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Founded (Auto)Epistemic Equilibrium Logic Satisfies Epistemic Splitting

机译：建立（自动）认知平衡逻辑，满足认知分裂

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摘要

In a recent line of research, two familiar concepts from logic programming semantics (unfounded sets and splitting) were extrapolated to the case of epistemic logic programs. The property of epistemic splitting provides a natural and modular way to understand programs without epistemic cycles but, surprisingly, was only fulfilled by Gelfond's original semantics (G91), among the many proposals in the literature. On the other hand, G91 may suffer from a kind of self-supported, unfounded derivations when epistemic cycles come into play. Recently, the absence of these derivations was also formalised as a property of epistemic semantics called foundedness. Moreover, a first semantics proved to satisfy foundedness was also proposed, the so-called Founded Autoepistemic Equilibrium Logic (FAEEL). In this paper, we prove that FAEEL also satisfies the epistemic splitting property something that, together with foundedness, was not fulfilled by any other approach up to date. To prove this result, we provide an alternative characterisation of FAEEL as a combination of G91 with a simpler logic we called Founded Epistemic Equilibrium Logic (FEEL), which is somehow an extrapolation of the stable model semantics to the modal logic S5.
机译：在最近的研究中，将逻辑编程语义学中的两个熟悉的概念（无根据的集合和拆分）外推到认知逻辑程序的情况。认知分裂的性质提供了一种自然且模块化的方式来理解程序，而无需认知循环，但令人惊讶的是，在文献中的许多建议中，只有盖芬德的原始语义学（G91）才能实现。另一方面，当认知周期开始起作用时，G91可能会遭受一种自立，无根据的推论。最近，这些衍生词的缺失也被正式化为认知语义学的一种特性，称为基础性。此外，还提出了证明满足基础性的第一种语义，即所谓的“建立的自动表观平衡逻辑”（FAEEL）。在本文中，我们证明了FAEEL还满足了认知分裂属性，而这与基础性一起，是迄今为止任何其他方法都无法实现的。为了证明这一结果，我们提供了FAEEL的另一种特征，即将G91与称为Founded Epistemic均衡逻辑（FEEL）的更简单逻辑相结合，这是将稳定的模型语义外推到模态逻辑S5的结果。

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