Comon, H., Haberstrau, M. & Jouannaud, J.-P. (1994), `Syntacticness, cyclesyntacticness and shallow theories', Information and Computation 111(1), 154 --191. Home/Search Document Details and Download
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Unification in Extensions of Shallow Equational Theories - Jacquemard, Meyer, Weidenbach (1998) (6 citations) (Correct)
....In addition, a lot of progress has been made towards syntactic characterizations of classes of equational theories or rewrite systems in which these problems are decidable. The class of shallow theories, axiomatized by equations in which variables occur at most at depth one, has been shown by Comon, Haberstrau Jouannaud (1994) to have a decidable unification problem. They exploit a transformation of the system into an equivalent cycle syntactic presentation (Kirchner 1986) By a termination analyses under basic superposition Nieuwenhuis (1996) generalized the result to so called standard theories. Furthermore, tree ....
....A procedure which transforms a sorted semi linear equational theory into an equivalent sorted shallow one is given in Section 4. This implies the decidability of unifiability modulo a set of (sorted) semi linear equations. This result strictly embeds previous ones concerning shallow theories by Comon et al. 1994). We show in Section 5 that with similar techniques, we can treat a generalization of standard theories as proposed by Nieuwenhuis (1996) In the same section, we also consider some other extensions for which our method does not work and discuss some related work on Eunification. For more details ....
[Article contains additional citation context not shown here]
Comon, H., Haberstrau, M. & Jouannaud, J.-P. (1994), `Syntacticness, cyclesyntacticness and shallow theories', Information and Computation 111(1), 154 --191.
Paramodulation-Based Theorem Proving - Nieuwenhuis, Rubio (2001) (24 citations) (Correct)
....theorem proving 59 ory of divisible torsion free abelian groups. The equational shallow theories, the ones axiomatized by equations where no variable occurs at depth more than one, are another fundamental class with decidable word and unification problems and even a decidable first order theory [Comon, Haberstrau and Jouannaud 1994]. In [Nieuwenhuis 1998] it is shown that for sets of Horn clauses with equality saturated under basic paramodulation, the word and unifiability problems are in NP, and the number of minimal unifiers is simply exponential; this can be applied to shallow Horn clauses with equality. For certain Horn ....
Comon H., Haberstrau M. and Jouannaud J.-P. [1994], `Syntacticness, Cycle-Syntacticness and Shallow Theories', Information and Computation 111(1), 154--191.
Unification in Extensions of Shallow Equational Theories - Jacquemard, Meyer, Weidenbach (1998) (6 citations) (Correct)
....In addition, a lot of progress has been made towards syntactic characterizations of classes of equational theories or rewrite systems in which these problems are decidable. The class of shallow theories, axiomatized by equations in which variables occur at most at depth one, has been shown by Comon, Haberstrau Jouannaud (1994) to have a decidable uni cation problem. They exploit a transformation of the system into an equivalent cycle syntactic presentation (Kirchner 1986) By a termination analyses under basic superposition Nieuwenhuis (1996) generalized the result to so called standard theories. Furthermore, tree ....
....A procedure which transforms a sorted semi linear equational theory into an equivalent sorted shallow one is given in Section 4. This implies the decidability of uni ability modulo a set of (sorted) semi linear equations. This result strictly embeds previous ones concerning shallow theories by Comon et al. 1994). We show in Section 5 that with similar techniques, we can treat a generalization of standard theories as proposed by Nieuwenhuis (1996) In the same section, we also consider some other extensions for which our method does not work and discuss some related work on Euni cation. For more details ....
[Article contains additional citation context not shown here]
Comon, H., Haberstrau, M. & Jouannaud, J.-P. (1994), `Syntacticness, cyclesyntacticness and shallow theories', Information and Computation 111(1), 154 {191.
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