Abstract
The paper deals with an expressive logic language LF and its calculus. Formulas of this language consist of some large-scale structural elements, such as type quantifiers. The language LF contains only two logic symbols—∀ and ∃, which form the set of logic connectives of the language. The logic calculus JF and complete strategy for automated proof search based on a single unary rule of inference are considered. This calculus has a number of other features which lead to the reduction of the combinatorial complexity of finding the deductions in comparison to the known systems for automated theorem proving as the Resolution method and Genzen calculus. Problems of effective implementation of JF as a program system for automated theorem proving are considered.
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References
Vasil’ev, S.N., Zherlov, A.K., Fedunov, E.A., and Fedosov, V.E., Intellektnoe upravlenie dinamicheskimi sistemami (Intellectual Management of Dynamical Systems), Moscow: Fizmatlit, 2000.
Zherlov, A.K. and Vasil’ev, S.N., Calculation of Positive-Oriented Formulae, in Aktual’nye problemy informatiki, prikladnoi matematiki i mekhaniki: Sb. nauchnykh trudov (Actual Problems of Informatics, Applied Mathematics and Mechanics. Collection of Scientific Papers), Krasnoyarsk, 1996, part 1.
Robinson, J.A., A Machine-Oriented Logic Based on Resolution Principle, J. ACM, 1965, no. 1, pp. 23–41.
Graf, P., Substitution Tree Indexing, Proc. 6th Int. Conf. on Rewriting Techniques and Applications, 1995, pp. 117–131.
Stickel, M., The Path-Indexing Method for Indexing Terms, Technical Note no.473, Artificial Intelligence Center, SRI International, Menlo Park, US, 1989.
Cherkashin, E.A., Splittable Data Structures in System of Automatic Theorem Proving KVANT/3, Vych. Tekhnol., 2008, vol. 13, pp. 102–107.
McCune, W.W., Experiments with Discrimination-Tree Indexing and Path Indexing for Term Retrieval, J. Autom. Reasoning, 1992, vol. 9, no. 2, pp. 147–167.
Davydov, A.V., The Calculus of Positively Constructed Formulae with Functional Symbols, in Prikladnye algoritmy v diskretnom analize: sb. nauch. tr., (Applied Algorithms in Discrete Analysis. Collection of Scientific papers), Korol’kov, Yu.D., Ed., Irkutsk: Irkutsk. Gos. Univ., 2008.
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Original Russian Text © A.V. Davydov, A.A. Larionov, E.A. Cherkashin, 2010, published in Modelirovanie i Analiz Informatsionnykh Sistem, 2010, No. 4, pp. 60–69.
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Davydov, A.V., Larionov, A.A. & Cherkashin, E.A. On the calculus of positively constructed formulas for automated theorem proving. Aut. Conrol Comp. Sci. 45, 402–407 (2011). https://doi.org/10.3103/S0146411611070054
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DOI: https://doi.org/10.3103/S0146411611070054