompletion of unit equations with built in theories (ranging from AC to commutative rings) [11, 12]. His completion procedure decides the ground word problem modulo AG by building a finite convergent rewrite system. However, his procedure is not refutation complete for equations with variables: in many cases it fails since it cannot handle symmetrisation at the non ground level. Full ....

C. Marche. Normalised Rewriting and Normalised Completion. In Ninth Annual IEEE Symposium on Logic in Computer Science, Paris, France, July 1994. IEEE Computer Society Press, Los Alamitos, CA, USA.

....specialized techniques to work efficiently with standard algebraic theories, since a nave handling of some axioms (like associativity and commutativity, AC) leads to an explosion of the search space. Paramodulation with built in abelian groups (AG) has been investigated by many authors [6, 23, 11, 12, 10, 21, 22, 18]. This is not surprising since abelian groups are of course ubiquitous in many applications of (semi )automated reasoning. But building in AG is also attractive for at least two more reasons. On the one hand, due to the fact that diophantine equation solving is easier in the integers than in the ....

....to restrict inferences to this maximal summand and to avoid the prolific inferences with extended equations that appear in the AC case. Symmetrisation is also exploited in Marche s framework for Knuth Bendixcompletion of unit equations with built in theories (ranging from AC to commutative rings) [11, 12]. His completion procedure decides the ground word problem modulo AG by building a finite convergent rewrite system. However, his procedure is not refutation complete for equations with variables: in many cases it fails since it cannot handle symmetrisation at the non ground level. Full ....

C. Marche. Normalised Rewriting and Normalised Completion. In Ninth Annual IEEE Symposium on Logic in Computer Science, Paris, France, July 1994. IEEE Computer Society Press, Los Alamitos, CA, USA.

....the critical pair lemma, still holds for some restricted cases [16] On the negative side, this framework lacks adequate termination proof methods. The only results that we know of [13, 14, 4] are far from meeting the practical needs. Computer systems like RRL [11] Saturate [17] or CiME [15] make available semi automated techniques for proving termination of first order rewrite rules by comparing their left and right hand sides in some reduction ordering, of which the most popular one is the recursive path ordering [5] Its principle is to generate recursively an ordering on terms ....

Claude March'e. Normalised rewriting and normalised completion. In Proceedings of the Ninth Annual IEEE Symposium on Logic in Computer Science, Paris, France, July 1994. IEEE Comp. Soc. Press.

....symbols are associative and commutative (AC) a finite convergent rewrite system can always be computed [Narendran and Rusinowitch, 1991, March e, 1991] by which the word problem is decidable. In the same class, the unification problem is also decidable [Narendran and Rusinowitch, 1993] see also [Marche, 1994] for decidability of word problems in ground presentations modulo several other theories different from AC) Some well known classes of first order formulae have been proved decidable by means of model theoretic methods, and satisfiability of their corresponding clause sets can also be decided by ....

Marche, C. (1994). Normalised Rewriting and Normalised Completion. In Ninth Annual IEEE Symposium on Logic in Computer Science, Paris, France. IEEE Computer Society Press, Los Alamitos, CA, USA.

....if term rewriting systems are to be applied to non trivial problems. Evaluation does not restrict the functionality of term rewriting systems in any respect. Therefore our method may also be employed in equational theorem proving. In particular it may be integrated in completion procedures like [28]. A further extension of our method is to use evaluation domains to decide equality in non canonical specifications. A formidable example of this are equational specifications of Boolean algebras with BDDs [3] as evaluation domain. ....

Marche, C.: Normalised rewriting and normalised completion. In Ninth Anual Symposium on Logic in Computer Science. IEEE Computer Society Press, 1994.

....stay in Barcelona. Partially supported by the EU Human Capital and Mobility Network Console. always a finite convergent rewrite system can be computed [NR91, Mar91] by which the word problem is efficiently decidable. In the same class, the unification problem is also decidable [NR93] see also [Mar94] for decidability of word problems in ground presentations modulo several other theories different from AC) Some well known classes of first order formulae have been proved decidable by means of modeltheoretic methods, and satisfiability of their corresponding clause sets can also be decided by ....

Claude Marche. Normalised Rewriting and Normalised Completion. In Ninth Annual IEEE Symposium on Logic in Computer Science, Paris, France, July 1994. IEEE Computer Society Press, Los Alamitos, CA, USA.

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Claude March'e. Normalised Rewriting and Normalised Completion. In Ninth Annual IEEE Symposium on Logic in Computer Science, Paris, France, July 1994. IEEE Computer Society Press, Los Alamitos, CA, USA.

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Claude March' e, 1994. Normalised rewriting and normalised completion. In Proc. IEEE Symposium on Logic in Computer Science. IEEE Comp. Soc. Press. To appear.

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