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Neighbourhood Semantics for Quantified Relevant Logics
Journal of Philosophical Logic ( IF 0.7 ) Pub Date : 2021-10-15 , DOI: 10.1007/s10992-021-09637-1
Andrew Tedder 1 , Nicholas Ferenz 2
Affiliation  

The Mares-Goldblatt semantics for quantified relevant logics have been developed for first-order extensions of R, and a range of other relevant logics and modal extensions thereof. All such work has taken place in the the ternary relation semantic framework, most famously developed by Sylvan (née Routley) and Meyer. In this paper, the Mares-Goldblatt technique for the interpretation of quantifiers is adapted to the more general neighbourhood semantic framework, developed by Sylvan, Meyer, and, more recently, Goble. This more algebraic semantics allows one to characterise a still wider range of logics, and provides the grist for some new results. To showcase this, we show, using some non-augmented models, that some quantified relevant logics are not conservatively extended by connectives the addition of which do conservatively extend the associated propositional logics, namely fusion and the dual implication. We close by proposing some further uses to which the neighbourhood Mares-Goldblatt semantics may be put.



中文翻译:

量化相关逻辑的邻域语义

量化相关逻辑的 Mares-Goldblatt 语义已经为R 的一阶扩展以及一系列其他相关逻辑和模态扩展开发。所有这些工作都发生在三元关系语义框架中,最著名的是由 Sylvan (née Routley) 和 Meyer 开发的。在本文中,用于解释量词的 Mares-Goldblatt 技术适用于更一般的邻域语义框架,由 Sylvan、Meyer 和最近的 Goble 开发。这种更加代数的语义允许人们表征更广泛的逻辑,并为一些新结果提供了基础。为了展示这一点,我们使用一些非增广模型表明,一些量化的相关逻辑没有被连接词保守地扩展,而连接词的添加确实保守地扩展了相关的命题逻辑,即融合和对偶蕴涵。我们最后提出了一些进一步的用途,邻域 Mares-Goldblatt 语义可能会用到这些用途。

更新日期:2021-10-17
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