Abstract
We show that both the tableaux and the resolution methods can be understood as attempts to exploit the power of cut-elimination theorems in Gentzen-type calculi. Another, related goal is to provide a purely syntactic basis for both methods (in contrast to the semantic proofs concerning resolution that can be found in the textbooks). This allows the use of a fruitful combination of the methods and might be helpful in generalizing them to other logics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Avron, A., ‘Simple consequence relations’,Information and Computation 92, 105–139 (1991).
Bibel, W.,Automated Theorem Proving, Vieweg Verlag, Braunschweig (1982).
Bell, J. L. and Machover, M.,A Course in Mathematical Logic, North-Holland, Amsterdam (1977).
Bundy, A.,The Computer Modelling of Mathematical Reasoning, Academic Press, New York (1983).
Chang, C. and Lee, R. C.,Symbolic Logic and Mechanical Theorem Proving, Academic Press, New York (1973).
Fitting, M. C.,First Order Logic and Automated Theorem Proving, Springer-Verlag, New York (1989).
Gallier, J. H.,Logic and Computer Science — Foundations of Automatic Theorem Proving, Harper & Row, New York (1986).
Gentzen, G., ‘Investigations into logical deduction’, inThe Collected Work of Gerhard Gentzen, M.E. Szabo (Ed.), North Holland, Amsterdam (1969).
Girard, J. Y., Lafont, Y. and Taylor, P.,Proofs and Types, Cambridge University Press, Cambridge (1989).
Girard, J. Y.,Proof Theory and Logical Complexity, Bibliopolis (1987).
Kowalski, R.,Logic for Problem Solving, Elsevier/North-Holland, New York (1979).
Loveland, D. W.,Automated Theorem Proving: A Logical Basis, Elsevier/North-Holland, New York (1978).
Oppacher, F. and Suen, E., ‘Controlling deduction with proof condensation and heuristics’, inProceedings of CADE 8, pp. 364–393, Springer-Verlag, Berlin (1986).
Robinson, J. A.,Logic: Form and Function, Elsevier/North-Holland, New York (1979).
Smullyan, R. M.,First-Order Logic, Springer-Verlag, Berlin (1986).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Avron, A. Gentzen-type systems, resolution and tableaux. J Autom Reasoning 10, 265–281 (1993). https://doi.org/10.1007/BF00881838
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00881838