Sugihara代数与幺半群：多序对偶
Sugihara algebras and monoids: multisorted dualities
摘要：
作者在最近的一篇论文中发展了Sugihara代数的生成拟簇的自然对偶。因此，他们确定了这些拟簇的容许代数，通过Cabrer等人设计的测试空间方法，给出了一个可行的方法来研究相关逻辑中的可接受规则，特别是对演绎系统$R$ -mingle的扩展。本文建立在工作已经完成的理论的自然对偶杉原代数。它的目的是提供一个统一类型的多分类对偶定理的集成套件，包括Sugihara代数和Sugihara幺半群的双生成拟簇和簇，并包括奇数和偶数的情况。这里发展的多分类对偶理论的总体理论框架导致了自由代数的顺从表示。更广泛地说，它为进一步的应用提供了跳板。
英文摘要：
The authors developed in a recent paper natural dualities for finitely generated quasivarieties of Sugihara algebras. They thereby identified the admissibility algebras for these quasivarieties which, via the Test Spaces Method devised by Cabrer et al., give access to a viable method for studying admissible rules within relevance logic, specifically for extensions of the deductive system $R$-mingle. This paper builds on the work already done on the theory of natural dualities for Sugihara algebras. Its purpose is to provide an integrated suite of multisorted duality theorems of a uniform type, encompassing finitely generated quasivarieties and varieties of both Sugihara algebras and Sugihara monoids, and embracing both the odd and the even cases. The overarching theoretical framework of multisorted duality theory developed here leads on to amenable representations of free algebras. More widely, it provides a springboard to further applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
