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Kleene Algebra of Partial Predicates Cover
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|Jul 2018

References

  1. [1] Raymond Balbes and Philip Dwinger. Distributive Lattices. University of Missouri Press, 1975.
  2. [2] T.S. Blyth and J. Varlet. Ockham Algebras. Oxford science publications. Oxford University Press, 1994.10.1093/oso/9780198599388.001.0001
  3. [3] Diana Brignole and Antonio Monteiro. Caractérisation des algèbres de Nelson par des egalités. Instituto de Matemática, Universidad Nacional del Sur, Argentina, 1964.
  4. [4] Roberto Cignoli. Injective de Morgan and Kleene algebras. Proceedings of the American Mathematical Society, 47(2):269–278, 1975.10.1090/S0002-9939-1975-0357259-4
  5. [5] J.P. Cleave. A Study of Logics. Oxford logic guides. Clarendon Press, 1991. ISBN 9780198532118.
  6. [6] J.H. Conway. Regular algebra and finite machines. Chapman and Hall mathematics series. Chapman and Hall, 1971.
  7. [7] R.W. Floyd. Assigning meanings to programs. Mathematical aspects of computer science, 19(19–32), 1967.10.1090/psapm/019/0235771
  8. [8] Adam Grabowski. Robbins algebras vs. Boolean algebras. Formalized Mathematics, 9(4): 681–690, 2001.
  9. [9] C.A.R. Hoare. An axiomatic basis for computer programming. Commun. ACM, 12(10): 576–580, 1969.10.1145/363235.363259
  10. [10] Ievgen Ivanov. On the underapproximation of reach sets of abstract continuous-time systems. In Erika Ábrahám and Sergiy Bogomolov, editors, Proceedings 3rd International Workshop on Symbolic and Numerical Methods for Reachability Analysis, SNR@ETAPS 2017, Uppsala, Sweden, 22nd April 2017, volume 247 of EPTCS, pages 46–51, 2017. doi:10.4204/EPTCS.247.4.10.4204/EPTCS.247.4
  11. [11] Ievgen Ivanov. On representations of abstract systems with partial inputs and outputs. In T. V. Gopal, Manindra Agrawal, Angsheng Li, and S. Barry Cooper, editors, Theory and Applications of Models of Computation – 11th Annual Conference, TAMC 2014, Chennai, India, April 11–13, 2014. Proceedings, volume 8402 of Lecture Notes in Computer Science, pages 104–123. Springer, 2014. ISBN 978-3-319-06088-0. doi:10.1007/978-3-319-06089-7_8.10.1007/978-3-319-06089-7_8
  12. [12] Ievgen Ivanov. On local characterization of global timed bisimulation for abstract continuous-time systems. In Ichiro Hasuo, editor, Coalgebraic Methods in Computer Science – 13th IFIP WG 1.3 International Workshop, CMCS 2016, Colocated with ETAPS 2016, Eindhoven, The Netherlands, April 2–3, 2016, Revised Selected Papers, volume 9608 of Lecture Notes in Computer Science, pages 216–234. Springer, 2016. ISBN 978-3-319-40369-4. doi:10.1007/978-3-319-40370-0_13.10.1007/978-3-319-40370-0_13
  13. [13] Ievgen Ivanov, Mykola Nikitchenko, and Uri Abraham. On a Decidable Formal Theory for Abstract Continuous-Time Dynamical Systems, pages 78–99. Springer International Publishing, 2014. ISBN 978-3-319-13206-8. doi:10.1007/978-3-319-13206-8_4.10.1007/978-3-319-13206-8_4
  14. [14] Ievgen Ivanov, Mykola Nikitchenko, and Uri Abraham. Event-based proof of the mutual exclusion property of Peterson’s algorithm. Formalized Mathematics, 23(4):325–331, 2015. doi:10.1515/forma-2015-0026.10.1515/forma-2015-0026
  15. [15] Ievgen Ivanov, Mykola Nikitchenko, and Volodymyr G. Skobelev. Proving properties of programs on hierarchical nominative data. The Computer Science Journal of Moldova, 24(3):371–398, 2016.
  16. [16] J. A. Kalman. Lattices with involution. Transactions of the American Mathematical Society, 87(2):485–485, February 1958. doi:10.1090/s0002-9947-1958-0095135-x.10.1090/s0002-9947-1958-0095135-x
  17. [17] S.C. Kleene. Introduction to Metamathematics. North-Holland Publishing Co., Amsterdam, and P. Noordhoff, Groningen, 1952.
  18. [18] S. Körner. Experience and Theory: An Essay in the Philosophy of Science. International library of philosophy and scientific method. Routledge & Kegan Paul, 1966.
  19. [19] Artur Kornilowicz, Andrii Kryvolap, Mykola Nikitchenko, and Ievgen Ivanov. Formalization of the algebra of nominative data in Mizar. In Maria Ganzha, Leszek A. Maciaszek, and Marcin Paprzycki, editors, Proceedings of the 2017 Federated Conference on Computer Science and Information Systems, FedCSIS 2017, Prague, Czech Republic, September 3–6, 2017., pages 237–244, 2017. ISBN 978-83-946253-7-5. doi:10.15439/2017F301.10.15439/2017F301
  20. [20] Artur Korniłowicz, Andrii Kryvolap, Mykola Nikitchenko, and Ievgen Ivanov. An approach to formalization of an extension of Floyd-Hoare logic. In Vadim Ermolayev, Nick Bassiliades, Hans-Georg Fill, Vitaliy Yakovyna, Heinrich C. Mayr, Vyacheslav Kharchenko, Vladimir Peschanenko, Mariya Shyshkina, Mykola Nikitchenko, and Aleksander Spivakovsky, editors, Proceedings of the 13th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer, Kyiv, Ukraine, May 15–18, 2017, volume 1844 of CEUR Workshop Proceedings, pages 504–523. CEUR-WS.org, 2017.
  21. [21] Artur Korniłowicz, Andrii Kryvolap, Mykola Nikitchenko, and Ievgen Ivanov. Formalization of the Nominative Algorithmic Algebra in Mizar, pages 176–186. Springer International Publishing, 2018. ISBN 978-3-319-67229-8. doi:10.1007/978-3-319-67229-8_16.10.1007/978-3-319-67229-8_16
  22. [22] Dexter Kozen. On Kleene algebras and closed semirings, pages 26–47. Springer Berlin Heidelberg, 1990. doi:10.1007/BFb0029594.10.1007/BFb0029594
  23. [23] Andrii Kryvolap, Mykola Nikitchenko, and Wolfgang Schreiner. Extending Floyd-Hoare Logic for Partial Pre- and Postconditions, pages 355–378. Springer International Publishing, 2013. ISBN 978-3-319-03998-5. doi:10.1007/978-3-319-03998-5_18.10.1007/978-3-319-03998-5_18
  24. [24] Antonio Monteiro and Luiz Monteiro. Axiomes indépendants pour les algèbres de Nelson, de Łukasiewicz trivalentes, de de Morgan et de Kleene. Notas de lógica matemática, (40): 1–11, 1996.10.1305/ndjfl/1093894076
  25. [25] Maurizio Negri. Three valued semantics and DMF-algebras. Boll. Un. Mat. Ital. B (7), 10(3):733–760, 1996.
  26. [26] Maurizio Negri. DMF-algebras: representation and topological characterization. Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8), 1(2):369–390, 1998.
  27. [27] Maurizio Negri. Partial probability and Kleene logic, 2013.
  28. [28] M.S. Nikitchenko and S.S. Shkilniak. Mathematical logic and theory of algorithms. Publishing house of Taras Shevchenko National University of Kyiv, Ukraine (in Ukrainian), 2008.
  29. [29] M.S. Nikitchenko and S.S. Shkilniak. Applied logic. Publishing house of Taras Shevchenko National University of Kyiv, Ukraine (in Ukrainian), 2013.
  30. [30] Mykola Nikitchenko and Stepan Shkilniak. Algebras and logics of partial quasiary predicates. Algebra and Discrete Mathematics, 23(2):263–278, 2017.
  31. [31] Nikolaj S. Nikitchenko. A composition nominative approach to program semantics. Technical Report IT-TR 1998-020, Department of Information Technology, Technical University of Denmark, 1998.
  32. [32] Helena Rasiowa. An Algebraic Approach to Non-Classical Logics. North Holland, 1974.
  33. [33] Volodymyr G. Skobelev, Mykola Nikitchenko, and Ievgen Ivanov. On algebraic properties of nominative data and functions. In Vadim Ermolayev, Heinrich C. Mayr, Mykola Nikitchenko, Aleksander Spivakovsky, and Grygoriy Zholtkevych, editors, Information and Communication Technologies in Education, Research, and Industrial Applications – 10th International Conference, ICTERI 2014, Kherson, Ukraine, June 9–12, 2014, Revised Selected Papers, volume 469 of Communications in Computer and Information Science, pages 117–138. Springer, 2014. ISBN 978-3-319-13205-1. doi:10.1007/978-3-319-13206-8_6.10.1007/978-3-319-13206-8_6
DOI: https://doi.org/10.2478/forma-2018-0002 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Language: English
Page range: 11 - 20
Submitted on: Mar 27, 2018
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Published on: Jul 28, 2018
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2018 Artur Korniłowicz, Ievgen Ivanov, Mykola Nikitchenko, published by University of Białystok
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