This paper presents a Hilbert-style system for the logic of first-degree entailment defined in a Fmla-Fmla framework. The effective use of this formulation as a basis for a whole family of systems extending the logic of first-degree entailment in various directions is shown. By systematizing this family, some new systems are uncovered, and some other well-established logics (such as the first-degree entailment fragment of Priest's Logic of Paradox) obtain new axiomatization. Semantics for the key systems from the family is formulated.

中文翻译：

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一级蕴涵的希尔伯特式公理化及其一系列扩展

本文为Fmla-Fmla框架中定义的一阶蕴涵逻辑提出了一个 Hilbert 风格的系统。显示了有效地使用该公式作为在各个方向上扩展一级蕴涵逻辑的整个系统系列的基础。通过对这个家族进行系统化，一些新的系统被发现，一些其他已经确立的逻辑（例如牧师悖论逻辑的一级蕴涵片段）获得了新的公理化。制定了家庭关键系统的语义。