Abstract
Hyper tableau reasoning is a version of clausal form tableau reasoning where all negative literals in a clause are resolved away in a single inference step. Constrained hyper tableaux are a generalization of hyper tableaux, where branch closing substitutions, from the point of view of model generation, give rise to constraints on satisfying assignments for the branch. These variable constraints eliminate the need for the awkward ‘purifying substitutions’ of hyper tableaux. The paper presents a non-destructive and proof confluent calculus for constrained hyper tableaux, together with a soundness and completeness proof, with completeness based on a new way to generate models from open tableaux. It is pointed out that the variable constraint approach applies to free variable tableau reasoning in general.
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.
Similar content being viewed by others
References
Baumgartner, P. Hyper tableaux —the next generation. In Proceedings International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (1998), H. d. Swart, Ed., no. 1397 in Lecture Notes in Computer Science, Springer, pp. 60–76.
Bpaumgartner, P., Fröhlich, P., AND Niemelä, I. Hyper tableaux. In Proceedings JELIA 96 (1996), Lecture Notes in Artificial Intelligence, Springer.
Fitting, M.First-order Logic and Automated Theorem Proving; Second Edition. Springer Verlag, Berlin, 1996.
Giese, M. Proof search without backtracking using instance streams, position paper. In Proc. Int. Workshop on First-Order Theorem Proving, St. Andrews, Scotland (2000). Available online at http://i12www.ira.uka.de/key/doc/2000/giese00.ps.gz.
Giese, M. Incremental closure of free variable tableaux. In IJCAR 2001 Proceedings (2001).
Hähnle, R. Tableaux and related methods. In Handbook of Automated Reasoning, A. Robinson and A. Voronkov, Eds. Elsevier Science Publishers, to appear, 2001.
Jones, S. P., Hughes, J., et al. Report on the programming language Haskell 98. Available from the Haskell homepage: http://www.haskell.org, 1999.
Kühn, M. Rigid hypertableaux. In KI-97: Advances in Artificial Intelligence (1997), G. Brewka, C. Habel, and B. Nebel, Eds., pp. 87–98.
Robinson, J. Automated deduction with hyper-resolution. International Journal of Computer Mathematics 1 (1965), 227–234.
Van Eijck, J. Model generation from constrained free variable tableaux. In IJCAR 2001-Short Papers (Siena, 2001), R. Goré, A. Leitsch, and T. Nipkov, Eds., pp. 160–169.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
van Eijck, J. (2001). Constrained Hyper Tableaux. In: Fribourg, L. (eds) Computer Science Logic. CSL 2001. Lecture Notes in Computer Science, vol 2142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44802-0_17
Download citation
DOI: https://doi.org/10.1007/3-540-44802-0_17
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42554-0
Online ISBN: 978-3-540-44802-0
eBook Packages: Springer Book Archive