Kripke-Feferman真理的模态逻辑
The Modal Logics of Kripke-Feferman Truth
摘要：
我们通过Solovay式完备性结果确定了Solomon Feferman的不动点真值模型的模态逻辑及其公理化。给定一个不动点模型$\mathcal{M}$或其公理化$S$，我们找到一个模态逻辑$M$，使得模态语句$φ$是$M$的一个定理当且仅当通过用真值谓词翻译模态算子得到的语句$φ^*$在$\mathcal{M}$中为真，或在所有这样的翻译下都是$S$的一个定理。为此，我们引入了一个新版本的可能世界的语义，具有经典和非经典的世界，并建立了一个家庭的非全等模态逻辑，其内部逻辑是亚经典的这种语义的完整性。
英文摘要：
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.
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。
