具有不动点的对合一致逻辑具有有限强标准完备性

IF 0.3 4区数学 Q1 Arts and Humanities

Archive for Mathematical Logic Pub Date : 2022-07-22 DOI:10.1007/s00153-022-00839-1

Sándor Jenei

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引用次数: 2

摘要

给出了具有不动点的对合一致逻辑有限强标准完备性的一个代数证明(\({{\mathbf {IUL}}^{fp}}\))。它可能为解决G. Metcalfe, F. Montagna提出的对合一致逻辑(\({\mathbf {IUL}}\))的标准完备性问题提供了第一步。(J符号学报72:834-864,2007))基于一类具有有限多个正幂等元的奇对合FL \(_e\) -链的结构描述，利用嵌入定理证明了这一结果。

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Involutive Uninorm Logic with Fixed Point enjoys finite strong standard completeness

An algebraic proof is presented for the finite strong standard completeness of the Involutive Uninorm Logic with Fixed Point (\({{\mathbf {IUL}}^{fp}}\)). It may provide a first step towards settling the standard completeness problem for the Involutive Uninorm Logic (\({\mathbf {IUL}}\), posed in G. Metcalfe, F. Montagna. (J Symb Log 72:834–864, 2007)) in an algebraic manner. The result is proved via an embedding theorem which is based on the structural description of the class of odd involutive FL\(_e\)-chains which have finitely many positive idempotent elements.

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来源期刊

Archive for Mathematical Logic MATHEMATICS-LOGIC

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.