Abstract
Few year ago we have developed an Automated Deduction approach to model building. The method, called RAMC looks simultaneously for inconsistencies and models for a given formula. The capabilities of RAMC have been extended both for model building and for unsatisfiability detection by including in it the use of semantic strategies. In the present work we go further in this direction and define more general and powerful semantic rules. These rules are an extension of Slagle's semantic resolution. The robustness of our approach is evidenced by proving that the method is also a decision procedure for a wide range of classes decidable by semantic resolution and in particular by hyper-resolution. Moreover, the method builds models for satisfiable formulae in these classes, in particular, for satisfiable formulae that do not have any finite model.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Egon BÖRGER. Decision problems in predicate logic. In G. Longo G. Lolli and A. Marcja, editors, Logic Colloquium'82, pages 263–301. North-Holland, 1984.
Ricardo CAFERRA and Nicolas PELTIER. Extending semantic resolution via automated model building: applications. In Proceeding of IJCAI'95. Morgan Kaufmann, 1995.
Ricardo CAFERRA and Nicolas PELTIER. Model building and interactive theory discovery. In Proceeding of Tableaux'95, LNAI 918, pages 154–168. Springer-Verlag, 1995.
Ricardo Caferra and Nicolas Zabel. A method for simultaneous search for refutations and models by equational constraint solving. Journal of Symbolic Computation, 13:613–641, 1992.
Burton DREBEN and Warren D. GOLDFARB. The Decision Problem, Solvable Classes of Quantificational Formulas. Addison-Wesley, 1979.
Christian FERMÜLLER and Alexander LEITSCH. Model building by resolution. In Computer Science Logic, CSL '92, pages 134–148. Springer-Verlag, LNCS 702, 1992.
Christian FERMÃœLLER and A. LEITSCH. Hyperresolution and automated model building. Journal of Logic and Computation, 1995. To appear.
C. FERMÃœLLER, A. LEITSCH, T. TAMMET, and N. ZAMOV. Resolution Methods for the Decision Problem. LNAI 679, Springer-Verlag, 1993.
W.H. Joyner. Resolution strategies as decision procedures. Journal of the ACM, 23:398–417, 1976.
Alexander Leitsch. Deciding clause classes by semantic clash resolution. Fundamenta Informaticae, 18:163–182, 1993.
Harry LEWIS. Unsolvable classes of quantificational formulas. Addison-Wesley, 1979.
William McCune and Lawrence Henschen. Experiments with semantic paramodulation. Journal of Automated Reasoning, 1:231–261, 1985.
Grigori E. Mints. Proof theory in the USSR 1925–1969. Journal of Symbolic Logic, 56(2):385–424, June 1991.
James R. Slagle. Automatic theorem proving with renamable and semantic resolution. Journal of the ACM, 14(4):687–697, October 1967.
Tanel Tammet. Using resolution for deciding solvable classes and building finite models. In Baltic Computer Science, pages 33–64. Springer-Verlag, LNCS 502, 1991.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Caferra, R., Peltier, N. (1996). Decision procedures using model building techniques. In: Kleine Büning, H. (eds) Computer Science Logic. CSL 1995. Lecture Notes in Computer Science, vol 1092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61377-3_35
Download citation
DOI: https://doi.org/10.1007/3-540-61377-3_35
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61377-0
Online ISBN: 978-3-540-68507-4
eBook Packages: Springer Book Archive