Abstract Epistemic specifications extend disjunctive answer-set programs by an epistemic modal operator that may occur in the body of rules. Their semantics is in terms of world views, which are sets of answer sets, and the idea is that the epistemic modal operator quantifies over these answer sets. Several such semantics were proposed in the literature. We here propose a new semantics that is based on the logic of here-and-there: we add epistemic modal operators to its language and define epistemic here-and-there models. We then successively define epistemic equilibrium models and autoepistemic equilibrium models. The former are obtained from epistemic here-and-there models in exactly the same way as Pearce's equilibrium models are obtained from here-and-there models, viz. by minimising truth; they provide an epistemic extension of equilibrium logic. The latter are obtained from the former by maximising the set of epistemic possibilities, and they provide a new semantics for Gelfond's epistemic specifications. For both semantics we establish a strong equivalence result: we characterise strong equivalence of two epistemic programs by means of logical equivalence in epistemic here-and-there logic. We finally compare our approach to the existing semantics of epistemic specifications and discuss which formalisms provide more intuitive results by pointing out some formal properties a semantics proposal should satisfy.

中文翻译：

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自认知均衡逻辑和认知规范

摘要 认知规范通过可能出现在规则体中的认知模态算子扩展析取答案集程序。它们的语义是根据世界观，即答案集的集合，其思想是认知模态运算符对这些答案集进行量化。文献中提出了几个这样的语义。我们在这里提出了一种基于此处和那里逻辑的新语义：我们将认知模态运算符添加到其语言中并定义认知的此处和那里模型。然后我们依次定义了认知均衡模型和自认知均衡模型。前者是从认知的 here-and-there 模型中获得的，与 Pearce 的均衡模型是从 here-and-there 模型中获得的方式完全相同，即。通过最小化真相；它们提供了均衡逻辑的认知扩展。后者是通过最大化认知可能性集而从前者获得的，它们为 Gelfond 的认知规范提供了新的语义。对于这两种语义，我们都建立了强等价结果：我们通过认知 here-and-the 逻辑中的逻辑等价来刻画两个认知程序的强等价性。我们最终将我们的方法与认知规范的现有语义进行比较，并通过指出语义建议应该满足的一些形式属性来讨论哪些形式主义提供更直观的结果。对于这两种语义，我们都建立了强等价结果：我们通过认知 here-and-the 逻辑中的逻辑等价来刻画两个认知程序的强等价性。我们最终将我们的方法与认知规范的现有语义进行比较，并通过指出语义建议应该满足的一些形式属性来讨论哪些形式主义提供更直观的结果。对于这两种语义，我们都建立了强等价结果：我们通过认知 here-and-the 逻辑中的逻辑等价来刻画两个认知程序的强等价性。我们最终将我们的方法与认知规范的现有语义进行比较，并通过指出语义建议应该满足的一些形式属性来讨论哪些形式主义提供更直观的结果。