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Consistent disjunctive sequent calculi and Scott domains

Published online by Cambridge University Press:  17 August 2021

Longchun Wang Open the ORCID record for Longchun Wang [Opens in a new window]  and
Qingguo Li Open the ORCID record for Qingguo Li [Opens in a new window]
Longchun Wang
Affiliation:
School of Mathematics, Hunan University, Changsha410086, China School of Mathematical Sciences, Qufu Normal University, Qufu273165, China
Qingguo Li*
Affiliation:
School of Mathematics, Hunan University, Changsha410086, China
*
*Corresponding author. Email: [email protected]
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Abstract

Based on the framework of disjunctive propositional logic, we first provide a syntactic representation for Scott domains. Precisely, we establish a category of consistent disjunctive sequent calculi with consequence relations, and show it is equivalent to that of Scott domains with Scott-continuous functions. Furthermore, we illustrate the approach to solving recursive domain equations by introducing some standard domain constructions, such as lifting and sums. The subsystems relation on consistent finitary disjunctive sequent calculi makes these domain constructions continuous. Solutions to recursive domain equations are given by constructing the least fixed point of a continuous function.

Keywords

Consistent disjunctive sequent calculusScott domaincategorical equivalencefixed pointdomain equation
Type
Special Issue: Theory and Applications of Models of Computation (TAMC 2020)
Information
Mathematical Structures in Computer Science , Volume 32 , Issue 2: Theory and Applications of Models of Computation (TAMC 2020) , February 2022 , pp. 127 - 150
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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