不一致性演算I：句子逻辑
A Calculus of Inconsistency I: Sentential Logic
摘要：
我们描述了一个图论语法的自指公式以及四值逻辑，包括矛盾和独立的公式。然后，我们探讨在我们的理论中广义真假值表可以实现的程度，并继续描述微积分的模型论，其中允许模型包括矛盾（如“说谎者”）和公式，这些公式作为其结构的一个组成部分。这为我们构建包含矛盾的集合论模型的续集奠定了基础。
英文摘要：
We describe a graph-theoretic syntax for self-referential formulas as well as a four-valued logic to include contradictory and independent formulas. We then explore the degree to which generalized truth tables can be realized in our theory, and go on to describe a model theory for sentential calculus, wherein models are allowed to include contradictions (such as the ``Liar'') and formulas that result from them as an integral part of their structure. This sets the groundwork for a sequel in which we construct models of set theory that include contradictions.
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。
