Abstract
The clause-linking technique of Lee and Plaisted proves the unsatisfiability of a set of first-order clauses by generating a sufficiently large set of instances of these clauses that can be shown to be propositionally unsatisfiable. In recent years, this approach has been refined in several directions, leading to both tableau-based methods, such as the disconnection tableau calculus, and saturation-based methods, such as primal partial instantiation and resolution-based instance generation. We investigate the relationship between these calculi and answer the question to what extent refutation or consistency proofs in one calculus can be simulated in another one.
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Baumgartner, P.: FDPLL – a first-order Davis-Putnam-Logeman-Loveland procedure. In: McAllester, D. (ed.) CADE-17 – The 17th International Conference on Automated Deduction, Pittsburgh, PA, pp. 200–219. (2000)
Baumgartner, P., Tinelli, C.: The model evolution calculus. In: Baader, F. (ed.) CADE-19 – The 19th International Conference on Automated Deduction, Miami, Florida, pp. 350–364. (2003)
Billon, J.-P.: The disconnection method: a confluent integration of unification in the analytic framework. In: Miglioli, P., Moscato, U., Mundici, D., Ornaghi, M. (eds.) Automated Reasoning with Analytic Tableaux and Related Methods: International Conference, Palermo, Italy, pp. 110–126. (1996)
Davis, M., Logemann, G., Loveland, D.: A machine program for theorem proving. Communications of the ACM 5, 201–215 (1962)
Ganzinger, H., Korovin, K.: New directions in instantiation-based theorem proving. In: Proc. 18th IEEE Symposium on Logic in Computer Science, pp. 55–64. (2003)
Hooker, J.N., Rago, G., Chandru, V., Rivastava, A.: Partial instantiation methods for inference in first-order logic. J. Autom. Reason. 28, 371–396 (2002)
Jacobs, S.: Instance generation methods for automated reasoning. Diploma thesis, Universität des Saarlandes (2004). (Available at http://www.mpi-sb.mpg.de/~sjacobs/publications)
Lee, S.-J., Plaisted, D.A.: Eliminating duplication with the hyper-linking strategy. J. Autom. Reason. 13, 25–42 (1992)
Letz, R., Stenz, G.: Proof and model generation with disconnection tableaux. In: Nieuwenhuis, R., Voronkov, A. (eds.) Logic for Programming, Artificial Intelligence, and Reasoning: 8th International Conference, Havana, Cuba, pp. 142–156. (2001)
Letz, R., Stenz, G.: Generalised handling of variables in disconnection tableaux. In: Basin, D., Rusinowitch, M. (eds.) Automated Reasoning: Second International Joint Conference, Cork, Ireland, pp. 289–306. (2004)
Plaisted, D.A., Zhu, Y.: Ordered semantic hyper-linking. J. Autom. Reason. 25, 167–217 (2000)
Stenz, G.: The disconnection calculus. Ph.D. thesis, TU München (2002)
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This work was partly supported by the German Research Council (DFG) as part of the Transregional Collaborative Research Center “Automatic Verification and Analysis of Complex Systems” (SFB/TR 14 AVACS). See www.avacs.org for more information.
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Jacobs, S., Waldmann, U. Comparing Instance Generation Methods for Automated Reasoning. J Autom Reasoning 38, 57–78 (2007). https://doi.org/10.1007/s10817-006-9046-x
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DOI: https://doi.org/10.1007/s10817-006-9046-x