Interpolation Properties, Beth Definability Properties and Amalgamation Properties for Substructural Logics
Interpolation Properties, Beth Definability Properties and Amalgamation Properties for Substructural Logics
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子结构逻辑的插值属性、Beth 可定义性属性和合并属性
DOI：
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发表时间：
2010
影响因子：
0.7
通讯作者：
H. Ono
中科院分区：
文献类型：
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作者：
H. Kihara;H. Ono
本文全面研究了子结构逻辑的各种插值性质和Beth可定义性（BDPs），并通过融合性质（AP）和满射性对它们进行了代数刻画。一般来说，子结构逻辑是可代数化的，但缺乏模态逻辑和超直觉主义逻辑所享有的许多基本逻辑属性[Gabbay and Maksimova（2005，Oxford Logic Guides，Vol. 46）]。在这种情况下，仔细检查是必要的，看看这些逻辑和代数性质是如何相关的。为了准确地描述这些关系，引入了许多插值性质和边界条件的变体，以及相应的代数性质。由于它们的一般性，这里报告的结果不仅适用于子结构逻辑，而且还可以扩展到更一般的设置，如抽象代数逻辑[Andreka，Nemeti和Sain（哲学逻辑手册，第2卷，第2版，第10页）。133-247）以及Czelakowski和Pigozzi（1999，Vol. 203 of Lecture Notes in Pure and Applied Mathematics，pp. 187-265）]。
This article develops a comprehensive study of various types of interpolation properties and Beth definability properties (BDPs) for substructural logics, and their algebraic characterizations through amalgamation properties (APs) and epimorphisms surjectivity. In general, substructural logics are algebraizable but lack many of the basic logical properties that modal and superintuitionistic logics enjoy [Gabbay and Maksimova (2005, Oxford Logic Guides, Vol. 46)]. In this case, careful examination is necessary to see how these logical and algebraic properties are related. To describe these relations exactly, many variants of interpolation properties and BDPs, and also corresponding algebraic properties, are introduced. Because of their generality, the results reported here hold not only for substructural logics, but can also be extended to a more general setting such as abstract algebraic logic [Andreka, Nemeti and Sain (Handbook of Philosophical Logic, Vol. 2, 2nd edn, pp. 133–247) and Czelakowski and Pigozzi (1999, Vol. 203 of Lecture Notes in Pure and Applied Mathematics, pp. 187–265)].