A logical approach to stable domains

Theoretical Computer Science

Volumn 368, Issue 1-2, 2006, Pages 124-148

  Chen, Yi Xiang ^a   Jung, Achim ^b  

^a SHANGHAI NORMAL UNIVERSITY   (China)

^b UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

Disjunctive propositional logic; Domain theory; Domain theory in logical form; Information system; L domain

Indexed keywords

ALGEBRA; FORMAL LOGIC; INFORMATION TECHNOLOGY; LOGIC PROGRAMMING;

DISJUNCTIVE PROPOSITIONAL LOGIC; DOMAIN THEORY; INFORMATION SYSTEMS; L-DOMAIN; LOGICAL FORM;

COMPUTER SCIENCE;

EID: 33750729219     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2006.09.005     Document Type: Article

References (31)

1. Abramsky S. A domain equation for bisimulation. Inform. and Comput. 92 (1991) 161-218
2. Abramsky S. Domain theory in logical form. Ann. Pure Appl. Logic 51 (1991) 1-77
3. Abramsky S., and Jung A. Domain theory. In: Abramsky S., Gabbay D.M., and Maibaum T.S.E. (Eds). Handbook of Logic in Computer Science Vol. 3 (1994), Clarendon Press, Oxford 1-168
4. Abramsky S., and Ong L. Full abstraction in the lazy lambda calculus. Inform. and Comput. 105 (1993) 159-267
5. Amadio R., and Curien P.-L. Domains and Lambda Calculi. Cambridge Tracts in Theoretical Computer Science Vol. 46 (1998), Cambridge University Press, Cambridge
6. G. Berry, Stable models of typed λ-calculi, in: Proc. Fifth Internat. Colloq. on Automata, Languages and Programming, Lecture Notes in Computer Science, Vol. 62, Springer, Berlin, 1978, pp. 72-89.
7. Berry G., Curien P.-L., and Lévy J.-J. Full abstraction for sequential languages: the state of the art. In: Nivat M., and Reynolds J. (Eds). Algebraic Semantics (1985), Cambridge University Press, Cambridge 89-132
8. Chen Y. Stone duality and representation of stable domains. Comput. Math. Appl. 34 (1997) 27-41
9. Coquand T. Categories of embeddings. Theoret. Comput. Sci. 68 (1989) 221-238
10. M. Coste, Localisation dans les catégories de modèles, 1977, Thèse de doctorat, Université Paris-Nord.
11. T. Ehrhard, P. Malacaria, Stone duality for stable functions, in: D.H. Pitt, P.-L. Curien, S. Abramsky, A.M. Pitts, A. Poigné, D.E. Rydeheard (Eds.), Category Theory and Computer Science 1991, Lecture Notes in Computer Science, Vol. 530, Springer, Berlin, 1991, pp.74-93.
12. Freyd P. Aspects of topoi. Bulle. Australian Math. Soc. 7 (1972) 1-76
13. Gentzen G. Untersuchungen über das logische Schließen. Math. Z. 39 (1934) 176-210 405-431 (Reprint 1969, Wissenschaftliche Buchgesellschaft Darmstadt)
14. 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, Cambridge
15. Isbell J. Completion of a construction of Johnstone. Proc. Amer. Math. Soc. 85 (1982) 333-334
16. P.T. Johnstone, A syntactic approach to Diers' localizable categories, in: M.P. Fourman, C.J. Mulvey, D.S. Scott (Eds.), Applications of Sheaves, Proceedings Durham 1977, Lecture Notes in Mathematics, Vol. 753, Springer, Berlin, 1979, pp. 466-478.
17. P.T. Johnstone, Scott is not always sober, in: B. Banaschewski, R.-E. Hoffmann (Eds.), Continuous Lattices, Proceedings Bremen 1979, Lecture Notes in Mathematics, Vol. 871, Springer, Berlin, 1981, pp. 282-283.
18. Johnstone P.T. Stone Spaces. Cambridge Studies in Advanced Mathematics Vol. 3 (1982), Cambridge University Press, Cambridge
19. P.T. Johnstone, S.J. Vickers, Preframe presentations present, in: A. Carboni, M.C. Pedicchio, G. Rosolini (Eds.), Category Theory-Proceedings, Como 1990, Lecture Notes in Mathematics, Vol. 1488, Springer, Berlin, 1991, pp. 193-212.
20. Jung A. Cartesian closed categories of algebraic CPO's. Theoret. Comput. Sci. 70 (1990) 233-250
21. Jung A., Kegelmann M., and Moshier M.A. Multi lingual sequent calculus and coherent spaces. Fundamenta Inform. 37 (1999) 369-412
22. J. R. Longley, Notions of computability at higher types i, in: R. Cori, A. Razborov, S.Todorcevic, C. Wood (Eds.), Logic Colloq. 2000, Lecture Notes in Logic, Vol. 19, Association for Symbolic Logic, 2005, pp. 32-142.
23. Mac Lane S. Categories for the Working Mathematician. Graduate Texts in Mathematics Vol. 5 (1971), Springer, Berlin
24. Meinke K., and Tucker J.V. Universal algebra. In: Abramsky S., Gabbay D.M., and Maibaum T.S.E. (Eds). Handbook of Logic in Computer Science Vol. 1 (1992), Clarendon Press, Oxford
25. D.S. Scott, Domains for denotational semantics, in: M. Nielson, E.M. Schmidt (Eds.), Internat. Colloq. on Automata, Languages and Programs, Lecture Notes in Computer Science, Vol. 140, Springer, Berlin, 1982, pp. 577-613.
26. Taylor P. An algebraic approach to stable domains. Pure Appl. Algebra 64 (1990) 171-203
27. Vickers S.J. Topology Via Logic. Cambridge Tracts in Theoretical Computer Science Vol. 5 (1989), Cambridge University Press, Cambridge
28. G.-Q. Zhang, Logic of Domains, Progress in Theoretical Computer Science. Birkhäuser, Basel, 1991.
29. Zhang G.-Q. dI-domains as prime information systems. Inform. and Comput. 100 2 (1992) 151-177
30. G.-Q. Zhang, Disjunctive systems and L-domains, in: W. Kuich (Ed.), Internat. Conf. on Automata, Languages and Programming, Vienna 1992, Lecture Notes in Computer Science, Vol. 623, Springer, 1992, pp. 284-295.
31. Zhang G.-Q. Stable neighbourhoods. Theoret. Comput. Sci. 93 (1992) 143-157