Connexive Conditional Logic. Part I
Connexive Conditional Logic. Part I
复制标题
连接条件逻辑。
DOI：
10.12775/llp.2018.018
复制
发表时间：
2018
影响因子：
0.5
通讯作者：
M. Unterhuber
中科院分区：
文献类型：
--
作者：
H. Wansing;M. Unterhuber
本文首先从语义上引入了一些基于 Belnap 和 Dunn 有用的一级蕴涵四值逻辑的命题条件逻辑，然后将其转化为弱且无限制连接的条件逻辑系统。这些逻辑的通用框架语义使用一组允许的（或允许的）扩展/反扩展对。接下来，提出这些逻辑的合理且完整的表格演算。此外，还考虑通过建设性含义扩展基本条件连接逻辑，这为讨论最近的相关工作提供了机会，其动机是指示性条件和反事实条件的结合。基本构造性连接条件逻辑的 Tableau 演算已被定义，并且在语义方面被证明是合理且完整的。这种语义必须确保关于用于解释构造性含义的前序的持久性属性。
In this paper, first some propositional conditional logics based on Belnap and Dunn’s useful four-valued logic of first-degree entailment are introduced semantically, which are then turned into systems of weakly and unrestrictedly connexive conditional logic. The general frame semantics for these logics makes use of a set of allowable (or admissible) extension/antiextension pairs. Next, sound and complete tableau calculi for these logics are presented. Moreover, an expansion of the basic conditional connexive logics by a constructive implication is considered, which gives an opportunity to discuss recent related work, motivated by the combination of indicative and counterfactual conditionals. Tableau calculi for the basic constructive connexive conditional logics are defined and shown to be sound and complete with respect to their semantics. This semantics has to ensure a persistence property with respect to the preorder that is used to interpret the constructive implication.