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A representation of proper BC domains based on conjunctive sequent calculi

Published online by Cambridge University Press:  16 October 2019

Longchun Wang  and
Qingguo Li
Longchun Wang
Affiliation:
College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, China
Qingguo Li*
Affiliation:
College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China
*
*Corresponding author. Email: liqingguoli@aliyun.com
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Abstract

We build a logical system named a conjunctive sequent calculus which is a conjunctive fragment of the classical propositional sequent calculus in the sense of proof theory. We prove that a special class of formulae of a consistent conjunctive sequent calculus forms a bounded complete continuous domain without greatest element (for short, a proper BC domain), and each proper BC domain can be obtained in this way. More generally, we present conjunctive consequence relations as morphisms between consistent conjunctive sequent calculi and build a category which is equivalent to that of proper BC domains with Scott-continuous functions. A logical characterization of purely syntactic form for proper BC domains is obtained.

Keywords

Conjunctive sequent calculusproper BC domaincategorical equivalence

Information

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 30 , Issue 1 , January 2020 , pp. 1 - 13
Copyright
© Cambridge University Press 2019 

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Footnotes

†

This research Supported by the National Natural Science Foundation of China(11771134).

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