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On the strongest three-valued paraconsistent logic contained in classical logic and its dual

机译：关于古典逻辑及其双重的最强大的三价滞后逻辑

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摘要

LP superset of,F is a three-valued paraconsistent propositional logic that is essentially the same as J3. It has the most properties that have been proposed as desirable properties of a reasonable paraconsistent propositional logic. However, it follows easily from already published results that there are exactly 8192 different three-valued paraconsistent propositional logics that have the properties concerned. In this paper, properties concerning the logical equivalence relation of a logic are used to distinguish LP superset of,F from the others. As one of the bonuses of focusing on the logical equivalence relation, it is found that only 32 of the 8192 logics have a logical equivalence relation that satisfies the identity, annihilation, idempotent and commutative laws for conjunction and disjunction. For most properties of LP superset of,F that have been proposed as desirable properties of a reasonable paraconsistent propositional logic, its paracomplete analogue has a comparable property. In this paper, properties concerning the logical equivalence relation of a logic are also used to distinguish the paracomplete analogue of LP superset of,F from the other three-valued paracomplete propositional logics with those comparable properties.
机译：LP超标，F是一个三值的恶作剧命题逻辑，与J3基本相同。它具有最多的属性，这些属性是合理的恶作剧命题逻辑的理想性质。但是，它从已经发表的结果中容易遵循，即恰好存在有关属性的8192种不同的三价滞后命题逻辑。在本文中，有关逻辑逻辑等效关系的属性用于区分来自其他逻辑的LP超集。作为专注于逻辑等价关系的奖励之一，发现8192个逻辑中只有32个具有逻辑等效关系，满足了合并和分离的身份，湮灭，空缺和交换法律。对于LP超级特性的大多数属性，所述F的合理性脱节致命逻辑的理想性质，其副间型类似物具有可比性。在本文中，关于逻辑的逻辑等效关系的特性也用于区分LP超标仪的副间综合征类似于与这些可比属性的其他三维剖腹产逻辑。

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