|$\textrm{LP}^{\mathbin{\supset },{\mathsf{F}}}$| 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 |$\textrm{LP}^{\mathbin{\supset },{\mathsf{F}}}$| 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 |$\textrm{LP}^{\mathbin{\supset },{\mathsf{F}}}$| 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 |$\textrm{LP}^{\mathbin{\supset },{\mathsf{F}}}$| from the other three-valued paracomplete propositional logics with those comparable properties.

中文翻译：

---

关于经典逻辑及其对偶中最强的三值超一致逻辑

| $ \ textrm {LP} ^ {\ mathbin {\ supset}，{\ mathsf {F}}} $$ | 是一个三值超常命题逻辑，与J3基本上相同。它具有被提议为合理的超一致命题逻辑的理想特性的最多特性。但是，从已经发表的结果可以很容易地得出结论，确切地说，有8192个具有相关属性的不同的三值超一致命题逻辑。在本文中，使用与逻辑的逻辑等价关系有关的属性来区分| $ \ textrm {LP} ^ {\ mathbin {\ supset}，{\ mathsf {F}}} $ |。从其他。作为专注于逻辑等价关系的一项奖励，发现8192个逻辑中只有32个具有满足对合和相加的恒等式，an灭，等幂和交换定律的逻辑等价关系。对于| $ \ textrm {LP} ^ {\ mathbin {\ supset}的大多数属性，{\ mathsf {F}}} $$ 由于已经被提出为合理的超一致命题逻辑的理想性质，其超完全类似物具有可比较的性质。在本文中，还使用与逻辑的逻辑等效关系有关的属性来区分| $ \ textrm {LP} ^ {\ mathbin {\ supset}，{\ mathsf {F}}} $ |的超完全类似物。从具有这些可比较属性的其他三值超完备命题逻辑中得出。