论文标题
Kripke-Feferman真相的模态逻辑
The Modal Logics of Kripke-Feferman Truth
论文作者
论文摘要
我们通过Solomon Feferman通过Solovay式的完整性结果来确定真实点模型及其公理的模态逻辑。给定定点模型$ \ MATHCAL {m} $或其套件$ s $，我们发现模态逻辑$ m $ $，使得Modal句子$φ$是$ m $的一个理论，并且仅当句子$φ^*$通过$ \ mathcal $ \ s的$ slypripations trimal pranther trime trime trime trime trime trime trime trime trime of trimh pransion $ \ mathcal s}或s m} a} a} m} m} {m} {m} {m}。为此，我们介绍了一种可能的世界语义的新颖版本，具有古典世界和非经典世界，并建立了一个非统一模态逻辑家族的完整性，其内部逻辑在这种语义方面是次级分类的。
We determine the modal logic of fixed-point models of truth and their axiomatizations by Solomon Feferman via Solovay-style completeness results. Given a fixed-point model $\mathcal{M}$, or an axiomatization $S$ thereof, we find a modal logic $M$ such that a modal sentence $φ$ is a theorem of $M$ if and only if the sentence $φ^*$ obtained by translating the modal operator with the truth predicate is true in $\mathcal{M}$ or a theorem of $S$ under all such translations. To this end, we introduce a novel version of possible worlds semantics featuring both classical and nonclassical worlds and establish the completeness of a family of non-congruent modal logics whose internal logic is subclassical with respect to this semantics.
