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Non-deterministic Multiple-valued Structures

机译：非确定性多值结构

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摘要

The ordinary concept of a multiple-valued matrix is generalized by introducing non-deterministic matrices (Nmatrices), in which non-deterministic computations of truth-values are allowed. It is shown that some important logics for reasoning under uncertainty can be characterized by finite Nmatrices (and so they are decidable), although they have only infinite characteristic ordinary (deterministic) matrices. A generalized compactness theorem that applies to all finite Nmatrices is then proved. Finally, a strong connection is established between the admissibility of the cut rule in canonical Gentzen-type propositional systems, non-triviality of such systems, and the existence of sound and complete non-deterministic two-valued semantics for them. This connection is used for providing a complete solution for the old 'Tonk' problem of Prior.
机译：多值矩阵的一般概念是通过引入非确定性矩阵（Nmatrices）来概括的，其中允许对真值进行非确定性计算。研究表明，不确定性下的一些重要逻辑可以用有限N矩阵来表征（因此它们是可判定的），尽管它们只有无限特征性的普通（确定性）矩阵。然后证明了适用于所有有限N矩阵的广义紧性定理。最终，在规范的Gentzen型命题系统中割断规则的可采性，此类系统的平凡性与它们的健全和完整的非确定性二值语义之间存在着牢固的联系。此连接用于为Prior的旧“ Tonk”问题提供完整的解决方案。

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