Connexive Modal Logic
Connexive Modal Logic
复制标题
连接模态逻辑
DOI：
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复制
发表时间：
2004
期刊：
影响因子：
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通讯作者：
H. Wansing
中科院分区：
文献类型：
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作者：
H. Wansing
连接逻辑是非经典逻辑中一个被忽视的方向。本文首先给出了一个关联命题逻辑的公理系统。这种逻辑，C，被证明是健全的和完整的一类关系模型。事实上，这种语义学似乎是第一个已知的对联结逻辑系统的直觉上合理的解释。C的提出表明，连接逻辑是建设性的。它是大卫纳尔逊的强否定的构造性逻辑的变体。在纳尔逊逻辑中，蕴涵的验证条件是动态的，而所有证伪条件都是现场证伪的静态条件。在C语言中，蕴涵的证实条件和证伪条件都是动态的。这足以确保C是连通的，并且可以根据信息状态给出可理解和清晰的解释。在第二步中，系统C的语言被模态算子和谓词扩展以获得最小正规模态命题逻辑K的连接模拟。针对K的一个连接类似物，通过模态翻译，它可以忠实地嵌入到QC中，量化C，我们得到了一个系统，将被称为CK，连接K。系统CK是在[12]中描述的构造模态逻辑FSK的连接版本。CK被证明是健全的和完整的关系模型，是可判定的。我们还将批判性地讨论模态算子的求值子句，这些求值子句是由模态命题逻辑到一阶逻辑的标准翻译所诱导的。在联结基础逻辑的语境中，由标准翻译所导出的公式A的证伪子句在直觉上似乎是不可信的。无论如何，两个句法二元性公理A ♦ A和♦ A都不成立。CK似乎是模态逻辑文献中考虑的第一个连接模态逻辑系统。因此，本文可以被看作是一个贡献，建立连接模态逻辑作为一个值得尊敬的分支模态逻辑。模态逻辑进展，第5卷。c © 2005，Heinrich Wansing. 368 Heinrich Wansing 1 Aristotle's Theses and Boethius' Theses下面的原理被称为“Aristotle's Thesis”：
Connexive logic is a neglected direction in non-classical logic. In the present paper, first an axiomatic system of connexive propositional logic is presented. This logic, C, is shown to be sound and complete with respect to a class of relational models. It seems that this semantics is, in fact, the first known intuitively plausible interpretation of a system of connexive logic. The presentation of C suggests that connexive logic is constructive. It is a variant of David Nelson’s constructive logics with strong negation. In Nelson’s logics the verification conditions of implications are dynamic, whereas all falsification conditions are static conditions of falsification on the spot. In C, both the verification and the falsification conditions of implications are dynamic. This is enough to ensure that C is connexive and can be given a comprehensible and clear interpretation in terms of information states. In a second step, the language of the system C is extended by the modal operators and ♦ to obtain a connexive analogue of the smallest normal modal propositional logic K. Aiming at a connexive analogue of K that can be faithfully embedded by a modal translation into QC, quantified C, we arrive at a system that will be called CK, connexive K. The system CK is a connexive version of the constructive modal logic FSK characterized in [12]. CK is shown to be sound and complete with respect to relational models and to be decidable. We shall also critically discuss the evaluation clauses for the modal operators that are induced by the standard translation from modal propositional logic into first-order logic. In the context of the connexive base logic, the falsification clauses of formulas A induced by the standard translation appear to be intuitively implausible. In any case, both syntactic duality axioms ∼ A ↔ ♦ ∼ A and ∼ ♦ ↔ ∼ A fail to hold. It seems that CK is the first system of connexive modal logic considered in the modal logic literature. This paper may therefore be seen as a contribution to establishing connexive modal logic as a respectable branch of modal logic. Advances in Modal Logic, Volume 5. c © 2005, Heinrich Wansing. 368 Heinrich Wansing 1 Aristotle’s Theses and Boethius’ Theses The following principle is well-known as “Aristotle’s Thesis”:
用于双格否定的 Gentzen 型方法
DOI：
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发表时间：
2005
期刊：
Studia Logica 80
影响因子：
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作者：
上出哲広;上出哲広
通讯作者：
上出哲広