@article{KYB_1979_15_Suppl_a0,
author = {Kramosil, Ivan},
title = {Statistical approach to proof theory},
journal = {Kybernetika},
pages = {1--97},
year = {1979},
volume = {15},
number = {Suppl},
mrnumber = {0562376},
zbl = {0445.68068},
language = {en},
url = {http://geodesic.mathdoc.fr/item/KYB_1979_15_Suppl_a0/}
}
Kramosil, Ivan. Statistical approach to proof theory. Kybernetika, Tome 15 (1979), pp. 1-97. http://geodesic.mathdoc.fr/item/KYB_1979_15_Suppl_a0/
[1] C. L. Chang R. T. C. Lee: Symbolic logic and mechanical theorem proving. Academic Press, New York and London 1973. | MR
[2] R. Descartes: Discours sur la méthode. Paris 1637.
[3] N. J. Nillson: A mobile automaton: An application of artificial intelligence techniques. Proc. of the First lnternat. Joint Conf. on Artificial Intelligence, Washington. D. C, 509 - 520.
[4] M. Presburger: Über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation herrvortritt. Comptes rendus du 1-er Congrès des Mathématiciens des Pays Slaves, Warsaw, 1930, 92-101.
[5] M. O. Rabin: Theoretical impediments to artificial intelligence. In: Information Processing 1974, North Holland Publ. Comp., Amsterdam 1974, 615-619. | MR | Zbl
[6] J. A. Robinson: A machine oriented logic based on the resolution principle. J. of the Assoc. for Comp. Machinery 12 (1965), 1, 23-41. | MR | Zbl
[7] A. M. Turing: Computing machinery and intelligence. Mind 59 (1950), 433 - 460, also in: Computers and thought (E. A. Feigenbaum and J. Feldman, Eds.), McGraw-Hill, New York 1967. (Russian translation: Moscow 1973.) | MR
[1] A. Church: Introduction to Mathematical Logic I. Princeton University Press, Princeton, New Jersey 1956. (Russian translation: I1L, Moscow 1960). | MR | Zbl
[2] H. B. Curry: Foundations of Mathematical Logic. McGraw-Hill Book Comp., New York - San Francisco-Toronto -London 1963. (Russian translation: Mir, Moscow 1969.) | MR | Zbl
[3] A. Grzegorczyk: Zarys logiki matematycznej. Second edition, PWN, Warszawa 1969. | MR
[4] S. C. Kleene: Mathematical Logic. John Wiley and Sons, New York -London -Sydney 1967. (Russian translation: Mir, Moscow 1973.) | MR | Zbl
[5] S. C. Kleene: Introduction to Metamathematics. D. van Nostrand Comp., New York -Toronto 1952. (Russian translation: IIL, Moscow 1957.) | MR | Zbl
[6] A. Mostowski: Logika matematyczna. Warszawa, Wroclaw 1948. | MR
[7] H. Rasiowa R. Sikorski: The Mathematics of Metamathematics. PWN, Warszawa 1970. | MR
[8] L. Rieger: Algebraic Methods of Mathematical Logic. Academia, Prague 1967. | Zbl
[9] J. R. Shoenfield: Mathematical Logic. Addison-Wesley Publ. Comp., 1967. (Russian translation: Nauka, Moscow 1975). | MR | Zbl
[10] A. Tarski: Introduction to Logic and to the Methodology of Deductive Sciences. Oxford Univ. Press, 1965. (Czech translation: Academia, Prague 1966). | MR
[11] Hao Wang: A Survey of Symbolic Logic. North-Holland Publ. Comp., Amsterdam 1962.
[12] A. N. Whitehead B. Russell: Principia Mathematica, vol. 1-3. Cambridge Univ. Press, Cambridge 1925-27.
[1 ] A. Church: An Unsolvable Problem of Number Theory. Amer. J. Math. 58 (1936), 345 - 363. | MR
[2] M. Davis H. Putnam: A Computing Procedure for Quantification Theory. Journal of the Assoc. for Comp. Machinery 7 (1960), 3, 201-215. | MR
[3] P. C. Gilmore: A Proof Method for Quantification Theory; its Justification and Realization. IBM Journal of Research and Development 1 (1960), 28 - 35. | MR | Zbl
[4] A. M. Turing: On Computable Numbers with an Application to the "Entscheidungsproblem". Proc. of the London Math. Soc. 42 (1963), 230-265. | MR
[1] I. Kramosil: Random Axiomatic Systems. Research Rep., Institute of Information Theory and Automation, Prague 1973.
[2] I. Kramosil: Gentzen-Like Random Axiomatic Systems. Transactions of the 7th Prague Conference on Information Theory, . .., 1974", Academia, Prague 1977, 345-352. | MR
[3] E. L. Lehmann: Testing Statistical Hypotheses. John Wiley and Sons, New York 1959. (Russian translation: Moscow, Mir 1964.) | MR | Zbl
[4] A. Wald: Sequential Analysis. John Wiley and Sons, New York 1947. (Russian Translation: Moscow, Mir 1960.) | MR | Zbl
[5] A. Wald: Statistical Decision Functions. John Wiley and Sons, New York 1960. | MR
[1] V. Fabian: Základní statistické metody. NČSAV (Publishing House of the Czechoslovak Academy of Sciences), Prague 1963. | MR
[2] W. Feller: An Introduction to Probability Theory and its Applications. vol. I and II. John Wiley and Sons, Chapman and Hall, New York -London, vol. I (second edition) 1957, vol. 2 (first edition) 1966. (Russian translation: Mir, Moscow 1964, 1967.) | MR | Zbl
[3] G. Gentzen: Untersuchungen über das logische Schliessen. Mathem. Zeitschrift 39 (1934-5), 176-210, 405-431. | Zbl
[4] Б. B. Гнеденко: Kypс теории вероятностей. Физматгиз, Mocквa 1961.
[5] J. Janko: Statistické tabulky. NČSAV (Publishing House of the Czechoslovak Academy of Sciences), Prague 1958. | MR
[6] I. Kramosil: Statistical Estimation of Deducibility in Polyadic Algebras. Kybernetika 7 (1971), 3, 181-200. | MR | Zbl
[7] I. Kramosil: A Method for Random Sampling of Well-Formed Formulas. Kybernetika 8 (1972), 2, 133-148. | MR | Zbl
[8] I. Kramosil: Statistical Estimation of Deducibility in Formalized Theories. In: Proceedings of the Fourth Conference on Probability Theory, Braşov, 1971, Editura Academici RSR, 1973, 281-298. | MR
[9] I. Kramosil: A Method for Statistical Testing of an at Random Sampled Formula. Kybernetika 9 (1973), 3, 162-173. | MR | Zbl
[10] I. Kramosil: Konstruktivní test délky formalizovaných důkazů. Research Report no. 869, Institute of Information Theory and Automation, September 1978.
[11] I. Kramosil J. Šindelář: Statistical Deducibility Testing with Stochastic Parameters. Kybernetika 14 (1978), 6, 385-396. | MR
[12] M. Loève: Probability Theory. D. van Nostrand Comp., Princeton, N. J. Toronto, New York, London 1960. (Russian translation: IIL Moscow, 1962.) | MR
[13] A. Rényi: Probability Theory. Akadémiai Kiadó, Budapest 1970. (Czech translation: Academia, Prague 1972.)
[14] Ohama Shigeo: On a Formalism which Makes any Sequence of Symbols Well-Formed. Nagoya Math. J. 32 (1968), 1-4. | MR
[15] R. Sikorski: Boolean Algebras. Second Edition. Springer-Verlag, Berlin - Gottingen - Heidelberg- New York 1964. (Russian translation: Mir, Moscow, 1969.) | MR | Zbl
[16] A. Špaček: Statistical Estimation of Provability in Boolean Logics. In: Transactions of the Second Prague Conference on Information Theory, Prague 1959. NČSAV (Publishing House of the Czechoslovak Academy of Sciences), Prague 1960, 609 - 626. | MR
[17] A. Špaček. : Statistical Estimation of Semantic Provability. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics, 1960, vol. I, 655 - 688 | MR
[1] I. Kramosil: Statistical Estimation of Deducibility in a Random Sequence of Formulas. Transactions of the Sixth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes. Academia, Prague 1973, pp. 449-463. | MR | Zbl
[2] I. Kramosil: A Statistical Model for Theorem Proving with a Limited Instantaneous Memory. Proceedings of the 9. European Meeting of Statisticians, Colloquia Mathematica Societatis János Bolyai, Budapest 1972, pp. 425-453. | MR
[1] E. W. Beth: Formal Methods. D. Reidel Publ. Comp., Dordrecht 1962. | MR | Zbl
[2] B. C. Чернышевский: Об oдном классе нормальных алгорифмов Mapковa. Cборник ,,Логические исследования", Mocквa 1959, 263-299.
[3] M. Davis: Computability and Unsolvability. Mc Graw-Hill Book Company, New York 1958. | MR | Zbl
[4] C. Jordan: Calculus of Finite Differences. Chelsea, New York 1950. | Zbl
[5] A. H. Macлов: Вероятностные машины Тюринга и рекурсивные функсии. Доклады AH CCCP 203 (1972), 5, 1018-1020. | Zbl
[6] C. Ю. Macлов: O noиске вывода в исчислении общего типа. Исследования по конструктивной математике и математической логике V., Hayкa, Ленинград 1972, 59-65.
[7] C. Ю. Macлов E. Д. Pycaков: Вероятностные канонические исчисления. Исследования по конструктивной математике и математической логике V., Hayкa, Ленинград 1972, 66-76.
[8] A. Paz: Introduction to Probabilistic Automata. Academic Press, 1971. | MR | Zbl
[9] E. L. Post: Formal Reductions of the General Combinatorial Decision Problem. Amer. Math. J. 65 (1943), 2, 197-215. | MR | Zbl
[10] Б. A. Tpaхтенброт Я. M. Барздинъ: Конечные автоматы (поведение и синтез). Mocквa 1970.
[11] S. C. van Westrhenen: A Probabilistic Machine for the Estimation of Provability in the First Order Predicate Calculus. Z. für math. Logik und Grundlagen der Math. 15 (1969), 291-297. | MR | Zbl
[12] S. C. van Westrhenen: Statistical Studies of Theoremhood in Classical Prepositional and First Order Predicate Calculus. J. of the Assoc. for Comp. Machinery 19 (1972), 2, 347-365. | MR
[1] I. M. Havel I. Kramosil: Probabilistic Methods in Robot Decision Making. In: Sborník prací celostátní konference o kybernetice, Praha 1976, 66-80.
[2] I. M. Havel I. Kramosil: A Stochastic Approach to Robot Pдan Formation. Kybernetika 14 (1978), 3, 143-173. | MR
[3] I. Kramosil: Stochastické plány v problematice robotů s vyšším stupněm inteligence. In: "Aplikovaná robotika 77", Karlovy Vary 1977, 91 - 109.
[4] I. Kramosil: Pravděpodobnostní redukce větvících se plánů pro činnost automatu s cílovým chováním. Research Report, Institute of Information Theory and Automation, 1977.
[5] I. Kramosil: A probabilistic Restriction of Branching Plans. In: Mathematical Foundations of Computer Science, 1977, Lecture Notes in Computer Science 53, Springer-Verlag, Berlin-Heidelberg-New York 1977, 342-349. | MR | Zbl
[6] O. Štěpánková I. M. Havel: A Logical Theory of Robot Problem Solving. Artificial Intelligence 7 (1976), 129-161. | MR
[7] O. Štěpánková I. M. Havel: Incidental and State-Dependent Phenomena in Robot Problem Solving. Kybernetika 13 (1977), 6, 421-438. (Cf. also the preliminary version In: Proceedings of the AISB Summer Conference, Edinburgh 1976, 266-278). | MR
[1] I. Kramosil: A Probabilistic Approach to Automaton-Environment Systems. Kybernetika 11 (1975), 3, 173-206. | MR | Zbl
[2] I. Kramosil: A Selection-Based Formal Representation of an Environment. Kybernetika 12 (1976), 3, 127-150. | MR
[3] I. Kramosil: Mechanized Experiment Planning in Automaton-Environment Systems. Kybernetika 13 (1974), 4, 225-244. | MR
[4] I. Kramosil: Some Remarks on Probabilities over Formalized Languages. In: Transactions of the Eight Prague Conference on Information Theory, ..., Academia, Prague 1978, vol. A, 371-382. | MR | Zbl
[5] I. Kramosil: Statistical Testing Procedure for Lengths of Formalized Proofs. Submitted for publication. | Zbl
[6] R. T. C. Lee: Fuzzy Logic and the Resolution Principle. Journal of the Association for Computing Machinery 19 (1972), 1, 109-119. | MR | Zbl
[7] J. V. Mayega: Statistical Decidability of Theorems. In: Creation in Mathematics 7 (1974), (J. Reichbach, ed.), Tel-Aviv 1974, 3-11. | Zbl
[8] J. Pavelka: On Fuzzy-Logic I, II, III. To appear in Zeitschrift für Mathematische Logik und Grundlagen der Mathematik. | MR
[9] J. Reichbach: Generalized Models, Probability of Formulas, Decisions and Statistical Decidability of Theorems. Jokohama Math. Journal 20 (1972), 2, 79-98. | MR | Zbl
[10] L. Zadeh: Fuzzy Sets. Information and Control 8 (1965), 338-353. | MR | Zbl