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**Publications by Karlis Podnieks**

**ORCID
0000-0002-8835-6516****ResearchGate
profile****Karlis.Podnieks@lu.lvProfessorUniversity
of LatviaFaculty of Computing**

**Papers**

1. On cut points of some probabilistic automata.
*Avtomatika i Vychislitel'naya Tekhnika*,
1970, N5, pp. 90–91 (in Russian, English translation: *Automatic
Control and Computer Sciences*).

2. On stability measure of decompositions of
stochastic matrices. *Avtomatika i
Vychislitel'naya Tekhnika*, 1971, N4, pp.
91–93 (in Russian, English translation: *Automatic
Control and Computer Sciences*).

3. On stable decompositions of stochastic matrices.
In: *Problems of Synthesis of Finite Automata*,
Riga, Zinatne Publishers, 1972, pp. 75–78 (in Russian).

4. On effective decomposition of stochastic matrices.
*Avtomatika i Vychislitel'naya Tekhnika*,
1972, N3, pp. 18–20 (in Russian, online copy: PDF,
English translation: *Automatic Control and
Computer Sciences*).

5. On the reducibility of function classes. In:
*Equations of Mathematical Physics and Theory
of Algorithms*, Riga, Latvia State
University, 1972, pp. 120–139 (in Russian).

6. (With R.Sranka) Reliability of switching circuits
with sufficiently reliable switches. *Avtomatika
i Vychislitel'naya Tekhnika*, 1973, N4, pp.
44–48 (in Russian, English translation: *Automatic
Control and Computer Sciences*).

7. (With J.Barzdins) Towards a theory of inductive inference. Proceedings of 2nd Symposium and Summer School on Mathematical Foundations of Computer Science, Strbske Pleso, High Tatras, Czechoslovakia, September 3–8, 1973, pp. 9–15 (in Russian, online copy: PDF)

8. Comparing various concepts of function prediction.
Part 1. *Scientific Proceedings of Latvia
State University*, 1974, Vol. 210, pp. 68–81
(in Russian, online copy: PDF).

9. (With J.Barzdins, E.Kinber) On speeding up
synthesis and prediction of functions. *Scientific
Proceedings of Latvia State University*,
1974, Vol. 210, pp. 117–128 (in Russian, online copy: PDF).

10. (With R.Freivalds) On computation in the limit by
non-deterministic Turing machines. *Scientific
Proceedings of Latvia State University*,
1974, Vol. 210, pp. 25–31 (in Russian, online copy: PDF).

11. Comparing various concepts of function
prediction. Part 2. *Scientific Proceedings of
Latvia State University*, 1975, Vol. 233, pp.
35–44 (in Russian, online copy: PDF).

12. Probabilistic prediction of computable functions.
*Scientific Proceedings of Latvia State
University*, 1975, Vol. 233, pp. 57–76
(in Russian).

13. The double-incompleteness theorem. *Scientific
Proceedings of Latvia State University*,
1975, Vol. 233, pp. 191–200 (in Russian, online copy: PDF,
online English translation: PDF)

14. Probabilistic synthesis of enumerated classes of
functions. *Dokl.Akad.Nauk SSSR*,
1975, Vol. 223, N5, pp. 1071–1074 (in Russian, English
translation: *Soviet Math. Dokl.*,
1975, Vol.16, N4, pp. 1042–1045, online English translation:
HTML, PDF).

15. The double-incompleteness theorem. *Proceedings
of Fourth
All-Union Conference on Mathematical Logic*,
1976, Stiinca, Kishinev, p.118 (in Russian, online copy: PDF,
online English translation: PDF)

16. Probabilistic programs synthesis. In: *Theory
of Algorithms and Programs*, Vol. 3, Latvia
State University, 1977, pp. 57–88 (in Russian, online copy:
PDF, online
English translation: HTML, PDF).

17. Computational complexity of prediction
strategies. In: *Theory of Algorithms and
Programs*, Vol. 3, Latvia State University,
1977, pp. 89–102 (in Russian, online copy: PDF)

18. Prediction of the next value of a function.
*Izvestija Vyssh. Uchebn. Zaved. Matematika*,
1981, N5, pp. 71–77 (in Russian, available online,
PDF).

19. An approach to database design. In: *Latvia
Archive of algorithms and programs*, 1986, 25
pp. (in Russian).

20. Platonism, intuition and the nature of
mathematics. *Abstracts of: "Heyting'88.
Summer School & Conference on Mathematical Logic, Chaika,
Bulgaria, September 1988"*, Sofia,
Bulgarian Academy of Sciences, 1988, pp. 50–51 (online copy:
PDF).

21. Methodological consequences of Gödel's
incompleteness theorem. *European Summer
Meeting of the Association for Symbolic Logic, Berlin, 1989, *The
Journal of Symbolic Logic, Vol. 57, No. 1, March, 1992, pp.326-327
(online copy).

22. Platonism, intuition and the nature of
mathematics. In: *Semiotika i informatika*,
Moscow, VINITI, 1990, Vol. 31, pp. 150–180 (in Russian, English
translation: PDF).

23. (With R.Freivalds, J.Barzdins) Inductive
inference of recursive functions: complexity bounds. *Lecture
Notes in Computer Science*, Vol. 502,
Springer, 1991, pp. 111–155 (online copy: PDF).

24. (With A.Kalnins, J.Barzdins) GRADE V1.0: Modelling and development environment for GRAPES-86 and GRAPES/4GL: Language description. Siemens Nixdorf, Munich, Germany, 1993, 246 pp.

25. (With A.Kalnins, J.Barzdins, I.Etmane et al.) Unified specification language and Integrated CASE tools for information system development. Proceedings of Baltic Workshop on National Infrastructure Databases, May 17–20, 1994, Trakai/Vilnius, Lithuania,Vol. 2, pp. 24–34.

26. (With A.Kalnins, J.Barzdins, I.Etmane et al.) GRADE Windows: an integrated CASE tool for information system development. Proceedings of the 6th International Conference on Software Engineering and Knowledge Engineering (SEKE'94), June 22–24, 1994, Jurmala, Latvia, pp. 54–61.

27. Platonism, intuition and the nature of
mathematics. In: *QED
Mailing List Archive, Mathematics and Computer Science, Argonne
National Laboratory*, November 1994 (available
online: parts 1,
2,
3,
4,
5)

28. (With A.Kalnins, J.Barzdins). GRADE V2.0 (MS-Windows). Modelling and development environment for GRAPES-86 and GRAPES/4GL: Language description. Part 1. Siemens Nixdorf, Munich, Germany, 1995, 314 pp.

29. (With A.Kalnins, J.Barzdins, I.Etmane). Towards
integrated computer aided systems and software engineering tool for
information systems design. Proceedings of 2nd International Workshop
on Advances in Databases and Information Systems (ADBIS'95), June
27–30, 1995, Moscow, Russia, *Workshops
in Computing*, Springer, 1996, pp. 3–11.

30. (With A.Kalnins, J.Barzdins, A.Auzins,et al.) Business Modeling Language GRAPES-BM and Related CASE Tools. Proceedings of 2nd International Baltic Workshop on Databases and Information Systems, June 12–14, 1996, Tallinn, Estonia, Vol. 2, pp. 3–16 (online copy: HTML).

31. (With U.Sarkans, J.Barzdins, A.Kalnins). Towards a metamodel-based universal graphical editor. Proceedings of 3rd International Baltic Workshop on Databases and Information Systems, April 15–17, 1998, Riga, Latvia, pp. 187–197.

32. (With A.Kalnins, J.Barzdins). MiniGRADE – a
tool for conceptual modeling by class diagrams. Proceedings of 18th
International Conference on Conceptual Modeling, November, 15–18,
1999, Paris, France, *Lecture Notes in
Computer Science*, Vol. 1728, Springer, 1999,
pp. 11–12 (online copy: PDF).

33. (With
A.Kalnins, J.Barzdins). Modeling languages and tools: state of the
art. *Proceedings
of the 2nd international conference* “Simulation,
Gaming, Training and Business Process Reengineering in Operations
Research”, Riga,
Latvia, September 8–9, 2000
, Riga Technical
University, 2000, pp. 211–214 (online copy: PDF).

34. (With A.Kalnins, A.Zarins, E.Celms, J.Barzdins).
Editor definition language and its implementation. Proceedings of 4th
Andrei Ershov International Conference on Perspectives of System
Informatics, July 3–6, 2001, Novosibirsk, Russia, *Lecture
Notes in Computer Science*, Vol. 2244,
Springer, 2001, pp. 530–537 (online copy: PDF)

35. (With A.Kalnins, J.Barzdins, E.Celms et al.) The first step towards generic modeling tool. Proceedings of 5th International Baltic Conference on Databases and Information Systems, June 3–6, 2002, Tallinn, Estonia, Vol. 2, pp. 167–180 (online copy: PDF).

36. MDA: correctness of model transformations. Which
models are schemas? Selected papers from 6th International Baltic
Conference on Databases and Information Systems, June 6–9,
2004, Riga, Latvia, *Frontiers in Artificial
Intelligence and Applications*, IOS Press,
Vol. 118, 2005, pp. 185–197 (online copy: PDF).

37. (With J. Barzdins, G. Barzdins, R. Balodis et
al.) Towards semantic Latvia. P*roceedings of
7th International Baltic Conference on Databases and Information
Systems*, July 3–6, 2006, Vilnius,
Lithuania, pp. 203–218 (online copy: PDF).

38. Indispensability Argument and Set Theory.
*The Reasoner*, Vol. 2, N 11, November 2008, pp. 8–9.
ISSN 1757-0522 (available online).

39. Is Scientific Modeling an Indirect Methodology?
*The Reasoner*, Vol. 3, N 1, January 2009, pp. 4–5. ISSN
1757-0522 (available online).

40. Towards Model-Based Model of Cognition. *The Reasoner*,
Vol. 3, N 6, June 2009, pp. 5–6. ISSN 1757-0522 (available
online).

41. Gödel's
Incompleteness Theorem. In: *Matematika XX veka. Vzglyad iz
Peterburga**, Ed. A. M. Vershik, *MCNMO, Moscow, 2010,
pp.170–174 (in Russian, online copy: PDF),
ISBN 978-5-94059-586-3.

42. (With John Tabak). The Nature of Mathematics – an
interview with Professor Karlis Podnieks. In: *John Tabak. Numbers:
Computers, Philosophers, and the Search for Meaning.* Revised
Edition. Facts on File, 2011, 243 pp. (Afterword, pp.188–197,
online copy: PDF),
ISBN 978-0-8160-7940-7.

43. Frege’s
Puzzle from a Model-Based Point of View. *The
Reasoner*,
Vol. 6, N 1, January 2012, pp. 5–6. ISSN 1757-0522 (available
online).

44.
(With J.
Iraids, K. Balodis, J. Cernenoks, M. Opmanis, R. Opmanis). Integer
Complexity: Experimental and Analytical Results. *Scientific
Papers University of Latvia, Computer Science and Information
Technologies*,
Vol. 787, 2012, pp. 153–179 (available online).

45. The Dappled World Perspective Refined. *The Reasoner*,
Vol. 8, N 1, January 2014, pp. 3–4. ISSN 1757-0522 (available
online).

46. Fourteen Arguments in Favour of a Formalist Philosophy of Real
Mathematics. *Baltic J. Modern Computing*, Vol. 3 (2015), N 1,
pp. 1–15 (available online).

47. (With J.
Cernenoks, J. Iraids, M. Opmanis, R. Opmanis). Integer Complexity:
Experimental and Analytical Results II. *Proceedings
of 17th International Workshop Descriptional Complexity of Formal
Systems, DCFS 2015, Waterloo, Canada, June 25-27, 2015*,
Lecture Notes in Computer Science, Vol. 9118, Springer, 2015, pp.
58–69. DOI: 10.1007/978-3-319-19225-3_5 (available online).

48. Locally Constrained Ontologies. *Baltic J. Modern Computing*,
Vol. 4 (2016), N 4, pp. 694–720 (available online).

1. Around Gödel’s Theorem, 1^{st}
edition., Riga, Latvia State University, 1981, 105 pp.
(in Russian, online copy of Chapter 1: PDF).

2. Assembly language programming in OS/360. Riga, Latvia State University, 1981, 88 pp. (in Russian).

3. Data base management system IMS: the batch mode. Riga, Latvia State University, 1982, 25 pp. (in Russian).

4. (With M.Auguston, R.Balodis, J.Barzdin et al.)
Programming in PL/1 OS/360, 2^{nd} ed. Moscow, Finances and
Statistics Publishers, 1984, 327 pp. (in Russian).

5. Platonism, intuition and the nature of mathematics. Riga, Latvia State University, 1988, 22 pp. (in Russian).

6. Around Gödel’s Theorem, 2^{nd}
edition., Riga, “Zinatne”, 1992, 192 pp. (in
Russian, online copy: PDF).

7. Probabilities. Tutorial for Secondary Schools. Riga, 1992 (in Latvian, online copy: PDF).

8. What is Mathematics? Gödel’s Theorem and Around. Hyper-textbook for students, 1997–2015 (online book: PDF).

9. (With V.Detlovs) Introduction to Mathematical Logic. Hyper-textbook for students, 2000–2016 (online book: PDF).

10. Logic and Foundations of Mathematics. Gödel's
Theorem. Chapter VI in: *Symbolic Logic*,
St. Petersburg State University, St.Petersburg, 2005, pp.180–221
(in Russian).

**1.
The
Limits of Modeling. ***PhilSci
Archive***,
July 15, 2010.**

Developed further in: K. Podnieks. **The Dappled World
Perspective Refined.** *The Reasoner*, Vol. 8, N 1, January
2014, pp. 3–4 (available online).

**2.
The Formalist
Picture of Cognition. Towards a Total Demystification.
***SciRePrints
Archive***,****
****ID
Code 157, 25 November 2010.**

**3.
Towards a
General Definition of Modeling. ***SciRePrints
Archive***,
ID Code 155, 25 November 2010.**

Developed further in: K. Podnieks. **The Dappled World
Perspective Refined.** *The Reasoner*, Vol. 8, N 1, January
2014, pp. 3–4 (available online).

**4.
Some
Neglected Arguments in Favour of Formalism. ***E-resource
repository of the University of Latvia***,
ID Code 1405, 30 March, 2013.**

Published as: K. Podnieks. **Fourteen Arguments in Favour of a
Formalist Philosophy of Real Mathematics.** *Baltic J. Modern
Computing*, Vol. 3, N 1, 2015, pp. 1–15 (available online).

5. Truth Demystified. ResearchGate, ID Code 282860865, October 2015.

**1.
Hegel, Marx, and Gödel's theorem.
April 1999.**

**2.
Digital mathematics and non-digital
mathematics. October 1999.**

**3.
Towards a real finitism? December 2005.**

**4.
The nature of
mathematics. June 2006.**

Developed further in: K. Podnieks. **Fourteen Arguments in Favour
of a Formalist Philosophy of Real Mathematics.** *Baltic J.
Modern Computing*, Vol. 3, N 1, 2015, pp. 1–15 (available
online).

**5.
****What
is Science? Science is Modeling!****
****February
2007.**

**Developed
further in: K. Podnieks. ****The
Dappled World Perspective Refined.****
***The
Reasoner***,
Vol. 8, N 1, January 2014, pp. 3–4 (available online).**