代数和逻辑中的结构完备性和普遍完备性

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2023-12-16 DOI:10.1016/j.apal.2023.103391

Paolo Aglianò , Sara Ugolini

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引用次数: 0

摘要

在这项研究中，我们从代数和逻辑的角度研究了结构完备性和普遍完备性的概念。特别是，我们提供了主动和被动普遍完备性以及被动结构完备性准变元的新代数特征。我们将这些一般性结果应用于有界网格的变体以及与子结构逻辑相关的准变体。特别是，我们证明了满足弱化的子结构逻辑是被动结构完备的，当且仅当每一个经典矛盾在其中都是爆炸性的。此外，我们还充分描述了 MTL-代数的被动结构完备性变种，即由链生成的有界交换积分残差格。

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Structural and universal completeness in algebra and logic

In this work we study the notions of structural and universal completeness both from the algebraic and logical point of view. In particular, we provide new algebraic characterizations of quasivarieties that are actively and passively universally complete, and passively structurally complete. We apply these general results to varieties of bounded lattices and to quasivarieties related to substructural logics. In particular we show that a substructural logic satisfying weakening is passively structurally complete if and only if every classical contradiction is explosive in it. Moreover, we fully characterize the passively structurally complete varieties of $MTL$ -algebras, i.e., bounded commutative integral residuated lattices generated by chains.

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来源期刊

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.