A correspondence framework between three-valued logics and similarity-based approximate reasoning

Fundamenta Informaticae

Volumn 75, Issue 1-4, 2007, Pages 179-193

  Doherty, Patrick ^a   Szałas, Andrzej ^a,b  

^a LINKÖPING UNIVERSITY   (Sweden)

^b Inst of Comp Sci and Econometrics   (Poland)

Author keywords

Approximate reasoning; Rough sets; Similarity relation; Three valued logics

Indexed keywords

FORMAL LOGIC; ROUGH SET THEORY;

ACCESSIBILITY RELATION; APPROXIMATE REASONING; SIMILARITY SPACES; THREE VALUED LOGICS;

APPROXIMATION THEORY;

EID: 33847794110     PISSN: 01692968     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. Ackermann, W.: Untersuchungen über das Eliminationsproblem der mathematischen Logik, Mathematische Annalen, 110, 1935, 390-413.
2. Busch, D.: Sequent Formalizations of Three-Valued Logics, in: Partiality, Modality and Nonmonotonicity (P. Doherty, Ed.), CSLI Publications, 1996, 45-75.
3. Demri, S., Orłowska, E.: Incomplete Information: Structure, Inference, Complexity, EATCS Monographs, Springer, 2002.
4. Doherty, P., Łukaszewicz, W., Skowron, A., Szałas, A.: Approximation Transducers and Trees: A Technique for Combining Rough and Crisp Knowledge, Rough-Neuro Computing: Techniques for Computing with Words (S. Pal, L. Polkowski, A. Skowron, Eds.), Cognitive Technologies, Cognitive Technologies, Springer-Verlag, 2003, 189-218.
5. Doherty, P., Łukaszewicz, W., Szałas, A.: Computing Circumscription Revisited, Journal of Automated Reasoning, 18(3), 1997, 297-336.
6. Doherty, P., Łukaszewicz, W., Szałas, A.: Information Granules for Intelligent Knowledge Structures, Proc. 9th Conf. RSFDGrC (WangG., Q. Liu, Y. Yao, A. Skowron, Eds.), LNCS, vol. 2639 of LNCS, Springer-Verlag, 2003, 405-412.
7. Doherty, P., Łukaszewicz, W., Szałas, A.: Similarity, Approximations and Vagueness, Proc. RSFDGrC'05 (e. a. Slezak D., Ed.), LNA1, number 3641 in LNAI, Springer-Verlag, 2003, 541-550.
8. Doherty, P., Łukaszewicz, W., Szałas, A.: Tolerance Spaces and Approximative Representational Structures, Proc. 26th German Conf. on AI, KI'2003 (A. Günter, R. Kruse, B. Neumann, Eds.), LNAI, vol. 2821 of LNAI, Springer-Verlag, 2003, 475-489.
9. Doherty, P., Łukaszewicz, W., Szałas, A.: Approximate Databases and Query Techniques for Agents with Heterogenous Perceptual Capabilities, Proceedings of the 7th Int. Conf. on Information Fusion, FUSION'2004, 2004, 175-182.
10. Doherty, P., Szałas, A.: On the Correspondence between Approximations and Similarity, Proc. of 4th Int. Conf. RSCTC'2004 (S. Tsumoto, R. Slowinski, J. Komorowski, J. Grzymala-Busse, Eds.), LNAI, vol. 3066 of LAAI, Springer-Verlag, 2004, 143-152.
11. Fitting, M.: A Kripke-Kleene Semantics for Logic Programs, Journal Logic Programming, 2(4), 1985, 295-312.
12. Gabbay, D., Ohlbach, H.: Quantifier Elimination in Second-Order Predicate Logic, South African Computer Journal, 7, 1992, 35-43.
13. Konikowska, B.: A logic for reasoning about relative similarity, Studia Logica, 58(1), 1997, 185-226.
14. Magnusson, M.: DLS*, http://www.ida.liu.se/labs/kplab/projects/ dlsstar/, 2005.
15. Nonnengart, A., Ohlbach, H., Szałas, A.: Elimination of Predicate Quantifiers, Logic, Language and Reasoning. Essays in Honor of Dov Gabbay, Part I (H. Ohlbach, U. Reyle, Eds.), Kluwer, 1999, 159-181.
16. Nonnengart, A., Szałas, A.: A Fixpoint Approach to Second-Order Quantifier Elimination with Applications to Correspondence Theory, Logic at Work: Essays Dedicated to the Memory of Helena Rasiowa (E. Orlowska, Ed.), Studies in Fuzziness and Soft Computing, vol. 24 of Studies in Fuzziness and Soft Computing, Springer Physica-Verlag, 1998, 307-328.
17. Pawlak, Z.: Information systems - theoretical foundations, Information Systems, 6, 1981, 205-218.
18. Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, Dordrecht, 1991.
19. Przymusinski, T., Przymusinska, H.: Semantic issues in deductive databases and logic programs, Formal Techniques in AI (R. Banerji, Ed.), North Holland, 1990, 321-367.
20. Skowron, A., Stepaniuk, J.: Tolerance Approximation Spaces, Fundamenta Informaticae, 27, 1996, 245-253.
21. Słwiński, R., Vanderpooten, D.: Similarity relation as a basis for rough approximations, Advances in Machine Intelligence & Soft Computing (P. Wang, Ed.), Bookwrights, Raleigh NC, 1997, 17-33.
22. Słowiński, R., Vanderpooten, D.: A generalized definition of rough approximations based on similarity, IEEE Trans. on Data and Knowledge Engineering, 12(2), 2000, 331-336.
23. Szałas, A.: On the Correspondence between Modal and Classical Logic: An Automated Approach, Journal of Logic and Computation, 3, 1993, 605-620.
24. Van Benthem, J.: Correspondence Theory, Handbook of Philosophical Logic (D. Gabbay, F. Guenthner, Eds.), vol. 2, D. Reidel Pub. Co., 1984, 167-247.