Abstract
We give some algorithms for constructing models from sets of clauses saturated by Ordered Resolution (with Selection rules). In the ground case, we give an efficient algorithm for constructing a minimal model. Then we generalize minimal models to preferred models, which may be useful for verification. For the ground case, we also show how to construct all models for a set of clauses saturated by Ordered Resolution, in time polynomial in the number of models. We also generalize our results to nonground models, where we add a restricted splitting rule to our inference rules, and show that for any set of clauses saturated by Ordered Resolution (with Selection), a query about the truth of a particular atom in the model can be decided.
This work was supported by NSF grant number CCR-0098270.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bachmair, L., Ganzinger, H.: Resolution theorem proving. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 19–99. North-Holland (2001)
Basin, D., Ganzinger, H.: Automated complexity analysis based on ordered resolution. J. Association for Computing Machinery 48(1), 70–109 (2001)
Davis, M., Logemman, G., Loveland, D.: A Machine Program for Theorem Proving. Communications of the ACM 5, 394–397 (1962)
Dershowitz, N.: Termination of Rewriting. Journal of Symbolic Computation 3, 69–116 (1987)
Fermüller, C., Leitsch, A., Tammet, T., Zamov, N.: Resolution Methods for the Decision Problem. LNCS, vol. 679. Springer, Heidelberg (1993)
Fermüller, C., Moser, G.: Have Spass with OCC1Ng=. LPAR 7, 114-130 (2000)
Ganzinger, H.: Relating Semantic and Proof-Theoretic Concepts for Polynomial Time Decidability of Uniform Word Problems. In: Proceedings 16th IEEE Symposium on Logic in Computer Science, LICS 2001, Boston (2001)
McAllester, D.: Automated Recognition of Tractability in Inference Relations. Journal of the ACM 40(2), 284–303 (1993)
Peltier, N.: Building Infinite Models for Equational Clause Sets: Constructing Non-Ambiguous Formulae. Logic Journal of the IGPL 11(1), 97–129 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Lynch, C. (2013). Constructing Bachmair-Ganzinger Models. In: Voronkov, A., Weidenbach, C. (eds) Programming Logics. Lecture Notes in Computer Science, vol 7797. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37651-1_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-37651-1_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37650-4
Online ISBN: 978-3-642-37651-1
eBook Packages: Computer ScienceComputer Science (R0)