Satisfiability and meaning of formulas and sets of formulas in approximation spaces

Fundamenta Informaticae

Volumn 67, Issue 1-3, 2005, Pages 77-92

  Gomolińska, Anna ^a  

^a UNIVERSITY OF BIALYSTOK   (Poland)

Author keywords

Approximation space; Information granule; Pawlak information system; Rough applicability of a rule; Rough satisfiability meaning of formulas

Indexed keywords

APPROXIMATION THEORY; INFORMATION MANAGEMENT; LARGE SCALE SYSTEMS;

APPROXIMATION SPACE; INFORMATION GRANULE; PAWLAK INFORMATION SYSTEM; ROUGH APPLICABILITY OF A RULE; ROUGH SATISFIABILITY/MEANING OF FORMULAS;

SET THEORY;

EID: 33645301042     PISSN: 01692968     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (43)

1. Banerjee, M.: Rough truth, consequence, consistency and belief revision, Proc. 4th Int. Conf. Rough Sets and Current Trends in Computing (RSCTC'2004), Uppsala, Sweden, 2004, June 1-5, LNAI, 3066 (S. Tsumoto, R. Słowiński, J. Komorowski, J. W. Grzymała-Busse, Eds.), Springer, Berlin Heidelberg, 2004, 95-102.
2. Burns, T. R., Gomolińska, A.: The theory of socially embedded games: The mathematics of social relationships, rule complexes, and action modalities, Quality and Quantity Int. J. Methodology, 34(4), 2000, 379-406.
3. Burns, T. R., Gomolińska, A., Meeker, L. D.: The theory of socially embedded games: Applications and extensions to open and closed games, Quality and Quantity Int. J. Methodology, 35(1), 2001, 1-32.
4. Chakraborty, M. K., Banerjee, M.: Rough consequence, Bull. Polish Acad. Sci. Math., 41(4), 1993, 299-304.
5. Chakraborty, M. K., Banerjee, M.: Rough consequence and rough algebra, Rough Sets, Fuzzy Sets and Knowledge Discovery, Proc. Int. Workshop on Rough Sets and Knowledge Discovery (RSKD'93) (W. Ziarko, Ed.), Springer, 1994, 196-207.
6. Fagin, R., Halpern, J. Y., Megiddo, N.: A logic for reasoning about probabilities, Information and Computation, 87(1-2), 1990, 78-128.
7. Gomolińska, A.: A comparative study of some generalized rough approximations, Fundamenta Informaticae, 51(1-2), 2002, 103-119.
8. Gomolińska, A.: Fundamental mathematical notions of the theory of socially embedded games: A granular computing perspective, Rough-Neural Computing: Techniques for Computing with Words (S. K. Pal, L. Polkowski, A. Skowron, Eds.), Springer, Berlin Heidelberg, 2004, 411-434.
9. Gomolińska, A.: A graded applicability of rules, Proc. 4th Int. Conf. Rough Sets and Current Trends in Computing (RSCTC'2004), Uppsala, Sweden, 2004, June 1-5, LNAI, 3066 (S. Tsumoto, R. Słowiński, J. Komorowski, J. W. Grzymała-Busse, Eds.), Springer, Berlin Heidelberg, 2004, 213-218.
10. Gomolińska, A.: A graded meaning of formulas in approximation spaces, Fundamenta Informaticae, 60(1-4), 2004, 159-172.
11. Gomolińska, A.: Satisfiability and meaning in approximation spaces, Proc. Workshop Concurrency, Specification, and Programming (CS&P'2004), Caputh, Germany, 2004, September 24-26, Informatik-Berichte, 170 (G. Lindemann et al., Ed.), Humboldt-Universität zu Berlin, Berlin, 2004, 229-240.
12. Gomolińska, A.: Towards rough applicability of rules, Monitoring, Security, and Rescue Techniques in Multiagent Systems, Advances in Soft Computing (B. Dunin-Kȩplicz, A. Jankowski, A. Skowron, M. Szczuka, Eds.), Springer, Berlin Heidelberg, 2005, 203-214.
13. Jaeger, M.: Probabilistic role models and the guarded fragment, Proc. 10th Int. Conf. Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU'2004), Perugia, Italy, 2004, July 4-9, 2004, 235-242.
14. Keisler, H. J.: Probability quantifiers, Model-Theoretic Logics (J. Barwise, S. Feferman, Eds.), Springer, Berlin New York, 1985, 509-556.
15. Koller, D., Halpern, J. Y.: Irrelevance and conditioning in first-order probabilistic logic, Proc. 13th National Conf. on Artificial Intelligence (AAAI-96), 1996, 569-576.
16. Leśniewski, S.: Foundations of the general set theory 1 (in Polish), Works of the Polish Scientific Circle, 2, 1916,
17. See also Stanisław Leśniewski Collected Works (S. J. Surma et al., Ed.), Kluwer, Dordrecht, 1992, 128-173.
18. Łukasiewicz, J.: Die logischen Grundlagen der Wahrscheinlichkeitsrechnung, Jan Łukasiewicz - Selected Works (L. Borkowski, Ed.), North Holland, Polish Scientific Publ., Amsterdam London Warsaw, 1970, 16-63. First published in Kraków in 1913.
19. Nguyen, S. H., Skowron, A., Stepaniuk, J.: Granular computing: A rough set approach, J. Comput. Intelligence, 17(3), 2001, 514-544.
20. Ogata, N.: Towards dynamic probabilistic logics: A survey and a proposal, Presented at the 2nd Int. Workshop on Chance Discovery, Pacific Rim Int. Conf. on Artificial Intelligence (PRICAI'2002), Tokyo, Japan, 2002, August 18-22, 2002, 16-63, http://citeseer.ist.psu.edu/ogata02towards.html.
21. Pawlak, Z.: Information systems - Theoretical foundations, Information Systems, 6(3), 1981, 205-218.
22. Pawlak, Z.: Rough sets, Int. J. Computer and Information Sciences, 11, 1982, 341-356.
23. Pawlak, Z.: Rough logic, Bull Polish Acad. Sci. Tech., 35(5-6), 1987, 253-258.
24. Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning About Data, Kluwer, Dordrecht, 1991.
25. Pawlak, Z., Polkowski, L., Skowron, A.: Rough sets and rough logic: A KDD perspective, Rough Set Methods and Applications: New Developments in Knowledge Discovery in Information Systems (L. Polkowski, S. Tsumoto, T. Y. Lin, Eds.), Physica, Heidelberg New York, 2001, 583-646.
26. Peters, J. F.: Approximation space for intelligent system design patterns, Engineering Applications of Artificial Intelligence, 17(4), 2004, 1-8.
27. Peters, J. F., Skowron, A., Stepaniuk, J., Ramanna, S.: Towards an ontology of approximate reason, Fundamenta Informaticae, 51(1-2), 2002, 157-173.
28. Polkowski, L., Skowron, A.: Rough mereology, LNAI, 869, Springer, Berlin, 1994, 85-94.
29. Polkowski, L., Skowron, A.: Rough mereology: A new paradigm for approximate reasoning, Int. J. Approximated Reasoning, 15(4), 1996, 333-365.
30. Polkowski, L., Skowron, A.: Towards adaptive calculus of granules, Computing with Words in Information/Intelligent Systems (L. A. Zadeh, J. Kacprzyk, Eds.), 1, Physica, Heidelberg, 1999, 201-228.
31. Polkowski, L., Skowron, A.: Rough mereological calculi of granules: A rough set approach to computation, J. Comput. Intelligence, 17(3), 2001, 472-492.
32. Reiter, R.: A logic for default reasoning, Artificial Intelligence J., 13, 1980, 81-132.
33. Skowron, A., Stepaniuk, J.: Generalized approximation spaces, Proc. 3rd Int. Workshop on Rough Sets and Soft Computing, San Jose, USA, 1994, November 10-12, 1994, 156-163.
34. Skowron, A., Stepaniuk, J.: Tolerance approximation spaces, Fundamenta Informaticae, 27, 1996, 245-253.
35. Skowron, A., Stepaniuk, J.: Towards discovery of information granules, Proc. 3rd European Conf. Principles and Practice of Knowledge Discovery in Databases, Prague, Czech Republic, 1999, September 15-18, LNAI, 1704, Springer, Berlin, 1999, 542-547.
36. Skowron, A., Stepaniuk, J.: Information granules and rough-neural computing, Rough-Neural Computing: Techniques for Computing with Words (S. K. Pal, L. Polkowski, A. Skowron, Eds.), Springer, Berlin Heidelberg, 2004, 43-84.
37. Skowron, A., Stepaniuk, J., Peters, J. F.: Rough sets and infomorphisms: Towards approximation of relations in distributed environments, Fundamenta Informaticae, 54(2-3), 2003, 263-277.
38. Skowron, A., Swiniarski, R., Synak, P.: Approximation spaces and information granulation, Proc. 4th Int. Conf. Rough Sets and Current Trends in Computing (RSCTC'2004), Uppsala, Sweden, 2004, June 1-5, LNAI, 3066 (S. Tsumoto, R. Słowiński, J. Komorowski, J. W. Grzymała-Busse, Eds.), Springer, Berlin Heidelberg, 2004, 116-126.
39. Stepaniuk, J.: Knowledge discovery by application of rough set models, Rough Set Methods and Applications: New Developments in Knowledge Discovery in Information Systems (L. Polkowski, S. Tsumoto, T. Y. Lin, Eds.), Physica, Heidelberg New York, 2001, 137-233.
40. Wolski, M.: Galois connections and data analysis, Fundamenta Informaticae, 60(1-4), 2004,401-415.
41. Zadeh, L. A.: Outline of a new approach to the analysis of complex system and decision processes, IEEE Trans, on Systems, Man, and Cybernetics, 3, 1973, 28-44.
42. Ziarko, W.: Variable precision rough set model, J. Computer and System Sciences, 46(1), 1993, 39-59.
43. Ziarko, W.: Probabilistic decision tables in the variable precision rough set model, J. Comput. Intelligence, 17(3), 2001, 593-603.