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Continuous domains and their information system representation as logical systems. (English) Zbl 1261.68083

de Queiroz, Ruy (ed.) et al., WoLLIC’2002. Proceedings of the 9th workshop on logic, language, information and computation, Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, July 30–August 2, 2002. Amsterdam: Elsevier. Electronic Notes in Theoretical Computer Science 67, 96-115 (2002).
Summary: In this work, we introduce a finite information logic for continuous domains, as a complementary logic to continuous domain logic [the first author and B. M. Acílóly, “Logic of Plotkin continuous domains”, Lect. Notes Comput. Sci. 911, 195–206 (1995); “Using continuous domain logic to solve interval constraint satisfaction problems”, in: Memorias de la XXV conferencia latinoamericana de informática, CLEI’99, 661–672 (1999); M. Kegelmann, Continuous domains in logical form. Birmingham: University of Birmingham (PhD Thesis) (1999)]. Here, the logical aspects of a continuous domain are analysed instead of the whole class. In order to do so we will use the continuous information systems representation of continuous domains [R. Hoofman, Inf. Comput. 105, No. 1, 42–71 (1993; Zbl 0789.68090)] and we relate both structures via an isomorphism. This triple (continuous domain, isomorphism and continuous information system) are called continuous logical systems. From a continuous logical system we can define several notions, such as: satisfaction relation, information content, model, theory, logical consequence, information content order, etc. Based on the constructors of continuous domains and continuous information systems, we will define the respective constructors of continuous logical systems. Finally, we will extract a continuous domain logic from continuous logical systems and provide a soundness and completeness result for this logic based on the notion of model.
For the entire collection see [Zbl 1109.03311].

MSC:

68Q55 Semantics in the theory of computing
03B70 Logic in computer science
06B35 Continuous lattices and posets, applications

Citations:

Zbl 0789.68090
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References:

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