A logic for probabilities in semantics

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2471, Issue , 2002, Pages 216-232

  Moshier, M Andrew ^a   Jung, Achim ^b  

^a CHAPMAN UNIVERSITY   (United States)

^b UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

MODEL CHECKING; SEMANTICS;

DENOTATIONAL SEMANTICS; FURTHER WORKS; POWERDOMAINS; PROBABILISTIC ALGORITHM; PROBABILISTIC COMPUTATION; PROBABILISTIC POWERDOMAIN; SOUND AND COMPLETE;

COMPUTER CIRCUITS;

EID: 84947814679     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45793-3_15     Document Type: Conference Paper

References (38)

1. [1] S. Abramsky. The lazy lambda calculus. In D. Turner, editor, Research Topics in Functional Programming, pages 65-117. Addison Wesley, 1990.
2. [2] S. Abramsky. A domain equation for bisimulation. Information and Computation, 92:161-218, 1991.
3. [3] S. Abramsky and A. Jung. Domain theory. In S. Abramsky, D. M. Gabbay, and T. S. E. Maibaum, editors, Handbook of Logic in Computer Science, volume 3, pages 1-168. Clarendon Press, 1994.
4. [4] M. Alvarez-Manilla. Measure theoretic results for continuous valuations on partially ordered spaces. PhD thesis, Imperial College, University of London, 2001.
5. [5] M. Alvarez-Manilla, A. Edalat, and N. Saheb-Djahromi. An extension result for continuous valuations. Journal of the London Mathematical Society, 61:629-640, 2000.
6. [6] M. Alvarez-Manilla, A. Jung, and K. Keimel. Valuations on a stably compact space. In preparation.
7. [7] J. Desharnais, A. Edalat, and P. Panangaden. Bisimulation for labelled Markov processes. Information and Computation, to appear.
8. [8] Josee Desharnais, Abbas Edalat, and Prakash Panangaden. Bisimulation for labelled markov processes. In Proceedings of the 12th IEEE Symposium on Logic in Computer Science, pages 149-158, 1997.
9. [9] Josee Desharnais, Abbas Edalat, and Prakash Panangaden. A logical characterization of bisimulation for labeled markov processes. In Logic in Computer Science, pages 478-487, 1998.
10. [10] E. W. Dijkstra. A Discipline of Programming. Prentice-Hall, Englewood Cliffs, New Jersey, 1976.
11. [11] A. Edalat. Dynamical systems, measures and fractals via domain theory. Information and Computation, 120(1):32-48, 1995.
12. [12] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, and D. S. Scott. A Compendium of Continuous Lattices. Springer Verlag, 1980.
13. [13] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, and D. S. Scott. Continuous Lattices and Domains. Cambridge University Press, 2002. Revised edition of [12], forthcoming.
14. [14] R. Heckmann. Spaces of valuations. In S. Andima, R. C. Flagg, G. Itzkowitz, P. Misra, Y. Kong, and R. Kopperman, editors, Papers on General Topology and Applications: Eleventh Summer Conference at the University of Southern Maine, volume 806 of Annals of the New York Academy of Sciences, pages 174-200, 1996.
15. [15] Reinhold Heckmann. Probabilistic power domains, information systems, and locales. In S. Brookes, M. Main, A. Melton, M. Mislove, and D. Schmidt, editors, Mathematical Foundations of Programming Semantics VIII, pages 410-437, 1994. In LNCS 802:1994.
16. [16] C. Jones. Probabilistic Non-Determinism. PhD thesis, University of Edinburgh, Edinburgh, 1990. Also published as Technical Report No. CST-63-90.
17. [17] C. Jones and G. Plotkin. A probabilistic powerdomain of evaluations. In Proceedings of the 4th Annual Symposium on Logic in Computer Science, pages 186-195. IEEE Computer Society Press, 1989.
18. [18] A. Jung, M. Kegelmann, and M. A. Moshier. Multi lingual sequent calculus and coherent spaces. In S. Brookes and M. Mislove, editors, 13th Conference on Mathematical Foundations of Programming Semantics, volume 6 of Electronic Notes in Theoretical Computer Science. Elsevier Science Publishers B.V., 1997. 18 pages.
19. [19] A. Jung, M. Kegelmann, and M. A. Moshier. Stably compact spaces and closed relations. In S. Brookes and M. Mislove, editors, 17th Conference on Mathematical Foundations of Programming Semantics, volume 45 of Electronic Notes in Theoretical Computer Science. Elsevier Science Publishers B.V., 2001. 24 pages.
20. [20] A. Jung and Ph. Sünderhauf. On the duality of compact vs. open. In S. Andima, R. C. Flagg, G. Itzkowitz, P. Misra, Y. Kong, and R. Kopperman, editors, Papers on General Topology and Applications: Eleventh Summer Conference at the University of Southern Maine, volume 806 of Annals of the New York Academy of Sciences, pages 214-230, 1996.
21. [21] A. Jung and R. Tix. The troublesome probabilistic powerdomain. In A. Edalat, A. Jung, K. Keimel, and M. Kwiatkowska, editors, Proceedings of the Third Workshop on Computation and Approximation, volume 13 of Electronic Notes in Theoretical Computer Science. Elsevier Science Publishers B.V., 1998. 23 pages.
22. [22] Achim Jung, Mathias Kegelmann, and M. Andrew Moshier. Multi lingual sequent calculus and coherent spaces. Fundamenta Informaticae, 37:369-412, 1999.
23. [23] Achim Jung, Matthias Kegelmann, and M. Andrew Moshier. Stably compact spaces and closed relations. In Stephen Brookes and Michael Mislove, editors, Electronic Notes in Theoretical Computer Science, volume 45. Elsevier Science Publishers, 2001.
24. [24] M. Kegelmann. Factorisation systems on domains. Applied Categorical Structures, 7(1-2):113-128, 1999.
25. [25] D. Kozen. Semantics of probabilistic programs. Journal of Computer and System Sciences, 22:328-350, 1981.
26. [26] J. D. Lawson. Valuations on continuous lattices. In Rudolf-Eberhard Hoffmann, editor, Continuous Lattices and Related Topics, volume 27 of Mathematik Arbeitspapiere, pages 204-225. Universität Bremen, 1982.
27. [27] J.R. Longley. When is a functional program not a functional program? In Proceedings of Fourth ACM SIGPLAN International Conference on Functional Programming. ACM Press, 1999.
28. [28] Annabelle McIver. A generalisation of stationary distributions, and probabilistic program algebra. In Stephen Brookes and Michael Mislove, editors, Electronic Notes in Theoretical Computer Science, volume 45. Elsevier Science Publishers, 2001.
29. [29] M. W. Mislove. Nondeterminism and probabilistic choice: Obeying the law. In Proceedings 11th CONCUR, volume 1877 of Lecture Notes in Computer Science, pages 350-364. Springer Verlag, 2000.
30. [30] Carroll Morgan, Annabelle McIver, and Karen Seidel. Probabilistic predicate transformers. ACM Transactions on Programming Languages and Systems, 18(3):325-353, May 1996.
31. [31] N. Saheb-Djahromi. CPO’s of measures for nondeterminism. Theoretical Computer Science, 12:19-37, 1980.
32. [32] M. B. Smyth. Powerdomains and predicate transformers: a topological view. In J. Diaz, editor, Automata, Languages and Programming, volume 154 of Lecture Notes in Computer Science, pages 662-675. Springer Verlag, 1983.
33. [33] M. B. Smyth. Totally bounded spaces and compact ordered spaces as domains of computation. In G. M. Reed, A. W. Roscoe, and R. F. Wachter, editors, Topology and Category Theory in Computer Science, pages 207-229. Clarendon Press, 1991.
34. [34] M. B. Smyth. Stable compactification I. Journal of the London Mathematical Society, 45:321-340, 1992.
35. [35] M. B. Smyth. Topology. In S. Abramsky, D. M. Gabbay, and T. S. E. Maibaum, editors, Handbook of Logic in Computer Science, vol. 1, pages 641-761. Clarendon Press, 1992.
36. [36] R. Tix. Continuous D-Cones: Convexity and Powerdomain Constructions. PhD thesis, Technische Universit¨at Darmstadt, 1999.
37. [37] D. Varacca. The powerdomain of indexed valuations. In 17th Logic in Copmuter Science Conference. IEEE Computer Society Press, 2002.
38. [38] S. J. Vickers. Topology Via Logic, volume 5 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1989.