This paper is concerned with the first-order paraconsistent logic LPQ$^{\supset,\mathsf{F}}$. A sequent-style natural deduction proof system for this logic is presented and, for this proof system, both a model-theoretic justification and a logical justification by means of an embedding into first-order classical logic is given. For no logic that is essentially the same as LPQ$^{\supset,\mathsf{F}}$, a natural deduction proof system is currently available in the literature. The given embedding provides both a classical-logic explanation of this logic and a logical justification of its proof system. The major properties of LPQ$^{\supset,\mathsf{F}}$ are also treated.

翻译：本文涉及第一级准一致逻辑LPQ$ ⁇ supset,\ mathsf{F ⁇ $。 该逻辑的顺序式自然扣减验证系统被提出,对于这个验证系统,既提供了模型理论依据,又提供了逻辑依据,将其嵌入第一级古典逻辑。对于基本上与LPQ$ ⁇ supset,\mathsf{F ⁇ $相同的逻辑,文献中目前有一个自然扣减验证系统。给定的嵌入既提供了这一逻辑的古典逻辑解释,又提供了其验证系统的逻辑依据。LPQ$ ⁇ supset,\mathsf{F ⁇ $的主要属性也被处理。