Abstract
This paper extend the Abramsky approach to domain logic, in the sense, that we are considering Plotkin continuous domains instead of Scott domain or SFP-domain. Thus, we study the logical aspects of domains as used in the denotational semantics of non-deterministic programming languages with directed application in scientific computation. Using the alternative description of information system (Plotkin continuous), we give a concrete language for types, we eliminate some restrictions of the Abramsky approach, we increment new axioms and rules to the proof system, and we determinate the meaning of the atomical formulae.
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Samson Abramsky. Domain theory in logic form. In Proc. of second annual Symposium on Logic in Computer Science — LICS'87, 1987.
Benedito Melo Acióly. Fundamentação Computacional da Matemática Intervalar. PhD thesis, CPGCC da UFRGS, Porto Alegre, 1991.
Samson Abramsky and Achim Jung. Domain theory. In Handbook of Logic in Computer Science. page 109. To apears, 1994.
Benjamín René Callejas Bedregal. A representation of retract of sfp-domain. 1994.
Benjamín René Callejas Bedregal and Manoel Agamemnon Lopes. Sistemas de informação via sistemas semânticos. In Anais XX Conferencia Latinoamericana de Informática-CLEI, PANEL 94, Ciudad de Mexico, 19 a 23 de septiembre de 1994.
G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M. Mislove, and D.S. Scott. A Compendium of Continuous Lattices. Springer-Verlag, Berlim, 1980.
Carl L. Gunter. Comparing categories of domains. 1986.
Peter T. Johnstone. Stone Space, volume 3 of Cambridge Studies in Advanced Mathematics. Cambridge University Press., Cambridge-UK, 1982.
Jimmie D. Lawson. The versatile of continuous order. In M. Mislon M. Main, A. Melton and D. Schmidt, editors, Mathematical Foundations of Programming Languages Semantics, New Orleans, 1987. Proceeding 3rd Workshop Tulane University, Springer LNCS 298.
R.E. Moore. Reliability in Computing: the Role of Interval Methods in Scientific Computing. Van Nortrand, New York, 1988.
Gordon Plotkin. A powerdomain construction. SIAM J. Comput., (5):452–486, 1976.
A.W. Roscoe and G. M. Reed. Domains for Denotational Semantics. Prentice Hall, 1990.
Dana S. Scott. Domains for denotational semantics. In Automata, Languages and Programming, Berlim, 1982. Springer Verlag LNCS, 140.
Mike Smyth. Topology. In S. Abramsky, D.M Gabbay, and T.S.E. Mainbaum, editors, Handbook of Logic in Computer Science. Vol. 1. Oxford University Press, 1992.
S. J. Vickers. Topology via Logic. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge-UK, 1989.
Guo-Qiang Zhang. Logics of Domains. PhD thesis, University of Cambridge, Computer Laboratory, Cambridge, UK., 1989.
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© 1995 Springer-Verlag Berlin Heidelberg
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Bedregal, B.R.C., Acióly, B.M. (1995). Logic of plotkin continuous domain. In: Baeza-Yates, R., Goles, E., Poblete, P.V. (eds) LATIN '95: Theoretical Informatics. LATIN 1995. Lecture Notes in Computer Science, vol 911. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59175-3_89
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DOI: https://doi.org/10.1007/3-540-59175-3_89
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