Domain semantics of possibility computations

Information Sciences

Volumn 178, Issue 12, 2008, Pages 2661-2679

  Chen, Yixiang ^a   Wu, Hengyang ^b  

^a EAST CHINA NORMAL UNIVERSITY   (China)

^b HANGZHOU DIANZI UNIVERSITY   (China)

Author keywords

Domain theory; Non determinism; Possibility computations; Predicate transformers

Indexed keywords

COMPUTATION THEORY; FUZZY SYSTEMS;

DOMAIN THEORY; NON-DETERMINISM; POSSIBILITY COMPUTATIONS; PREDICATE TRANSFORMERS;

SEMANTICS;

EID: 41749123023     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2008.01.016     Document Type: Article

References (60)

1. Amadio R.M., and Curien P.-L. Domains and Lambda-Calculi (1998), Cambridge University Press
2. Benvenuti P., and Vivona D. General theory of the fuzzy integral. Mathware and Soft Computing 3 (1996) 199-209
3. Benvenuti P., and Mesiar R. Integrals with respect to a general fuzzy measure. In: Grabisch M., Murofushi T., and Sugeno M. (Eds). Fuzzy Measures and Applications Theory and Applications (2000), Physica Verlag, Heidelberg 205-232
4. Butnariu D. Additive fuzzy measure and integrals (I, II, III). Journal of Mathematical Analysis and Applications 93 (1983) 436-452 117 (1986) 385-410, 125 (1987) 288-303
5. Chen Y.-X., and Jung A. A Logical Approach to Stable Domains. Theoretical Computer Science 368 (2006) 124-148
6. Chen Y.-X., and Zhang G.-Q. Maximality and totality of stable functions in stable bifinite domains. An International Journal of Computers and Mathematics with Applications 51 (2006) 1011-1020
7. Chen Y. Stone duality and representation of stable domains. An International Journal of Computer and Mathematics with Applications 34 (1997) 27-41
8. Chen Y. On compactness of induced I(L)-fuzzy topological spaces. Fuzzy Sets and Systems 88 (1997) 373-378
9. Chen Y. Paracompactness on L-fuzzy topological spaces. Fuzzy Sets and Systems 53 (1993) 335-342
10. Chen Y.-X. Stable semantics of weakest pre-predicates. Journal of Software 14 Special Isues (2003) 161-167
11. Yi-Xiang Chen, Achim Jung, An introduction to fuzzy predicate transformers, The invited talk at the Third International Symposium on Domain Theory, May 2004, Shaanxi Normal University, Xi'an, China, 24 (Suppl.) 2003, pp. 161-167 (in Chinese).
12. Yi-Xiang Chen, Gordon Plotkin, Hengyang Wu, On healthy fuzzy predicate transformers, Invited talk at the Fourth International Symposium on Domain Theory, July 2006, Hunan University, Changsha, China.
13. Chen Y.-X., and Wu H. Implication-based fuzzy predicate transformers. In: Liu Y., Chen G., and Ying M. (Eds). Fuzzy LogicSoft Computing and Computational Intelligence (2005), Tsinghua University Springer Press July
14. In: de Cooman G., Ruan D., and Kerre E.E. (Eds). FAPT'95: Foundations and Applications of Possibility Theory. Advance in Fuzzy Systems-Applications and Theory vol. 8 (1995), World Scientific
15. Dijkstra E.W. A Discipline of Programming (1976), Prentice Hall International, Englewood Cliffs
16. Doberkat E.-E. Kleisli morphisms and randomized congruences for the Giry monad. Journal of Pure and Applied Algebra 211 (2007) 638-664
17. Doberkat E.-E. Stochastic Relations: Foundations for Markov Transition Systems (2007), Chapman & Hall/CRC Press, Boca Raton, New York
18. Dubois D., and Prade H. An alternative approach to the handling of subnormal possibility distributions - a critical comment on a proposal of Yager. Fuzzy Sets and Systems 24 (1987) 123-126
19. Dubois D., and Prade H. Possibility Theory. An Approach to Computerized Processing of Uncertainty (1988), Plenum Press, New York
20. Eilenberg S., and Moore J.C. Adjoint functors and triples. Illinois Journal of Mathematics 9 (1965) 381-398
21. Gierz G., Hofmann K.H., Keimel K., Lawson J.D., Mislove M., and Scott D.S. Continuous Lattices and Domains. Encyclopedia of Mathematics and its Applications vol. 93 (2003), Cambridge University Press
22. Giry M. A categorical approach to probability theory. Categorical Aspects of Topology and Analysis. Lecture Notes in Mathematics No. 915 (1981), Springer-Verlag, Berlin 68-85
23. He J., Seidel K., and McIver A.K. Probabilistic models for the guarded command language. Science of Computer Programming 28 (1997) 171-192
24. Heckmann R., and Huth M. Quantitative semantics, topology, and possibility measures. Topology and its Applications 89 (1998) 151-178
25. Huth M. A powerdomain of possibility measures. Electronic Notes in Theoretical Computer Science 6 (1997). http://www.elservier.nl/locate/entcs/volume6.html 12 pages
26. C. Jones, Probabilistic non-determinism, PhD thesis, Department of Computer Science, University of Edinburgh, Edinburgh, 1990, 201pp. Also published as Technical report No. CST-63-90.
27. Jones C., and Plotkin G. A probabilistic powerdomain of evaluations. Proceedings of the Fourth Annual Symposium on Logic in Computer Science (1989), IEEE Computer Society Press 186-195
28. Kleisli H. Every standard construction is induced by a pair of adjoint functions. Proceedings of the American Mathematical Society 16 (1965) 544-546
29. Larsen K.G., and Skou A. Bisimulation through probabilistic testing. Information and Computation 94 (1991) 1-28
30. Mac Lane S. Categories for the Working Mathematician. Graduate Texts in Mathematics vol. 5 (1971), Springer-Verlag Reprinted by World Publishing Corporation, Beijing China
31. Manes E.G. Algebraic Theories. Graduate Texts in Mathematics vol. 26 (1976), Springer-Verlag
32. Marichal J.L. On Sugeno integrals as an aggregation function. Fuzzy Sets and Systems 114 (2000) 347-365
33. Marichal J.-L. k-Intolerant capacities and Choquet integrals. European Journal of Operational Research 177 3 (2007) 1453-1468
34. Mesiar R. Fuzzy measure and integrals. Fuzzy Sets and Systems 156 (2005) 365-370
35. Moggi E. Notions of computation and monads. Information and Computation 93 (1991) 55-92
36. Narukawa Y., and Torra V. Fuzzy measures and integrals in evaluation of strategies. Information Science 177 (2007) 4686-4695
37. Oussalah M. On the normalization of subnormal possibility distributions: new investigations. International Journal of General Systems 31 3 (2002) 277-301
38. P. Panangaden, Stochastic techniques in concurrency, Technical report, BRICS, Department of Computer Science, University of Aarhus, 1997.
39. P. Panangaden, Probabilistic relations, in: C. Baier, M. Huth, M. Kwiatkowska, M. Ryan (Eds.), Proceedings of the PROBMIV, 1998, pp. 59-74.
40. Pei D. Unified full implication algorithms of fuzzy reasoning. Information Sciences 178 (2008) 520-530
41. Plotkin G.D. A powerdomain construction. SIAM Journal on Computing 5 (1976) 452-487
42. G.D. Plotkin, Dijkstra's predicate transformers and Smyth's powerdomains, in: D. Bjørner (Ed.), Abstract Software Specifications, Lecture Notes in Computer Science, vol. 86, 1980, pp. 527-553.
43. Plotkin G.D. A powerdomain for countable non-determinism. In: Nielsen M., and Schmidt E.M. (Eds). Automata, Languages and Programming. Lecture Notes in Computer Science vol. 140 (1982), EATCS, Springer-Verlag 412-428
44. G.D. Plotkin, Probabilistic powerdomains, in: Proceedings CAAP, 1982, pp. 271-287.
45. Saheb-Djahromi N. CPO's of measures for non-determinism. Theoretical Computer Science 12 1 (1980) 19-37
46. Smyth M.B. Powerdomains. Journal of Computer and Systems Science 16 (1978) 23-36
47. Smyth M.B. Powerdomains and predicate transformers: a topological view. In: Diaz J. (Ed). Automata, Languages and Programming. Lecture Notes in Computer Science vol. 154 (1983), Springer-Verlag, Berlin 662-675
48. Scott D.S. A type theoretical alternative to ISWIM, CUCH, OWHY. Theoretical Computer Science 121 (1993) 411-440 Reprint of a manuscript written in 1969
49. D.S. Scott, Outline of a mathematical theory of computation, in: Fourth Annual Princeton Conference on Information Science and Systems, 1970, pp. 169-176.
50. Scott D.S. Continuous lattices. In: Lawvere E. (Ed). Toposes, Algebraic Geometry and Logic. Lecture Notes in Mathematics vol. 274 (1972), Springer-Verlag 97-136
51. M. Sugeno, Theory of fuzzy integrals and its applications, Ph.D. Doctoral Dissertation, Tokyo Institute of Technology, 1974.
52. Tix R., Keimel K., and Plotkin G. Semantic domains for combining probability and non-determinism. Electronic Notes in Theoretical Computer Science 129 (2005) 1-104
53. van Breugel F., Mislove M., Ouaknine J., and Worrell J. Domain theory, testing and simulation for labelled Markov processes. Theoretical Computer Science 333 (2005) 171-197
54. Wang G.-J. On the logic foundation of fuzzy reasoning. Information Sciences 117 (1999) 47-88
55. Wang G.-J. Formalized theory of general fuzzy reasoning. Information Sciences 160 (2004) 251-266
56. Yager R.R. A modification of the certainty measure to handle subnormal distributions. Fuzzy Sets and Systems 20 (1986) 317-324
57. Ying M. Reasoning about probabilistic sequential programs in a probabilistic logic. Acta Informatica 39 (2003) 315-389
58. Zadeh L.A. Fuzzy sets. Information and Control 8 (1965) 338-353
59. Zadeh L.A. Probability measure of fuzzy events. Journal of Mathematical Analysis and Applications 23 (1968) 421-427
60. Zadeh L.A. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and System 1 (1978) 3-28