Consistent disjunctive sequent calculi and Scott domains. (17th February 2022)

• Record Type: Journal Article
• Authors: Wang, Longchun; Li, Qingguo
• Is Part Of: Mathematical structures in computer science. Volume 32:Number 2(2022)
• Page Start: 127
• Page End: 150
• Publication Date: 2022-02-17
• Subjects: Consistent disjunctive sequent calculus -- Scott domain -- categorical equivalence -- fixed point -- domain equation; Computer science -- Mathematics -- Periodicals; 004.015105
• DOI: 10.1017/S0960129521000086
• Languages: English
• ISSNs: 0960-1295

Abstract

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.