论文标题
在抽象的F系统上。用于涉及虚假谓词及其应用于论证框架的悖论的图形理论模型
On abstract F-systems. A graph-theoretic model for paradoxes involving a falsity predicate and its application to argumentation frameworks
论文作者
论文摘要
F-Systems是挖掘物，可以建模句子来鉴定其他句子的虚假性。可以使用该工具来分析骗子和Yablo之类的悖论，以查找图理论模式。在本文中，我们介绍了F-Systems模型从表达代表句子的所有功能的所有功能中抽象。所假定的只是句子的存在和二进制关系'...肯定了……的虚假性。还考虑了非指出句子的可能存在。为了模拟所有可以共同估值为真实句子的集合的集合，我们介绍了企业集团的概念，其存在保证了缺乏悖论。集团还可以表征参考矛盾，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错误的句子。提供了Kripke的样式固定点的固定点特征，并提供完整的固定点（这意味着每个句子被视为真或错误），并且一致（这意味着没有句子被视为真和错误）与企业集团通信。此外，论证框架是F系统的特殊情况。我们展示了当地集团与可读的论点之间的关系，并争论该概念对论证理论的有用性。
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.
