抽象F系统包含虚假谓词悖论的图论模型及其在论证框架中的应用
On abstract F-systems. A graph-theoretic model for paradoxes involving a falsity predicate and its application to argumentation frameworks
摘要：
F-系统是一种有向图，它能够对断言其他句子的虚假性的句子进行建模。像Liar和Yablo这样的Parases可以用这个工具来分析，以找到图论模式。在本文中，我们提出了F-系统模型抽象的所有功能的语言中表示的句子。所有这一切都是假设存在的句子和二元关系'.证实了...的虚假性”其中。非指称句的可能存在也被认为是。为了对所有可以共同被认为是真的句子的集合进行建模，我们引入了聚合的概念，它的存在保证了悖论的存在。聚合也能够表征指称矛盾，即由于与模型中其他句子的相互作用，在经典估值下只能是假的句子。一个克里普克的风格固定点表征的复杂性提供和不动点是完整的（意味着每个句子被认为是真或假）和一致的（意味着没有句子被认为是真和假）放在对应的企业集团。此外，论证框架是F-系统的特殊情况。我们展示了当地企业集团和容许的参数集之间的关系，并认为论证理论的概念的有用性。
英文摘要：
F-systems are digraphs that enable to model sentences that predicate the falsity of other sentences. Paradoxes like the Liar and Yablo's can be analyzed with that tool to find graph-theoretic patterns. In this paper we present the F-systems model abstracting from all the features of the language in which the represented sentences are expressed. All that is assumed is the existence of sentences and the binary relation '... affirms the falsity of ...' among them. The possible existence of non-referential sentences is also considered. To model the sets of all the sentences that can jointly be valued as true we introduce the notion of conglomerate, the existence of which guarantees the absence of paradox. Conglomerates also enable to characterize referential contradictions, i.e. sentences that can only be false under a classical valuation due to the interactions with other sentences in the model. A Kripke's style fixed point characterization of groundedness is offered and fixed points which are complete (meaning that every sentence is deemed either true or false) and consistent (meaning that no sentence is deemed true and false) are put in correspondence with conglomerates. Furthermore, argumentation frameworks are special cases of F-systems. We show the relation between local conglomerates and admissible sets of arguments and argue about the usefulness of the concept for argumentation theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
