Skip to main content
SpringerLink
Log in

Logics for Programs and Knowledge

  • Chapter
  • First Online:
Logic: Reference Book for Computer Scientists

Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 245))

  • 107 Accesses

Abstract

In this chapter we meet sentential dynamic logic (SDL), epistemic logics, logics of approximate containment of concepts couched in terms of mereology, and elements of Data Analysis in the form of Boolean reasoning in the environment of data along with the logic for functional dependence and the information logic.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Segerberg, K.: A completeness theorem in the modal logic of programs. Notices AMS 24(6), A-522, no. 77T-E69 (1977)

    Google Scholar 

  2. Kozen, D., Parikh, R.: Note. An elementary proof of the completeness of PDL. Theor. Comput. Sci. 14, 113–118 (1981). https://doi.org/10.1016/0304-3975(81)90019-0

  3. Fischer, M.J., Ladner, R.E.: Propositional modal logic of programs. J. Comput. Syst. Sci. 18, 194–211 (1979)

    Article  MATH  Google Scholar 

  4. Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. The MIT Press, Cambridge (2000)

    Book  MATH  Google Scholar 

  5. Hintikka, J.K.K.: Knowledge and Belief. Cornell University Press, Ithaca (1962)

    MATH  Google Scholar 

  6. Kripke, S.: Semantical analysis of modal logic I: Normal modal propositional calculi. Z. Math. Logik und Grundlagen der Mathematik 9(5–6), 67–96 (1963). https://doi.org/10.1002.19630090502

  7. Ladner, R.E.: The computational complexity of provability in systems of modal propositional logic. SIAM J. Comput. 6(3), 467–480 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  8. Halpern, J., Moses, Y.O.: A guide to completeness and complexity for modal logics of knowledge and belief. Artif. Intell. 54(2), 319–379 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  9. Lenzen, W.: Glauben, Wissen und Wahrscheinlichtkeit. Springer, Vienna (1980); see also: Recent work in epistemic logic. Acta Philosophica Fennica 30, 1–219 (1978)

    Google Scholar 

  10. Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001)

    Book  MATH  Google Scholar 

  11. Leśniewski, S.: Foundations of General Set Theory (in Polish: Podstawy Ogólnej Teoryi Mnogos̈ci). Polish Sci. Soc. Moscow (1916); also in: Topoi 2, 7–52 (1982)

    Google Scholar 

  12. Srzednicki, J., Surma, S.J., Barnett, D., Rickey, V.F. (eds.): Collected Works of Stanisław Leśniewski. Kluwer, Dordrecht (1992)

    Google Scholar 

  13. Leśniewski, S.: Über die Grundlagen der Ontologie. C.R. Soc. Sci. Lettr. Varsovie Cl.III, 23 Anneé, 111–132 (1930); also: [13]

    Google Scholar 

  14. Tarski, A.: Zur Grundlegung der Booleschen Algebra I. Fundam. Math. 24, 177–198 (1935)

    Article  MATH  Google Scholar 

  15. Lejewski, C.: Consistency of Leśniewski’s Mereology. J. Symb. Logic 34, 321–328 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  16. Polkowski, L.: Approximate Reasoning by Parts. An Introduction to Rough Mereology. Springer. ISRL 20, Berlin (2011)

    Google Scholar 

  17. Polkowski, L., Skowron, A.: Rough mereology: a new paradigm for approximate reasoning. Int. J. Approx. Reas. 15(4), 333–365 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  18. Łukasiewicz, J.: Die Logischen Grundlagen der Wahrscheinlichtkeitsrechnung. Cracow (1913); also in [17]

    Google Scholar 

  19. Borkowski, L.: Jan Łukasiewicz. Selected Works. North Holland, Amsterdam (1970)

    Google Scholar 

  20. Polkowski, L.: Introducing mass-based rough mereology in a mereological universe with relations to fuzzy logics and a generalization of the Łukasiewicz logical foundations of probability. Fundam. Inf. 166(3), 227–249 (2019)

    MathSciNet  MATH  Google Scholar 

  21. Polkowski, L.: On the compactness property of mereological spaces. Fundam. Inf. 172(1), 73–95 (2020)

    MathSciNet  MATH  Google Scholar 

  22. Gleason, A.M.: Projective topological spaces. Illinois J. Math. 2, 482–489 (1958)

    Article  MathSciNet  MATH  Google Scholar 

  23. Pawlak, Z.: Rough sets. Int. J. Inform. Comp. Sci. 11, 341–356 (1982)

    Article  MATH  Google Scholar 

  24. Pawlak, Z.: Rough Sets. Theoretical Aspects of reasoning about Data. Kluwer, Dordrecht (1991)

    MATH  Google Scholar 

  25. Fisher, R.A.: The use of multiple measurements in taxonomic problems. Ann. Eugen. 7(2), 179–188 (1936)

    Article  Google Scholar 

  26. Loemker, L. (ed. and trans.): G.W. Leibniz: Philosophical Papers and Letters, 2nd ed., Dordrecht, Reidel (1969)

    Google Scholar 

  27. Rauszer, C.M.: An equivalence between theory of functional dependencies and a fragment of intuitionistic logic. Bull. Polish Acad. Sci. Math. 33, 571–579 (1985)

    MathSciNet  MATH  Google Scholar 

  28. Gentzen, G.: Untersuchungen über das Logische Schliessen, I, II. Math. Z. 39, 176–210, 405–431 (1934/5)

    Google Scholar 

  29. Boole, G.: The mathematical Analysis of Logic. G. Bell, London (1847). (reprinted from the original: Philosophical Library, New York, 1948)

    MATH  Google Scholar 

  30. Blake, A.: Canonical expressions in Boolean algebra. PhD Dissertation. University of Chicago Libraries (1938)

    Google Scholar 

  31. Skowron, A., Rauszer, C.M.: The discernibility matrices and functions in information systems. In: Intelligent Decision Support. Kluwer (1992)

    Google Scholar 

  32. Pawlak, Z., Skowron, A.: Rough sets and Boolean reasoning. Inf. Sci. 177, 41–73 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  33. Nguyen, H.S.: Discretization of real value attributes, Boolean reasoning approach. Ph.D. thesis, Warsaw University, Warsaw (1997)

    Google Scholar 

  34. Vakarelov, D.: Modal logics for knowledge representation systems. LNCS 363, 257–277 (1989)

    MathSciNet  MATH  Google Scholar 

  35. Pavelka, J.: On fuzzy logic I, II, III. Zeit. Math. Logik. Grund. Math. 25, 45–52, 119–134, 447–464 (1979)

    Google Scholar 

  36. Manna, Z.: The correctness of programs. J. Comp. Sci. Syst. Sci. 3, 119–127 (1969)

    Google Scholar 

  37. Chellas, B.F.: Modal Logic. An Introduction. Cambridge University Press, Cambridge (1980)

    Book  MATH  Google Scholar 

  38. Polkowski, L.: Rough Sets. Mathematical Foundations. Physica-Verlag. A Springer Company, Heidelberg (2002)

    Book  MATH  Google Scholar 

  39. Novotný, M., Pawlak, Z.: Algebraic theory of independence in information systems. Fund. Inform. 14, 454–476 (1991)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Informatics, University of Warmia and Mazury, Olsztyn, Poland

    Lech T. Polkowski

Authors
  1. Lech T. Polkowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lech T. Polkowski .

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Polkowski, L.T. (2023). Logics for Programs and Knowledge. In: Logic: Reference Book for Computer Scientists. Intelligent Systems Reference Library, vol 245. Springer, Cham. https://doi.org/10.1007/978-3-031-42034-4_7

Download citation

Publish with us

Policies and ethics

Search

Navigation