重温达科斯塔的逻辑

Q1 Mathematics

Journal of Applied Logic Pub Date : 2016-07-01 DOI:10.1016/j.jal.2016.02.004

Mauricio Osorio Galindo , Verónica Borja Macías , José Ramón Enrique Arrazola Ramírez

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引用次数: 8

摘要

1996年，Priest开发了da Costa逻辑(daC);这是一个副一致逻辑，也是一个包含逻辑Cω的共同直觉逻辑。由于其有趣的性质，Castiglioni, Ertola和Ferguson对其进行了研究，并在[8]，[11]中给出了一些关于它及其扩展的显著结果。在本文中，我们继续研究daC，我们证明了daC的一个受限Hilbert系统，命名为DC，满足一些性质，这些性质帮助我们证明了这个逻辑不是一个极大副相容系统。我们还研究了daC的扩展，称为PH1，并给出了它的不同表征。最后，我们比较了daC和PH1与几种副一致逻辑。

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Revisiting da Costa logic

In [25] Priest developed the da Costa logic (daC); this is a paraconsistent logic which is also a co-intuitionistic logic that contains the logic $C_{ω}$ . Due to its interesting properties it has been studied by Castiglioni, Ertola and Ferguson, and some remarkable results about it and its extensions are shown in [8], [11]. In the present article we continue the study of daC, we prove that a restricted Hilbert system for daC, named DC, satisfies certain properties that help us show that this logic is not a maximal paraconsistent system. We also study an extension of daC called $P H_{1}$ and we give different characterizations of it. Finally we compare daC and $P H_{1}$ with several paraconsistent logics.