Weighted knowledge bases for description logics with typicality under a "concept-wise'' multi-preferential semantics provide a logical interpretation of MultiLayer Perceptrons. In this context, Answer Set Programming (ASP) has been shown to be suitable for addressing defeasible reasoning in the finitely many-valued case, providing a $\Pi^p_2$ upper bound on the complexity of the problem, nonetheless leaving unknown the exact complexity and only providing a proof-of-concept implementation. This paper fulfils the lack by providing a $P^{NP[log]}$-completeness result and new ASP encodings that deal with weighted knowledge bases with large search spaces.

翻译：摘要：在“逐概念”多优先语义下，基于典型性的描述逻辑加权知识库为多层感知器提供了逻辑解释。在此背景下，回答集编程已被证明适用于有限多值情形下的可废止推理，为该问题提供了$\Pi^p_2$上界，但精确复杂性仍属未知，且仅实现了概念验证性系统。本文通过给出$P^{NP[log]}$-完备性结果以及处理大规模搜索空间加权知识库的新的ASP编码，填补了这一空白。