Abstract
In this paper, we deal with various induction principles incorporated in an underlying tableau calculus with equality. The induction formulae are restricted to literals. Induction is formalized as modified closure conditions which are triggered by applications of the δ-rule. Examples dealing with (weak forms of) arithmetic and strings illustrate the simplicity and usability of our induction handling. We prove the correctness of the closure conditions and discuss possibilities to strengthen the induction principles.
The first author was supported by the FWF under grant P11934-MAT. The authors would like to thank Hans Tompits and the referees for their useful comments on an earlier version of this paper.
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References
R. Aubin. Mechanizing Structural Induction. Theoretical Computer Science, 9:329–362, 1980.
M. Baaz and C.G. Fermüller. Non-elementary speed-ups between Different Versions of Tableaux. In R. Hähnle P. Baumgartner and J. Posegga, editors, Theorem Proving with Analytic Tableaux and Related Methods (4th International Workshop TABLEAUX'95), pages 217–230. Springer, 1995.
M. Baaz and A. Leitsch. Methods of Functional Extension. In Collegium Logicum: Annals of the Kurt Gödel Society. Springer, 1994.
B. Beckert, R. Hähnle, and P.H. Schmitt. The Even More Liberalized δ-Rule in Free Variable Semantic Tableaux. In A. Leitsch G. Gottlob and D. Mundici, editors, Proceedings of the Kurt Gödel Colloquium. Springer, 1993.
W. Bibel. Automated Theorem Proving. Vieweg, Braunschweig, second edition, 1987.
R. S. Boyer and J. S. Moore. A Computational Logic. Academic Press, 1979.
A. Degtyarev and A. Voronkov. Equality elimination for the tableau method. In Proceedings of DISCO'96, 1996.
A. Degtyarev and A. Voronkov. Equality Reasoning in Sequent-Based Calculi. Technical Report No. 127, CS Department, Uppsala University, 1996.
A. Degtyarev and A. Voronkov. What you always wanted to know about rigid E-unification. In Proceedings of JELIA'96, 1996.
E. Eder. An Implementation of a Theorem Prover Based on the Connection Method. In W. Bibel and B. Petkoff, editors, AIMSA 84, Artificial Intelligence — Methodology, Systems, Applications, Varna, Bulgaria. North-Holland Publishing Company, 1984.
E. Eder. Relative Complexities of First Order Calculi. Vieweg, Braunschweig, 1992.
M. Fitting. First-Order Logic and Automated Theorem Proving. Springer, second edition, 1996.
P. Hájek and P. Pudlák. Metamathematics of First-Order Arithmetic. Springer Verlag, 1993.
D. Hilbert and P. Bernays. Grundlagen der Mathematik II. Springer, 1939.
D. R. Musser. On Proving Inductive Properties of Abstract Data Types. In Proc. Principles of Programming Languages, pages 154–162, 1980.
D. A. Plaisted and S. Greenbaum. A Structure-Preserving Clause Form Translation. J. Symbolic Computation, 2:293–304, 1986.
H. Zhang, editor. J. Automated Reasoning: Special Issue on Inductive Theorem Proving, volume 16, nos 1–2, 1996.
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Baaz, M., Egly, U., Fermüller, C.G. (1997). Lean induction principles for tableaux. In: Galmiche, D. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 1997. Lecture Notes in Computer Science, vol 1227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027405
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DOI: https://doi.org/10.1007/BFb0027405
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