A point-free perspective on lax extensions and predicate liftings

IF 0.4 4区 计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS Mathematical Structures in Computer Science Pub Date : 2023-12-01 DOI:10.1017/s096012952300035x
Sergey Goncharov, Dirk Hofmann, Pedro Nora, Lutz Schröder, Paul Wild
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引用次数: 2

Abstract

Lax extensions of set functors play a key role in various areas, including topology, concurrent systems, and modal logic, while predicate liftings provide a generic semantics of modal operators. We take a fresh look at the connection between lax extensions and predicate liftings from the point of view of quantale-enriched relations. Using this perspective, we show in particular that various fundamental concepts and results arise naturally and their proofs become very elementary. Ultimately, we prove that every lax extension is induced by a class of predicate liftings; we discuss several implications of this result.
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关于松弛扩展和谓词提升的无点视角
集合函子的松散扩展在各个领域发挥关键作用,包括拓扑、并发系统和模态逻辑,而谓词提升提供模态操作符的通用语义。我们从富量子关系的角度重新审视松弛扩展和谓词提升之间的联系。从这个角度来看,我们特别指出,各种基本概念和结果是自然产生的,它们的证明变得非常初级。最后,我们证明了每一个松弛扩展都是由一类谓词提升引起的;我们讨论了这一结果的几个含义。
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来源期刊
Mathematical Structures in Computer Science
Mathematical Structures in Computer Science 工程技术-计算机:理论方法
CiteScore
1.50
自引率
0.00%
发文量
30
审稿时长
12 months
期刊介绍: Mathematical Structures in Computer Science is a journal of theoretical computer science which focuses on the application of ideas from the structural side of mathematics and mathematical logic to computer science. The journal aims to bridge the gap between theoretical contributions and software design, publishing original papers of a high standard and broad surveys with original perspectives in all areas of computing, provided that ideas or results from logic, algebra, geometry, category theory or other areas of logic and mathematics form a basis for the work. The journal welcomes applications to computing based on the use of specific mathematical structures (e.g. topological and order-theoretic structures) as well as on proof-theoretic notions or results.
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