Statistical approach to proof theory

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1. C. L. Chang R. T. C. Lee, Symbolic logic and mechanical theorem proving, Academic Press, New York and London 1973. (1973) MR0441028
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. (1930) 
5. M. O. Rabin, Theoretical impediments to artificial intelligence, In: Information Processing 1974, North Holland Publ. Comp., Amsterdam 1974, 615-619. (1974) Zbl0296.68054MR0421186
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. (1965) Zbl0139.12303MR0170494
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.) (1950) MR0037064
8. A. Church, Introduction to Mathematical Logic I, Princeton University Press, Princeton, New Jersey 1956. (Russian translation: I1L, Moscow 1960). (1956) Zbl0073.24301MR0010511
9. H. B. Curry, Foundations of Mathematical Logic, McGraw-Hill Book Comp., New York - San Francisco-Toronto -London 1963. (Russian translation: Mir, Moscow 1969.) (1963) Zbl0163.24209MR0148529
10. A. Grzegorczyk, Zarys logiki matematycznej, Second edition, PWN, Warszawa 1969. (1969) MR0655787
11. S. C. Kleene, Mathematical Logic, John Wiley and Sons, New York -London -Sydney 1967. (Russian translation: Mir, Moscow 1973.) (1967) Zbl0149.24309MR0216930
12. S. C. Kleene, Introduction to Metamathematics, D. van Nostrand Comp., New York -Toronto 1952. (Russian translation: IIL, Moscow 1957.) (1952) Zbl0047.00703MR0051790
13. A. Mostowski, Logika matematyczna, Warszawa, Wroclaw 1948. (1948) MR0026972
14. H. Rasiowa R. Sikorski, The Mathematics of Metamathematics, PWN, Warszawa 1970. (1970) MR0344067
15. L. Rieger, Algebraic Methods of Mathematical Logic, Academia, Prague 1967. (1967) Zbl0218.02001
16. J. R. Shoenfield, Mathematical Logic, Addison-Wesley Publ. Comp., 1967. (Russian translation: Nauka, Moscow 1975). (1967) Zbl0155.01102MR0225631
17. A. Tarski, Introduction to Logic and to the Methodology of Deductive Sciences, Oxford Univ. Press, 1965. (Czech translation: Academia, Prague 1966). (1965) MR0003375
18. Hao Wang, A Survey of Symbolic Logic, North-Holland Publ. Comp., Amsterdam 1962. (1962) 
19. A. N. Whitehead B. Russell, Principia Mathematica, vol. 1-3, Cambridge Univ. Press, Cambridge 1925-27. (1925) 
20. A. Church, An Unsolvable Problem of Number Theory, Amer. J. Math. 58 (1936), 345 - 363. (1936) MR1507159
21. M. Davis H. Putnam, A Computing Procedure for Quantification Theory, Journal of the Assoc. for Comp. Machinery 7 (1960), 3, 201-215. (1960) MR0134439
22. P. C. Gilmore, A Proof Method for Quantification Theory; its Justification and Realization, IBM Journal of Research and Development 1 (1960), 28 - 35. (1960) Zbl0097.00301MR0130081
23. A. M. Turing, On Computable Numbers with an Application to the "Entscheidungsproblem", Proc. of the London Math. Soc. 42 (1963), 230-265. (1963) MR1577030
24. I. Kramosil, Random Axiomatic Systems, Research Rep., Institute of Information Theory and Automation, Prague 1973. (1973) 
25. I. Kramosil, Gentzen-Like Random Axiomatic Systems, Transactions of the 7th Prague Conference on Information Theory, . .., 1974", Academia, Prague 1977, 345-352. (1974) MR0491008
26. E. L. Lehmann, Testing Statistical Hypotheses, John Wiley and Sons, New York 1959. (Russian translation: Moscow, Mir 1964.) (1959) Zbl0089.14102MR0107933
27. A. Wald, Sequential Analysis, John Wiley and Sons, New York 1947. (Russian Translation: Moscow, Mir 1960.) (1947) Zbl0041.26303MR0020764
28. A. Wald, Statistical Decision Functions, John Wiley and Sons, New York 1960. (1960) MR0036976
29. V. Fabian, Základní statistické metody, NČSAV (Publishing House of the Czechoslovak Academy of Sciences), Prague 1963. (1963) MR0170406
30. 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.) (1957) Zbl0077.12201MR0088081
31. G. Gentzen, Untersuchungen über das logische Schliessen, Mathem. Zeitschrift 39 (1934-5), 176-210, 405-431. (1934) Zbl0010.14601
32. Б. B. Гнеденко, Kypс теории вероятностей, Физматгиз, Mocквa 1961. (1961) 
33. J. Janko, Statistické tabulky, NČSAV (Publishing House of the Czechoslovak Academy of Sciences), Prague 1958. (1958) MR0150924
34. I. Kramosil, Statistical Estimation of Deducibility in Polyadic Algebras, Kybernetika 7 (1971), 3, 181-200. (1971) Zbl0216.29502MR0300881
35. I. Kramosil, A Method for Random Sampling of Well-Formed Formulas, Kybernetika 8 (1972), 2, 133-148. (1972) Zbl0242.02014MR0343414
36. 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. (1971) MR0432414
37. I. Kramosil, A Method for Statistical Testing of an at Random Sampled Formula, Kybernetika 9 (1973), 3, 162-173. (1973) Zbl0275.02018MR0343415
38. I. Kramosil, Konstruktivní test délky formalizovaných důkazů, Research Report no. 869, Institute of Information Theory and Automation, September 1978. (1978) 
39. I. Kramosil J. Šindelář, Statistical Deducibility Testing with Stochastic Parameters, Kybernetika 14 (1978), 6, 385-396. (1978) MR0529191
40. M. Loève, Probability Theory, D. van Nostrand Comp., Princeton, N. J. Toronto, New York, London 1960. (Russian translation: IIL Moscow, 1962.) (1960) MR0123342
41. A. Rényi, Probability Theory, Akadémiai Kiadó, Budapest 1970. (Czech translation: Academia, Prague 1972.) (1970) 
42. Ohama Shigeo, On a Formalism which Makes any Sequence of Symbols Well-Formed, Nagoya Math. J. 32 (1968), 1-4. (1968) MR0231705
43. R. Sikorski, Boolean Algebras, Second Edition. Springer-Verlag, Berlin - Gottingen - Heidelberg- New York 1964. (Russian translation: Mir, Moscow, 1969.) (1964) Zbl0123.01303MR0126393
44. 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. (1959) MR0123477
45. A. Špaček., Statistical Estimation of Semantic Provability, In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics, 1960, vol. I, 655 - 688 (1960) MR0136538
46. 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. (1973) Zbl0299.02014MR0538787
47. 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. (1972) MR0451906
48. E. W. Beth, Formal Methods, D. Reidel Publ. Comp., Dordrecht 1962. (1962) Zbl0105.24503MR0160709
49. B. C. Чернышевский, Об oдном классе нормальных алгорифмов Mapковa, Cборник ,,Логические исследования", Mocквa 1959, 263-299. (1959) 
50. M. Davis, Computability and Unsolvability, Mc Graw-Hill Book Company, New York 1958. (1958) Zbl0080.00902MR0124208
51. C. Jordan, Calculus of Finite Differences, Chelsea, New York 1950. (1950) Zbl0041.05401
52. A. H. Macлов, Вероятностные машины Тюринга и рекурсивные функсии, Доклады AH CCCP 203 (1972), 5, 1018-1020. (1972) Zbl0245.18003
53. C. Ю. Macлов, O noиске вывода в исчислении общего типа, Исследования по конструктивной математике и математической логике V., Hayкa, Ленинград 1972, 59-65. (1972) 
54. C. Ю. Macлов E. Д. Pycaков, Вероятностные канонические исчисления, Исследования по конструктивной математике и математической логике V., Hayкa, Ленинград 1972, 66-76. (1972) 
55. A. Paz, Introduction to Probabilistic Automata, Academic Press, 1971. (1971) Zbl0234.94055MR0289222
56. E. L. Post, Formal Reductions of the General Combinatorial Decision Problem, Amer. Math. J. 65 (1943), 2, 197-215. (1943) Zbl0063.06327MR0007893
57. Б. A. Tpaхтенброт Я. M. Барздинъ, Конечные автоматы (поведение и синтез), Mocквa 1970. (1970) 
58. 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. (1969) Zbl0216.28202MR0263635
59. 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. (1972) MR0297524
60. I. M. Havel I. Kramosil, Probabilistic Methods in Robot Decision Making, In: Sborník prací celostátní konference o kybernetice, Praha 1976, 66-80. (1976) 
61. I. M. Havel I. Kramosil, A Stochastic Approach to Robot Pдan Formation, Kybernetika 14 (1978), 3, 143-173. (1978) MR0506646
62. I. Kramosil, Stochastické plány v problematice robotů s vyšším stupněm inteligence, In: "Aplikovaná robotika 77", Karlovy Vary 1977, 91 - 109. (1977) 
63. I. Kramosil, Pravděpodobnostní redukce větvících se plánů pro činnost automatu s cílovým chováním, Research Report, Institute of Information Theory and Automation, 1977. (1977) 
64. 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. (1977) Zbl0365.94079MR0464771
65. O. Štěpánková I. M. Havel, A Logical Theory of Robot Problem Solving, Artificial Intelligence 7 (1976), 129-161. (1976) MR0413627
66. 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). (1977) MR0468377
67. I. Kramosil, A Probabilistic Approach to Automaton-Environment Systems, Kybernetika 11 (1975), 3, 173-206. (1975) Zbl0308.94045MR0444347
68. I. Kramosil, A Selection-Based Formal Representation of an Environment, Kybernetika 12 (1976), 3, 127-150. (1976) MR0439294
69. I. Kramosil, Mechanized Experiment Planning in Automaton-Environment Systems, Kybernetika 13 (1974), 4, 225-244. (1974) MR0469188
70. 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. (1978) Zbl0399.60005MR0536795
71. I. Kramosil, Statistical Testing Procedure for Lengths of Formalized Proofs, Submitted for publication. Zbl0444.03007
72. R. T. C. Lee, Fuzzy Logic and the Resolution Principle, Journal of the Association for Computing Machinery 19 (1972), 1, 109-119. (1972) Zbl0245.02020MR0383856
73. J. V. Mayega, Statistical Decidability of Theorems, In: Creation in Mathematics 7 (1974), (J. Reichbach, ed.), Tel-Aviv 1974, 3-11. (1974) Zbl0301.68085
74. J. Pavelka, On Fuzzy-Logic I, II, III, To appear in Zeitschrift für Mathematische Logik und Grundlagen der Mathematik. MR0524558
75. J. Reichbach, Generalized Models, Probability of Formulas, Decisions and Statistical Decidability of Theorems, Jokohama Math. Journal 20 (1972), 2, 79-98. (1972) Zbl0257.02049MR0307871
76. L. Zadeh, Fuzzy Sets, Information and Control 8 (1965), 338-353. (1965) Zbl0139.24606MR0219427

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