[1] C. L. Chang R. T. C. Lee:
Symbolic logic and mechanical theorem proving. Academic Press, New York and London 1973.
MR 0441028
[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 0421186 |
Zbl 0296.68054
[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 0170494 |
Zbl 0139.12303
[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 0037064
[1] A. Church:
Introduction to Mathematical Logic I. Princeton University Press, Princeton, New Jersey 1956. (Russian translation: I1L, Moscow 1960).
MR 0010511 |
Zbl 0073.24301
[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 0148529 |
Zbl 0163.24209
[3] A. Grzegorczyk:
Zarys logiki matematycznej. Second edition, PWN, Warszawa 1969.
MR 0655787
[4] S. C. Kleene:
Mathematical Logic. John Wiley and Sons, New York -London -Sydney 1967. (Russian translation: Mir, Moscow 1973.)
MR 0216930 |
Zbl 0149.24309
[5] S. C. Kleene:
Introduction to Metamathematics. D. van Nostrand Comp., New York -Toronto 1952. (Russian translation: IIL, Moscow 1957.)
MR 0051790 |
Zbl 0047.00703
[6] A. Mostowski:
Logika matematyczna. Warszawa, Wroclaw 1948.
MR 0026972
[7] H. Rasiowa R. Sikorski:
The Mathematics of Metamathematics. PWN, Warszawa 1970.
MR 0344067
[8] L. Rieger:
Algebraic Methods of Mathematical Logic. Academia, Prague 1967.
Zbl 0218.02001
[9] J. R. Shoenfield:
Mathematical Logic. Addison-Wesley Publ. Comp., 1967. (Russian translation: Nauka, Moscow 1975).
MR 0225631 |
Zbl 0155.01102
[10] A. Tarski:
Introduction to Logic and to the Methodology of Deductive Sciences. Oxford Univ. Press, 1965. (Czech translation: Academia, Prague 1966).
MR 0003375
[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 1507159
[2] M. Davis H. Putnam:
A Computing Procedure for Quantification Theory. Journal of the Assoc. for Comp. Machinery 7 (1960), 3, 201-215.
MR 0134439
[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 0130081 |
Zbl 0097.00301
[4] A. M. Turing:
On Computable Numbers with an Application to the "Entscheidungsproblem". Proc. of the London Math. Soc. 42 (1963), 230-265.
MR 1577030
[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 0491008
[3] E. L. Lehmann:
Testing Statistical Hypotheses. John Wiley and Sons, New York 1959. (Russian translation: Moscow, Mir 1964.)
MR 0107933 |
Zbl 0089.14102
[4] A. Wald:
Sequential Analysis. John Wiley and Sons, New York 1947. (Russian Translation: Moscow, Mir 1960.)
MR 0020764 |
Zbl 0041.26303
[5] A. Wald:
Statistical Decision Functions. John Wiley and Sons, New York 1960.
MR 0036976
[1] V. Fabian:
Základní statistické metody. NČSAV (Publishing House of the Czechoslovak Academy of Sciences), Prague 1963.
MR 0170406
[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 0088081 |
Zbl 0077.12201
[3] G. Gentzen:
Untersuchungen über das logische Schliessen. Mathem. Zeitschrift 39 (1934-5), 176-210, 405-431.
Zbl 0010.14601
[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 0150924
[6] I. Kramosil:
Statistical Estimation of Deducibility in Polyadic Algebras. Kybernetika 7 (1971), 3, 181-200.
MR 0300881 |
Zbl 0216.29502
[7] I. Kramosil:
A Method for Random Sampling of Well-Formed Formulas. Kybernetika 8 (1972), 2, 133-148.
MR 0343414 |
Zbl 0242.02014
[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 0432414
[9] I. Kramosil:
A Method for Statistical Testing of an at Random Sampled Formula. Kybernetika 9 (1973), 3, 162-173.
MR 0343415 |
Zbl 0275.02018
[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 0529191
[12] M. Loève:
Probability Theory. D. van Nostrand Comp., Princeton, N. J. Toronto, New York, London 1960. (Russian translation: IIL Moscow, 1962.)
MR 0123342
[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 0231705
[15] R. Sikorski:
Boolean Algebras. Second Edition. Springer-Verlag, Berlin - Gottingen - Heidelberg- New York 1964. (Russian translation: Mir, Moscow, 1969.)
MR 0126393 |
Zbl 0123.01303
[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 0123477
[17] A. Špaček. :
Statistical Estimation of Semantic Provability. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics, 1960, vol. I, 655 - 688
MR 0136538
[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 0538787 |
Zbl 0299.02014
[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 0451906
[2] B. C. Чернышевский: Об oдном классе нормальных алгорифмов Mapковa. Cборник ,,Логические исследования", Mocквa 1959, 263-299.
[4] C. Jordan:
Calculus of Finite Differences. Chelsea, New York 1950.
Zbl 0041.05401
[5] A. H. Macлов:
Вероятностные машины Тюринга и рекурсивные функсии. Доклады AH CCCP 203 (1972), 5, 1018-1020.
Zbl 0245.18003
[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.
[9] E. L. Post:
Formal Reductions of the General Combinatorial Decision Problem. Amer. Math. J. 65 (1943), 2, 197-215.
MR 0007893 |
Zbl 0063.06327
[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 0263635 |
Zbl 0216.28202
[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 0297524
[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 0506646
[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 0464771 |
Zbl 0365.94079
[6] O. Štěpánková I. M. Havel:
A Logical Theory of Robot Problem Solving. Artificial Intelligence 7 (1976), 129-161.
MR 0413627
[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 0468377
[1] I. Kramosil:
A Probabilistic Approach to Automaton-Environment Systems. Kybernetika 11 (1975), 3, 173-206.
MR 0444347 |
Zbl 0308.94045
[2] I. Kramosil:
A Selection-Based Formal Representation of an Environment. Kybernetika 12 (1976), 3, 127-150.
MR 0439294
[3] I. Kramosil:
Mechanized Experiment Planning in Automaton-Environment Systems. Kybernetika 13 (1974), 4, 225-244.
MR 0469188
[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 0536795 |
Zbl 0399.60005
[5] I. Kramosil:
Statistical Testing Procedure for Lengths of Formalized Proofs. Submitted for publication.
Zbl 0444.03007
[6] R. T. C. Lee:
Fuzzy Logic and the Resolution Principle. Journal of the Association for Computing Machinery 19 (1972), 1, 109-119.
MR 0383856 |
Zbl 0245.02020
[7] J. V. Mayega:
Statistical Decidability of Theorems. In: Creation in Mathematics 7 (1974), (J. Reichbach, ed.), Tel-Aviv 1974, 3-11.
Zbl 0301.68085
[8] J. Pavelka:
On Fuzzy-Logic I, II, III. To appear in Zeitschrift für Mathematische Logik und Grundlagen der Mathematik.
MR 0524558
[9] J. Reichbach:
Generalized Models, Probability of Formulas, Decisions and Statistical Decidability of Theorems. Jokohama Math. Journal 20 (1972), 2, 79-98.
MR 0307871 |
Zbl 0257.02049