Qualitative Choice Logic (QCL) and Conjunctive Choice Logic (CCL) are formalisms for preference handling, with especially QCL being well established in the field of AI. So far, analyses of these logics need to be done on a case-by-case basis, albeit they share several common features. This calls for a more general choice logic framework, with QCL and CCL as well as some of their derivatives being particular instantiations. We provide such a framework, which allows us, on the one hand, to easily define new choice logics and, on the other hand, to examine properties of different choice logics in a uniform setting. In particular, we investigate strong equivalence, a core concept in non-classical logics for understanding formula simplification, and computational complexity. Our analysis also yields new results for QCL and CCL. For example, we show that the main reasoning task regarding preferred models is $\Theta^p_2$-complete for QCL and CCL, while being $\Delta^p_2$-complete for a newly introduced choice logic.

翻译：定性选择逻辑(QCL)和组合选择逻辑(CCCL)是处理优惠的正规形式,特别是AI领域已经完全建立了QCL。到目前为止,对这些逻辑的分析需要逐案分析,尽管这些逻辑具有一些共同特征。这要求更一般性的选择逻辑框架,而QCL和CCL及其衍生物的某些衍生物是特殊的即时反应。我们提供了这样一个框架,一方面让我们能够轻松地界定新的选择逻辑,另一方面在统一的环境下审查不同选择逻辑的特性。特别是,我们调查强等等等值,这是非经典逻辑中理解公式简化和计算复杂性的核心概念。我们的分析也为QCL和CCL带来新的结果。例如,我们表明,关于首选模型的主要推理任务为 $\ Theta ⁇ p_2美元,对于QCL和CCL来说是完整的,而对于新引入的选择逻辑则是$\Delta_p_2美元。