论文标题
非分配逻辑的表征结果
A Characterization Result for Non-Distributive Logics
论文作者
论文摘要
最近发表的工作解决了非分配逻辑的Shalqvist对应问题。出现的自然问题是识别与逻辑相对应的一阶逻辑的片段，而无需分发，将模态逻辑的表征提升到了这种新设置。执行该项目的是本文的贡献。 该文章旨在作为将非分配逻辑减少到（分类）残留模态逻辑的项目的演示和应用。降低是该作者最新表示结果的应用，并将其概括性地概括为将亚条件逻辑语言的规范和完全抽象的翻译概括为其同伴的语言，分类了残留的模态逻辑。通过适应和重复现有结果，将非分配逻辑减少到分类的模态逻辑上几乎毫不费力地证明了非分配逻辑的表征几乎毫不费力地证明了这种方法在研究可能缺乏分布的逻辑中的有用性和适用性。
Recent published work has addressed the Shalqvist correspondence problem for non-distributive logics. The natural question that arises is to identify the fragment of first-order logic that corresponds to logics without distribution, lifting van Benthem's characterization result for modal logic to this new setting. Carrying out this project is the contribution of the present article. The article is intended as a demonstration and application of a project of reduction of non-distributive logics to (sorted) residuated modal logics. The reduction is an application of recent representation results by this author for normal lattice expansions and a generalization of a canonical and fully abstract translation of the language of substructural logics into the language of their companion sorted, residuated modal logics. The reduction of non-distributive logics to sorted modal logics makes the proof of a van Benthem characterization of non-distributive logics nearly effortless, by adapting and reusing existing results, demonstrating the usefulness and suitability of this approach in studying logics that may lack distribution.
