Interpolation in Hájek's basic logic

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2025-05-26 DOI:10.1016/j.apal.2025.103615

Wesley Fussner , Simon Santschi

引用次数: 0

Abstract

We exhaustively classify varieties of BL-algebras with the amalgamation property, showing that there are only countably many of them and solving an open problem of Montagna. As a consequence of this classification, we obtain a complete description of which axiomatic extensions of Hájek's basic fuzzy logic BL have the deductive interpolation property. Along the way, we provide similar classifications of varieties of basic hoops with the amalgamation property and axiomatic extensions of the negation-free fragment of BL with the deductive interpolation property.

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插值在Hájek的基本逻辑

我们对具有合并性质的bl -代数进行了详尽的分类，证明了它们只有可数的几个，并解决了Montagna的一个开放问题。作为这种分类的结果，我们得到了Hájek的基本模糊逻辑BL的公理扩展具有演绎插值性质的完整描述。在此过程中，我们提供了具有合并性质的各种基本环的类似分类，以及具有演绎插值性质的BL无负片段的公理化扩展。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.