论文标题
组合逻辑的模块化多值语义
Modular many-valued semantics for combined logics
论文作者
论文摘要
我们首次获得了用于组合逻辑的模块化多价值语义，该语义是直接从用于合并的逻辑的多个价值语义构建的，该语义是通过对部分非确定性逻辑矩阵进行的合适的通用操作。我们的构造在多结论逻辑的背景下保留了有限价值，而毫不奇怪的是，它可能在单一结论逻辑的背景下丢失。除了说明我们在广泛示例中的结构外，我们还开发了语义特征的具体应用，即，关于加强给定的多个值得贴现的逻辑的语义，对给定逻辑的条件的研究可能会被视为具有更简单定义的片段的范围，并可以将其视为具有独立范围的范围的组合，并且可以将其组合在一起。由组合机制保存。
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic logical matrices. Our constructions preserve finite-valuedness in the context of multiple-conclusion logics whereas, unsurprisingly, it may be lost in the context of single-conclusion logics. Besides illustrating our constructions over a wide range of examples, we also develop concrete applications of our semantic characterizations, namely regarding the semantics of strengthening a given many-valued logic with additional axioms, the study of conditions under which a given logic may be seen as a combination of simpler syntactically defined fragments whose calculi can be obtained independently and put together to form a calculus for the whole logic, and also general conditions for decidability to be preserved by the combination mechanism.
