Double Residuated Lattices and Their Applications

1. G. Allwein and M. Dunn (1993). “Kripke models for linear logic”. Journal of Symbolic Logic58, No 2, pp. 514–545.

   Article  MATH  MathSciNet  Google Scholar 

2. Ph. Balbiani and E. Orłowska (1999). “A hierarchy of modal logics with relative accessibility relations”. Journal of Applied Non-Classical Logics 9, No 2-3, pp. 303–328, special issue in the memory of George Gargov.

   MATH  MathSciNet  Google Scholar 

3. K. Blount and C. Tsinakis (2001). “The structure of residuated lattices”. Preprint.

   Google Scholar 

4. L. Farinas del Cerro and H. Prade (1986) “Rough sets, fuzzy sets and modal logic”. Fuzziness in indiscernibility and partial information. In: A. Di Nola and A. G. Ventre (eds), The Mathematics of Fuzzy Systems, Verlag TÜV Rheinland.

   Google Scholar 

5. C. C. Chang (1958) “Algebraic analysis of many-valued logics”. Transactions of the American Mathematical Society 88, pp. 467–490.

   Article  MATH  MathSciNet  Google Scholar 

6. S. Demri, E Orłowska and D. Vakarelov (1999). “Indiscernibility and complementarity relations in information systems”. In: J. Gerbrandy, M. Marx, M. de Rijke and Y. Venema (eds) JFAK. Essays Dedicated to Johan van Benthem on the Occasion of his 50th Birthday. Amsterdam University Press.

   Google Scholar 

7. S. Demri and E Orłowska (2002). Incomplete Information: Structure, Inference, Complexity. EATCS Monographs in Theoretical Computer Science, Springer, forthcoming.

   Google Scholar 

8. R. P. Dilworth and N. Ward (1939) “Residuated lattices”. Transactions of the American Mathematical Society 45, pp. 335–354.

   Article  MATH  MathSciNet  Google Scholar 

9. I. Düntsch and E. Orłowska (2000). “Logics of complementarity in information systems”. Mathematical Logic Quarterly 46, pp. 267–288.

   Article  MATH  Google Scholar 

10. I. Düntsch and E. Orłowska (2000). “Beyond modalities: suficiency and mixed algebras”. In: E. Orłowska and A. Szałas (eds) Relational Methods for Computer Science Applications, Physica Verlag, Heidelberg, pp. 263–285.

    Google Scholar 

11. I. Düntsch and E. Orłowska (2001). “Algebraic structures for qualitative reasoning”. Alfred Tarski Centenary Conference, Warsaw, Poland.

    Google Scholar 

12. F. Esteva and L. Godo (2001) “Monoidal t-norm based logic: towards a logic for left-continuous t-norms”. Fuzzy Sets and Systems 124, pp. 271–288.

    Article  MATH  MathSciNet  Google Scholar 

13. F. Esteva and L. Godo (2001). “On complete residuated many-valued logics with tnorm conjunction”. Proceedings of the 31st International Symposium on Multiple-Valued Logic, Warsaw, Poland, pp. 81–86.

    Google Scholar 

14. P. Flondor, G. Georgescu, and A. Iorgulecu (2001). “Psedo-t-norms and pseudo-BL algebras”. Soft Computing 5, No 5, pp. 355–371.

    Article  MATH  Google Scholar 

15. S. Gottwald (2001). A Treatise on Many-Valued Logics, Studies in Logic and Computation 9, Research Studies Press: Baldock, Hertfordshire, England.

    Google Scholar 

16. J. A. Gougen (1967). “L-fuzzy sets”. Journal of Mathematical Analysis and Applications 18, pp. 145–174.

    Article  MathSciNet  Google Scholar 

17. P. Hajek (1998). Metamathematics of Fuzzy Logic, Kluwer, Dordrecht.

    Google Scholar 

18. J. B. Hart, L. Rafter, and C. Tsinakis (2001). “The structure of commutative residuated lattices”. Preprint.

    Google Scholar 

19. C. A. R. Hoare and H. Jifeng (1986). “The weakest prespecification”. Part I: Fundamenta Informaticae IX, pp. 51–84. Part II: Fundamenta Informaticae IX, pp. 217-252.

    Google Scholar 

20. U. Höhle and U.P. Klement (eds) (1996). Non-Classical Logics and their Applications to Fuzzy Subsets, Kluwer, Dordrecht.

    Google Scholar 

21. U. Höhle (1996). “Commutative, residuated l-monoids”. In [20], pp. 53–106.

    Google Scholar 

22. I. Humberstone (1983). “Inaccessible words”. Notre Dame Journal of Formal Logic 24, pp. 346–352.

    Article  MATH  MathSciNet  Google Scholar 

23. P. Jipsen (2001). “A Gentzen system and decidability for residuated lattices”. Preprint.

    Google Scholar 

24. B. Konikowska (1997). “ogic for reasoning about relative similarity” Studia Logica 58, pp. 185–226.

    Article  MATH  MathSciNet  Google Scholar 

25. R. K. Meyer and R. Routley (1972). “Algebraic analysis of entailment”, Logique et analyse 15, pp. 6.

    Google Scholar 

26. E. Orłowska (1988). “Kripke models with relative accessibility and their application to inferences from incomplete information”. In: Mirkowska, G. and Rasiowa, H. (eds), Mathematical Problems in Computation Theory. Banach Center Publications 21, pp. 329–339.

    Google Scholar 

27. E. Orłowska (ed) (1998). Incomplete Information — Rough Set Analysis, Studies in Fuzziness and Soft Computing, Springer-Verlag.

    Google Scholar 

28. E. Orłowska (1999). “Many-valuedness and uncertainty”. Multiple-Valued Logic 4, pp. 207–227.

    MATH  MathSciNet  Google Scholar 

29. E. Orłowska and A. M. Radzikowska (2001). “Information relations and operators based on double residuated lattices”. In H. de Swart (ed), Proceedings of the 6th Seminar on Relational Methods in Computer Science RelMiCS’2001, pp. 185–199.

    Google Scholar 

30. A. M. Radzikowska and E. E. Kerre (2002) “A comparative study of fuzzy rough sets”. Fuzzy Sets and Systems 126 No 2, pp. 137–155.

    Article  MATH  MathSciNet  Google Scholar 

31. A. M. Radzikowska, E. E. Kerre (2002) “A general calculus of fuzzy rough sets”. Submitted.

    Google Scholar 

32. A. M. Radzikowska and E. E. Kerre (2001). “On some classes of fuzzy information relations”. Proceedings of the 31st International Symposium on Multiple-Valued Logic, Warsaw, Poland, pp. 75–80.

    Google Scholar 

33. A. M. Radzikowska and E. E. Kerre (2001) “Towards studying of fuzzy information relations”. To appear in Proceedings of EUSFLAT-2001, Leicester, UK.

    Google Scholar 

34. H. Rasiowa and R. Sikorski (1970). The Mathematics of Metamathematics, Warszawa.

    Google Scholar 

35. C. Rauszer (1974). “Semi-Boolean algebras and their applications to intuitionistic logic with dual operations”. Fundamenta Mathematicae 83, pp. 219–249.

    MATH  MathSciNet  Google Scholar 

36. B. Schweizer and A. Sklar (1983). Probabilistic Metric Spaces. North Holland, Amsterdam.

    Google Scholar 

37. E. Turunen (1999) Mathematics Behind Fuzzy Logic, Springer-Verlag.

    Google Scholar 

38. D. Vakarelov (1998). “Information systems, similarity relations and modal logics”. In [27], pp. 492–550.

    Google Scholar 

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