Paraconsistent Logic, Evidence, and Justification
Paraconsistent Logic, Evidence, and Justification
复制标题
次相一致的逻辑、证据和理由
DOI：
10.1007/s11225-017-9714-3
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发表时间：
2017
期刊：
影响因子：
0.7
通讯作者：
M. Fitting
中科院分区：
文献类型：
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作者：
M. Fitting
Walter Carnielli和Abilio Rodrigues在即将发表的一篇论文中提出了一种基本证据逻辑（Basic Logic of Evidence，BLE），它的自然演绎规则被认为是证据而不是真理，它等价于纳尔逊的次协调逻辑N4，是在没有直觉否定的情况下，在直觉主义逻辑中加入强否定的结果。Carnielli/Rodrigues对证据的理解是非正式的。在这里，我们提供了一个正式的替代方案，使用理由逻辑。首先，我们介绍一个模态逻辑，KX 4，其中可以被解读为断言有X的隐含证据，我们理解的证据允许矛盾。我们以与直觉主义逻辑嵌入S4相同的方式将BLE嵌入KX 4。在此基础上，提出了一种新的证明逻辑JX 4，该逻辑将KX 4的隐含证据显式化，并通过一个实现定理将KX 4嵌入到JX 4中。ThusBLE在形式意义上既有隐含的也有明确的可能相互矛盾的证据解释。
In a forthcoming paper, Walter Carnielli and Abilio Rodrigues propose aBasic Logic of Evidence(BLE) whose natural deduction rules are thought of as preservingevidenceinstead of truth.BLEturns out to be equivalent to Nelson’s paraconsistent logicN4, resulting from adding strong negation to Intuitionistic logic without Intuitionistic negation. The Carnielli/Rodrigues understanding of evidence is informal. Here we provide a formal alternative, using justification logic. First we introduce a modal logic,KX4, in whichcan be read as asserting there is implicit evidence forX, where we understand evidence to permit contradictions. We showBLEembeds intoKX4in the same way that Intuitionistic logic embeds intoS4. Then we formulate a new justification logic,JX4, in which the implicit evidence motivatingKX4is made explicit.KX4embeds intoJX4via a realization theorem. ThusBLEhas both implicit and explicit possibly contradictory evidence interpretations in a formal sense.