A note on axiomatizations of Pavelka-style complete fuzzy logics
A note on axiomatizations of Pavelka-style complete fuzzy logics
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DOI：
10.1016/j.fss.2014.11.021
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发表时间：
2016-06-01
影响因子：
3.9
通讯作者：
Cintula, Petr
中科院分区：
文献类型：
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作者：
Cintula, Petr
帕维尔卡式的完整性是一种与可证明性和真实性程度相关的属性，以前主要在具有连续连接词的逻辑背景下进行研究。众所周知，在一些其他逻辑中，可以使用无限演绎规则来保留这种形式的完整性。本文对模糊逻辑的这一思想进行了系统的研究，该模糊逻辑扩展了 MTL，并由固定的标准代数给出。我们通过理性真值常数探索任何此类逻辑的所有“合理”扩展的类结构，并且对于几个突出的情况，提供享有帕维尔卡式完整性的特定扩展的公理化。 (C) 2014 Elsevier B.V. 保留所有权利。
Pavelka-style completeness, a property relating degrees of provability and truth, was previously studied mainly in the context of logics with continuous connectives. It is known that in some other logics one can use infinitary deduction rule(s) to retain this form of completeness. The present paper offers a systematic study of this idea for fuzzy logics which expand MTL and are given by a fixed standard algebra. We explore the structure of the class of all 'reasonable' expansions of any such logic by rational truth constants and, for several prominent cases, provide axiomatizations of particular expansions enjoying the Pavelka-style completeness. (C) 2014 Elsevier B.V. All rights reserved.