Abstract
We describe in this paper a general algorithm for solving first-order constraints in the theory T of the evaluated trees which is a combination of the theory of finite or infinite trees and the theory of the rational numbers with addition, subtraction and a linear dense order relation. It transforms a first-order formula ϕ, which can possibly contain free variables, into a disjunction φ of solved formulas which is equivalent in T, without new free variables and such that φ is either \(\mathit{true}\) or \(\mathit{false}\) or a formula having at least one free variable and being equivalent neither to \(\mathit{true}\) nor to \(\mathit{false}\) in T.
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References
Benhamou, F., et al.: Le manuel de Prolog IV, PrologIA, Marseille, France (1996)
Colmerauer, A.: An introduction to Prolog III. Comm. of the ACM 33(7), 68–90 (1990)
Comon, H.: Résolution de contraintes dans des algèbres de termes. Rapport d’Habilitation, Université de Paris Sud (1992)
Dao, T.: Résolution de contraintes du premier ordre dans la théorie des arbres finis ou infinis. Thèse d’informatique, Université de la Méditerranée (2000)
Dao, T.B.H., Djelloul, K.: Solving First-Order Constraints in the Theory of the Evaluated Trees, Rapport de recherche LIFO RR-2006-05, http://www.univ-orleans.fr/lifo/rapports.php
Djelloul, K.: About the Combination of Trees and Rational Numbers in a Complete First-Order Theory. In: Gramlich, B. (ed.) FroCos 2005. LNCS (LNAI), vol. 3717, pp. 106–121. Springer, Heidelberg (2005)
Maher, M.: Complete axiomatization of the algebra of finite, rational and infinite trees. Technical report, IBM - T.J.Watson Research Center (1988)
Vorobyov, S.: An Improved Lower Bound for the Elementary Theories of Trees. In: McRobbie, M.A., Slaney, J.K. (eds.) CADE 1996. LNCS, vol. 1104, pp. 275–287. Springer, Heidelberg (1996)
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Dao, TBH., Djelloul, K. (2006). Solving First-Order Constraints in the Theory of the Evaluated Trees. In: Etalle, S., Truszczyński, M. (eds) Logic Programming. ICLP 2006. Lecture Notes in Computer Science, vol 4079. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11799573_32
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DOI: https://doi.org/10.1007/11799573_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-36635-5
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