Abstract
Herbrand models for clausal theories are useful in several areas of computer science. In most cases, however, the conventional model generation algorithms are inappropriate because they generate nonminimal Herbrand models and can be inefficient. This article describes a novel approach for generating minimal Herbrand models of clausal theories. The approach builds upon positive unit hyperresolution (PUHR) tableaux, that are in general smaller than conventional tableaux. To generate only minimal Herbrand models, a complement splitting expansion rule and a specific search strategy are applied. The proposed procedure is optimal in the sense that each minimal model is generated only once, and nonminimal models are rejected before their complete construction. First measurements on an implementation point to its efficiency.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
M. Denecker and D. Schreye. A framework for indeterministic model generation with equality. In Proc. Conf. on Fifth Generation Computer Systems. 1992.
J.A. Fernández and J. Minker. Bottom-up evaluation of Hierarchical Disjunctive Deductive Databases. In Proc. 8 th Int. Conf. on Logic Programming, 660–675. MIT Press, 1991.
M. Fitting. First-Order Logic and Automated Theorem Proving. Springer-Verlag, 1987.
H. Schüz and T. Geisler. Efficient model generation through compilation. Tech. Rep. PMS-96-2, Inst. für Informatik, Munich University, 1996. Submitted for publication.
J. Hintikka. Model minimization — an alternative to circumscription. J. Automated Reasoning, Vol. 4, 1–13, 1988.
K. Inoue, M. Koshimura, and R. Hasegawa. Embedding negation as failure into a model generation theorem prover. In Proc. 11 th Int. Conf. on Automated Deduction, 1992.
R. Letz, K. Mayr, and C. Goller. Controlled integration of the cut rule into connection tableau calculi. J. Automated Reasoning, Vol. 13 No. 3, 297–338, 1994.
R. Manthey and F. Bry. Satchmo: a theorem prover implemented in Prolog. In Proc. 9 th Conf. on Automated Deduction, 456–459, 1988.
I. Niemelä. A tableau calculus for minimal model reasoning. In Proc. 5 th. Workshop on Theorem Proving with Analytic Tableaux and Related Methods, 1996. Springer-Verlag.
N. Olivetti. Tableaux and sequent calculus for minimal entailment. J. Automated Reasoning, Vol. 9, 99–139, 1992.
D. Prawitz. A new improved proof procedure Theoria, Vol. 26, 102–139, 1960.
J.A. Robinson. Automatic deduction with hyper-resoultion. Int. J. Computational Mathematics, Vol. 1, 227–234, 1965.
M. Suchenek. First-order syntactic characterizations of minimal entailment, domain minimal entailment and herbrand entailment. J. Automated Reasoning, Vol. 10, 237–236, 1993.
A. Yahya, J.A. Fernandez, and J. Minker. Ordered model trees: A normal form for disjunctive deductive databases. J. Automated Reasoning, Vol. 13 No. 1, 117–144, 1994.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bry, F., Yahya, A. (1996). Minimal model generation with positive unit hyper-resolution tableaux. In: Miglioli, P., Moscato, U., Mundici, D., Ornaghi, M. (eds) Theorem Proving with Analytic Tableaux and Related Methods. TABLEAUX 1996. Lecture Notes in Computer Science, vol 1071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61208-4_10
Download citation
DOI: https://doi.org/10.1007/3-540-61208-4_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61208-7
Online ISBN: 978-3-540-68368-1
eBook Packages: Springer Book Archive