论文标题
自我侵略和$σ_1$句子
Self Provers and $Σ_1$ Sentences
论文作者
论文摘要
该论文是2012年的第二篇论文中的第二篇。这三篇论文涉及可解释性逻辑和相关事项。在第一篇论文中，构造方法暴露在获取这些逻辑的模型中。使用这种方法，我们获得了一些完整的结果，有些已经知道，有些是新的。 在本文中，我们将设定施工方法以获得更多结果。首先，使用构造方法证明了逻辑$ {\ textbf {il}}} $的模态完整性。这不是一个新的结果，但是通过使用我们的新证明，我们可以获得新的结果。在这些新结果中，有一些$ {\ textbf {il}}（{\ sf m}）$和$ {\ textbf {gl}} $的可接受规则。 此外，新的证明将用于对所有本质上的$Δ_1$进行分类，以及所有本质上的$σ_1$公式的$ {\ textbf {il}}}（{\ sf m}）$。与$σ_1$句子紧密相关的是所谓的\ emph {self provers}。一个自我提示是一种公式$φ$，这意味着其自身的可预订性，即$φ\ to \boxφ$。每个公式$φ$都会生成一个自供他人$φ\ wedge \boxφ$。我们将使用构造方法来表征$ {\ textbf {gl}} $的句子，从而生成一个自事者，从某种意义上说，它是$σ_1$。
This paper from 2012 is the second in a series of three papers. All three papers deal with interpretability logics and related matters. In the first paper a construction method was exposed to obtain models of these logics. Using this method, we obtained some completeness results, some already known, and some new. In this paper, we will set the construction method to work to obtain more results. First, the modal completeness of the logic ${\textbf{IL}}({\sf M})$ is proved using the construction method. This is not a new result, but by using our new proof we can obtain new results. Among these new results are some admissible rules for ${\textbf{IL}}({\sf M})$ and ${\textbf{GL}}$. Moreover, the new proof will be used to classify all the essentially $Δ_1$ and also all the essentially $Σ_1$ formulas of ${\textbf{IL}}({\sf M})$. Closely related to essentially $Σ_1$ sentences are the so-called \emph{self provers}. A self-prover is a formula $φ$ which implies its own provability, that is $φ\to \Box φ$. Each formula $φ$ will generate a self prover $φ\wedge \Box φ$. We will use the construction method to characterize those sentences of ${\textbf{GL}}$ that generate a self prover that is trivial in the sense that it is $Σ_1$.
