Relational, closure and partition powerset theories

Mockor Jiri

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Relational, closure and partition powerset theories

机译：关系，封闭和分区Powerset理论

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For general powerset theories in categories, new notions of relational, closure, or partition powerset theories in these categories are introduced. These new types of powerset theories are defined as categories whose objects are the original powerset objects with relational, closure, or partition structures defined on these objects. This construction generalizes classical constructions realized on powerset objects of all subsets of a given set, or all fuzzy sets on a given set, and it enables to define these structures on more general powerset objects. Examples of these new powerset objects are also shown. (C) 2020 Elsevier B.V. All rights reserved.

机译：对于类别的通用Powerset理论，介绍了这些类别中的关系，关闭或分区Powerset理论的新概念。这些新类型的PowerSet理论被定义为对象是原始Powerset对象的类别，其具有与这些对象上定义的关系，封闭或分区结构。该构造概括了在给定集合的所有子集的Powerset对象上实现的经典结构，或者给定集中的所有模糊集，并且它能够在更常规的Powerset对象上定义这些结构。还显示了这些新的Powerset对象的示例。（c）2020 Elsevier B.V.保留所有权利。

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来源
《Fuzzy sets and systems》 |2021年第15期|100-122|共23页
作者
Mockor Jiri;
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作者单位

Univ Ostrava Ctr Excellence IT4Innovat Inst Res & Applicat Fuzzy Modeling 30 Dubna 22 Ostrava 70103 1 Czech Republic;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
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专利

1. Simulation of the nested relational algebra by the flat relational algebra, with an application to the complexity of evaluating powerset algebra expressions [J] . Van den Bussche J. Theoretical computer science . 2001,第1a2期

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2. Relationship of Algebraic Theories to Powerset Theories and Fuzzy Topological Theories for Lattice-Valued Mathematics [J] . S. E.Rodabaugh International journal of mathematics and mathematical sciences . 2007,第21期

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3. Forcing many positive polarized partition relations between a cardinal and its powerset [J] . Saharon Shelah, Lee J. Stanley Journal of Symbolic Logic . 2001,第3期

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4. Any algorithm in the complex object algebra with powerset needs exponential space to compute transitive closure [C] . Dan Suciu, Jan Paredaens ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems . 1994

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6. Behavior analysis relational frame theory and the challenge of human language and cognition: A reply to the commentaries on relational frame theory: A post-skinnerian account of human language and cognition [O] . Steven C. Hayes, Dermot Barnes-Holmes, Bryan Roche 2003

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7. Closure theories of powerset theories [O] . Jiří Močkǒ 2015

机译：封闭Powerset理论的理论

Relational, closure and partition powerset theories

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