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首页> 外文期刊>Journal of logic and computation >Logical Weak Completions Of Paraconsistent Logics
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Logical Weak Completions Of Paraconsistent Logics

机译：超常逻辑的逻辑弱完成

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Let P be an arbitrary theory and let X be any given logic. Let M be a set of atoms. We say that M is a X-stable model of P if M is a classical model of P and PU-M proves in logic X all atoms in M, this is denoted by PU-M-xM. We prove that being an X-stable model is an invariant property for disjunctive programmes under a large class of logics. Two kinds of logics are mainly considered: paraconsistent logics and normal modal logics. For modal logics we use a translation proposed by Gelfond that replaces -a with -□a. As a consequence we prove that several semantics (recently introduced) for non-monotonic reasoning are equivalent for disjunctive programmes. In addition, we show that such semantics can be characterized by a fixed-point operator in terms of classical logic. We also present a simple translation of a disjunctive programme D into a normal programme N, such that the PStable model semantics of N corresponds to the stable semantics of D over the common language. We present the formal proof of this statement.
机译：令P为任意理论，令X为任何给定逻辑。令M为一组原子。我们说如果M是P的经典模型，并且PU-M在逻辑X中证明M中的所有原子，则M是P的X稳定模型，这用PU-M-xM表示。我们证明，作为X稳定模型，对于大量逻辑下的析取程序来说是不变的。主要考虑两种逻辑：超一致逻辑和标准模态逻辑。对于模态逻辑，我们使用Gelfond提出的翻译，将-a替换为-□a。结果，我们证明了非单调推理的几种语义（最近引入）与析取程序是等效的。另外，我们证明了这种语义可以通过定点运算符来描述经典逻辑。我们还提出了将析取程序D转换为普通程序N的简单方法，以使N的PStable模型语义对应于D在公共语言上的稳定语义。我们提供此声明的正式证明。

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