In logic programming, negation can be interpreted in various ways. Probably best known is the concept of "negation as failure", where "$\mathit{not}\, p$" is true if we have no evidence for $p$. On the other hand, strong negation requires that we have evidence for $p$ being false. Defining semantics for logic programs containing both kinds of negation is a challenging task, and this becomes even more challenging when combining this with other extensions of logic programming, e.g. fuzziness. In this work, we use the framework of approximating fixpoint theory to formulate well-behaved semantics for fuzzy logic programs containing both "by-failure" and strong negation. We show that this framework generalizes several existing semantics as well as giving rise to a host of new semantics.

翻译：在逻辑程序中，否定可以以多种方式解释。最广为人知的可能是“失败即否定”概念，其中“$\mathit{not}\, p$”在缺乏$p$的证据时为真。另一方面，强否定要求我们有$p$为假的证据。为同时包含这两种否定的逻辑程序定义语义是一项具有挑战性的任务，当将其与逻辑程序的其他扩展（例如模糊性）结合时，这一挑战更加严峻。本文利用近似不动点理论框架，为同时包含“失败即否定”和强否定的模糊逻辑程序构建了性质良好的语义。我们证明，该框架不仅推广了若干现有语义，还催生了一系列新语义。