一元BL-代数：Hájek一元模糊逻辑的等价代数语义
Monadic BL-algebras: the equivalent algebraic semantics of Hájek's monadic fuzzy logic
摘要：
本文引入了一元BL-代数簇作为赋有两个一元算子$\forall$和$\exists$的BL-代数.经过研究的基本性质，这个品种，我们表明，这类是等价的代数语义的一元片段的哈耶克的基本谓词逻辑。此外，我们开始了一元BL-代数的主要子簇的系统研究，其中一些构成了著名的一元逻辑的代数语义：一元哥德尔逻辑和一元Kukasiewicz逻辑。在最后一节中，我们给出了全序一元BL-代数的一个完整刻画。
英文摘要：
In this article we introduce the variety of monadic BL-algebras as BL-algebras endowed with two monadic operators $\forall$ and $\exists$. After a study of the basic properties of this variety we show that this class is the equivalent algebraic semantics of the monadic fragment of Hájek's basic predicate logic. In addition, we start a systematic study of the main subvarieties of monadic BL-algebras, some of which constitute the algebraic semantics of well-known monadic logics: monadic Gödel logic and monadic Łukasiewicz logic. In the last section we give a complete characterization of totally ordered monadic BL-algebras.
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