Abstract
Strongly finite sequent structures have been introduced by Zhang as a logic-oriented representation of SFP domains. In this paper we extend his definition by demanding the existence of a distinguished element with the properties of a tautology. This is no restriction compared with Zhang’s approach, but has several advantages. Moreover, we show that the entailment relation of every strongly finite sequent structure can be derived from a preorder. A close connection between strongly finite sequent structures and certain preorders is exhibited. It helps clarifying the correspondence between strongly finite sequent structures and SFP domains. To every domain construction used in programming language semantics there is a similar construction for preorders from which the corresponding construction for sequent structures can be obtained in a uniform way.
This research has partially been supported by the DFG-RFFI grant “Domain-like Structures for Semantics and Computability”
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References
Abramksy, S., Domain theory in logical form, Annals of Pure and Applied Logic 51 (1991) 1–77.
Abramsky, S. and Jung, A., Domain Theory, In: S. Abramsky et al. (editors), Handbook of Logic in Computer Science, Vol. 3, Semantic Structures, Oxford University Press, 1994, 1–168.
Amadio, R. M. and Curien, P.-L., Domains and Lambda Calculi, Cambridge University Press, 1998.
Greb, R., The category of strongly finite sequent structures, Informatik-Bericht Nr. 02–98, University of Siegen, 1998.
Gunter, C., Semantics of Programming Languages, MIT Press, 1992.
Gunter, C. and Scott, D. S., Semantic domains, In: J. van Leeuven (editor), Handbook of Theoretical Computer Science, Vol. B, Formal Methods and Semantics, Elsevier, 1990, 633–674.
Jung, A., Cartesian closed categories of domains, CWI Tracts 66, Centrum voor Wiskunde en Informatica, Amsterdam, 1989.
Larsen, K. G. and Winskel, G., Using information systems to solve recursive domain equations effectively, In: G. Kahn et al. (editors), Semantics of Data Types, Lecture Notes in Computer Science 173, Springer, 1984, 109–130.
Plotkin, G. D., A powerdomain construction, SIAM J. Computing 5 (1976) 452–487.
Plotkin, G. D., Domains, Department of Computer Science, University of Edinburgh, 1983.
Scott, D. S., Outline of a mathematical theory of computation, Technical Monograph PR-2, Oxford University Computation Laboratory, 1970.
Scott, D. S., Domains for denotational semantics, In: M. Nielson et al. (editors), International Colloquium on Automata, Languages and Programming, Lecture Notes in Computer Science 140, Springer, 1982, 577–613.
Stoltenberg-Hansen, V., Lindstrom, I. and Griffor, E. R., Math- ematical Theory of Domains, Cambridge University Press, 1994.
Zhang, G. Q., Logic of Domains, Birkhauser, 1991.
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Spreen, D., Greb, R. (2003). A Note on Strongly Finite Sequent Structures. In: Zhang, G.Q., Lawson, J., Liu, YM., Luo, MK. (eds) Domain Theory, Logic and Computation. Semantic Structures in Computation, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1291-0_9
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DOI: https://doi.org/10.1007/978-94-017-1291-0_9
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