Abstract
In this paper, the current state of the System for Automated Deduction, SAD, is described briefly. The system may be considered as the modern vision of the Evidence Algorithm programme advanced by Academician V. Glushkov in early 1970s. V. Glushkov proposed to make investigation simultaneously into formalized languages for presenting mathematical texts in the form most appropriate for a user, formalization and evolutionary development of computer-made proof step, information environment having an influence on the evidence of a proof step, and man-assisted search for a proof. In this connection, SAD supports a number of formal languages for representing and processing mathematical knowledge along with the formal language ForTheL as their top representative, uses a sequent formalism developed for constructing an efficient technique of proof search within the signature of an initial theory, and gives a new way to organize the information environment for sharing mathematical knowledge among various computer services. The system SAD can be used to solve large variety of theorem proving problems including: establishing of the deducibility of sequents in first-order classical logic, theorem proving in ForTheL-environment, verifying correctness of self-contained ForTheL-texts, solving problems taken from the online library TPTP. A number of examples is given for illustrating the mathematical knowledge processing implemented in SAD.
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References
Aselderov, Z., Verchinine, K., Degtyarev, A., Lyaletski, A., Paskevich, A., Pavlov, A.: Linguistic tools and deductive technique of the System for Automated Deduction. In: Proc. 3rd International Workshop on the Implementation of Logics, Tbilisi, Georgia, pp. 21–24 (2002)
Bakhvalov, N.I., Zhidkov, N.P., Kobelkon, G.M.: Computational Methods (in Russian). BINOM Publisher (2003)
Barras, B., Boutin, S., Cornes, C., Courant, J., Filliatre, J., Giménez, E., Herbelin, H., Huet, G., Muñoz, C., Murthy, C., Parent, C., Paulin, C., Saïbi, A., Werner, B.: The Coq proof assistant reference manual – version v6.1. Technical Report 0203, INRIA (1997)
Benzmüller, C., Cheikhrouhou, L., Fehrer, D., Fiedler, A., Huang, X., Kerber, M., Kohlhase, M., Konrad, K., Meier, A., Melis, E., Schaarschmidt, W., Siekmann, J.H., Sorge, V.: Omega: Towards a mathematical assistant. In: McCune, W. (ed.) CADE 1997. LNCS, vol. 1249, pp. 252–255. Springer, Heidelberg (1997)
Brand, D.: Proving theorems with the modification method. SIAM Journal of Computing 4, 412–430 (1975)
Buchberger, B., Jebelean, T., Kriftner, F., Marin, M., Tomuta, E., Vasaru, D.: A survey of the Theorema project. In: Küchlin, W. (ed.) ISSAC 1997 – Proc. International Symposium on Symbolic and Algebraic Computation, Maui, Hawaii, USA, pp. 384–391. ACM Press, New York (1997)
Caprotti, O., Cohen, A.M.: Integrating computational and deduction systems using OpenMath. In: Armando, A., Jebelean, T. (eds.) Electronic Notes in Theoretical Computer Science, vol. 23. Elsevier, Amsterdam (2001)
Degtyarev, A., Lyaletski, A., Morokhovets, M.: Evidence Algorithm and sequent logical inference search. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds.) LPAR 1999. LNCS, vol. 1705, pp. 44–61. Springer, Heidelberg (1999)
Degtyarev, A., Lyaletski, A., Morokhovets, M.: On the EA-style integrated processing of self-contained mathematical texts. In: Kerber, M., Kohlhase, M. (eds.) Symbolic Computation and Automated Reasoning: The CALCULEMUS 2000 Symposium, pp. 126–141. A.K. Peters Ltd., USA (2001)
Gentzen, G.: Untersuchungen uber das Logische Schliessen. Math. Zeit. 39, 176–210 (1934)
Glushkov, V.M.: Some problems of automata theory and artificial intelligence (in Russian). Kibernetika 2, 3–13 (1970)
Graham, R.L.: Rudiments of Ramsey Theory. AMS (1981)
Letz, R., Stenz, G.: Model elimination and connection tableau procedures. In: Robinson, A., Voronkov, A. (eds.) Handbook for Automated Reasoning, vol. II, pp. 2017–2116. Elsevier Science, Amsterdam (2001)
Lyaletski, A., Morokhovets, M.: Evidential paradigm: a current state. In: Program of International Conference Mathematical Challenges of the 21st Century, University of California, Los Angeles, p. 48 (2000)
Lyaletski, A., Verchinine, K., Degtyarev, A., Paskevich, A.: System for Automated Deduction (SAD): Linguistic and deductive peculiarities. In: Klopotek, M.A., Wierzchon, S.T., Michalewicz, M. (eds.) Proc. IIS 2002 Symposium on Intelligent Information Systems 2002, Sopot, Poland, June 3-6, 2002. Advances in Soft Computing, pp. 413–422. Physica-Verlag, Heidelberg (2002)
Lyaletski, A., Verchinine, K., Paskevich, A.: On verification tools implemented in the System for Automated Deduction. In: Proc. 2nd CoLogNet Workshop on Implementation Technology for Computational Logic Systems (ITCLS 2003), Pisa, Italy, pp. 3–14 (2003)
McCune, W.: Otter 3.0 reference manual and guide. Tech. Report ANL-94/6, Argonne National Laboratory, Argonne, USA (1994)
Nipkow, T., Paulson, L.C., Wenzel, M.T.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)
Owre, S., Rushby, J.M., Shankar, N.: PVS: A prototype verification system. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 748–752. Springer, Heidelberg (1992)
Riazanov, A., Voronkov, A.: The design and implementation of VAMPIRE. AI Communications 15, 91–110 (2002)
Sutcliffe, G., Suttner, C.B., Yemenis, T.: The TPTP problem library. In: Bundy, A. (ed.) CADE 1994. LNCS, vol. 814, pp. 252–266. Springer, Heidelberg (1994), See also: http://tptp.org
Trybulec, A., Blair, H.: Computer assisted reasoning with Mizar. In: Proc. 9th International Joint Conference on Artificial Intelligence, pp. 26–28 (1985)
Verchinine, K., Degtyarev, A., Lyaleyski, A., Paskevich, A.: SAD, a System for Automated Deduction: a current state. In: Kamareddine, F. (ed.) Proc. Workshop on 35 Years of AUTOMATH. Heriot-Watt University, Edinburgh (2002)
Vershinin, K., Paskevich, A.: ForTheL – the language of formal theories. International Journal of Information Theories and Applications 7(3), 120–126 (2000)
Weidenbach, C.: System description: Spass version 1.0.0. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol. 1632, pp. 378–382. Springer, Heidelberg (1999)
Zimmer, J., Kohlhase, M.: System Description: The MathWeb Software Bus for Distributed Mathematical Reasoning. In: Voronkov, A. (ed.) CADE 2002. LNCS, vol. 2392, pp. 139–143. Springer, Heidelberg (2002)
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Lyaletski, A., Paskevich, A., Verchinine, K. (2004). Theorem Proving and Proof Verification in the System SAD. In: Asperti, A., Bancerek, G., Trybulec, A. (eds) Mathematical Knowledge Management. MKM 2004. Lecture Notes in Computer Science, vol 3119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27818-4_17
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DOI: https://doi.org/10.1007/978-3-540-27818-4_17
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