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Interpolation and Beth Definability in Default Logics

机译:默认逻辑中的插值和Beth可定义

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We investigate interpolation and Beth definability in default logics. To this end, we start by defining a general framework which is sufficiently abstract to encompass most of the usual definitions of a default logic. In this framework a default logic DL is built on a base, monotonic, logic L. We then investigate the question of when interpolation and Beth definability results transfer from L to DL. This investigation needs suitable notions of interpolation and Beth definability for default logics. We show both positive and negative general results: depending on how DL is defined and of the kind of interpolation/Beth definability involved, the property might or might not transfer from L to DL.
机译:我们调查默认逻辑中的插值和Beth可定义。为此,我们首先定义一般框架,该框架是足够的摘要来包含默认逻辑的大多数通常的定义。在本框架中,默认逻辑DL构建在基础,单调,逻辑L上。然后,我们调查插值和Beth可定定结果从L到DL转移时的问题。此调查需要适当的插值概念和默认逻辑的可防定能力。我们展示了正面和消极的一般结果:取决于DL如何定义和涉及的插值/ Beth可定定性的类型,可能或可能不会从L转移到DL。

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