The Syntax of Disjunctive Propositional Logic and Algebraic L-domains
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Based on the investigation of the proof system of a disjunctive propositional logic introduced by Yi-xiang Chen and Achim Jung, this paper establishes a purely syntactic representation of algebraic L-domains. The central tools used here are logical states which build a bridge between the logical proof systems and algebraic L-domains. A notion of consequence relation is also made to determine Scott-continuous functions between algebraic L-domains. More precisely, a category of certain proof systems with consequence relations is shown to be equivalent to that of algebraic L-domains with Scott-continuous functions. As an application, a subclass of disjunctive propositional logic is found to provide a logical representation for Scott domains. This allows gaining deep insight into the subject of capturing domains in terms of logic.
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