Abstract
We address the problems of combining satisfiability procedures and consider two combination scenarios: (i) the combination within the class of rewriting-based satisfiability procedures and (ii) the Nelson-Oppen combination of rewriting-based satisfiability procedures and arbitrary satisfiability procedures. In each scenario, we use meta-saturation, which schematizes saturation of the set containing the axioms of a given theory and an arbitrary set of ground literals, to syntactically decide sufficient conditions for the combinability of rewriting-based satisfiability procedures. For (i), we give a sufficient condition for the modular termination of meta-saturation. When meta-saturation for the union of theories halts, it yields a rewriting-based satisfiability procedure for the union. For (ii), we use meta-saturation to prove the stable infiniteness of the component theories and deduction completeness of their rewriting-based satisfiability procedures. These properties are important to establish the correctness of the Nelson-Oppen combination method and to obtain an efficient implementation.
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References
Armando, A., Bonacina, M.P., Ranise, S., Schulz, S.: On a Rewriting Approach to Satisfiability Procedures: Extension, Combination of Theories and an Experimental Appraisal. In: Gramlich, B. (ed.) FroCos 2005. LNCS (LNAI), vol. 3717, pp. 65–80. Springer, Heidelberg (2005)
Armando, A., Bonacina, M.P., Ranise, S., Schulz, S.: New results on rewrite-based satisfiability procedures (2006). Extended version of [1], Available at: http://arxiv.org/abs/cs.AI/0604054
Armando, A., Ranise, S., Rusinowitch, M.: A Rewriting Approach to Satisfiability Procedures. Info. and Comp. 183(2), 140–164 (2003)
Bonacina, M.P., Ghilardi, S., Nicolini, E., Ranise, S., Zucchelli, D.: Decidability and Undecidability Results for Nelson-Oppen and Rewrite-Based Decision Procedures. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 513–527. Springer, Heidelberg (2006)
Dershowitz, N., Jouannaud, J.-P.: Rewrite Systems. In: Handbook of Theoretical Computer Science, ch. 6, vol. B, Elsevier Science Publishers B. V, Amsterdam (1990)
Detlefs, D., Nelson, G., Saxe, J.B.: Simplify: A Theorem Prover for Program Checking. Technical Report HPL-2003-148, HP Laboratories (2003)
Kirchner, H., Ranise, S., Ringeissen, C., Tran, D.-K.: On superposition-based satisfiability procedures and their combination. In: Van Hung, D., Wirsing, M. (eds.) ICTAC 2005. LNCS, vol. 3722, pp. 594–608. Springer, Heidelberg (2005)
Lynch, C., Morawska, B.: Automatic decidability. In: Proc. of the IEEE Symposium on Logic in Computer Science (July 2002)
Nelson, G., Oppen, D.C.: Simplification by cooperating decision procedures. ACM Trans. on Programming Languages and Systems 1(2), 245–257 (1979)
Nieuwenhuis, R., Rubio, A.: Paramodulation-based theorem proving. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, ch. 7, vol. I, pp. 371–443. Elsevier Science, Amsterdam (2001)
Riazanov, A., Voronkov, A.: Splitting without backtracking. In: Seventeenth International Joint Conference on Artificial Intelligence, pp. 611–617 (2001)
van Dalen, D.: Logic and Structure, 2nd edn. Springer, Heidelberg (1989)
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Kirchner, H., Ranise, S., Ringeissen, C., Tran, DK. (2006). Automatic Combinability of Rewriting-Based Satisfiability Procedures. In: Hermann, M., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2006. Lecture Notes in Computer Science(), vol 4246. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11916277_37
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DOI: https://doi.org/10.1007/11916277_37
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