论文标题
酥脆的Godel模态逻辑的公理化
Axiomatization of crisp Godel modal logic
论文作者
论文摘要
在本文中，我们考虑了具有清晰可访问性的盒子和钻石的模态逻辑，其命题在Stan-Dard Godel代数[0,1] g上被重视。我们提供了一个公理系统，该系统从[3]中扩展了一个带有元模态逻辑的dunn Axiom的模型，并且展示了相对于预期的语义的强烈完成。也给出了最常见的框架限制的公理。我们还证明，在所研究的日志中不可能将盒子作为钻石的缩写，也不是反之亦然，这表明，确实我们所提出的公理系统并不与文献中任何单模式片段相吻合。
In this paper we consider the modal logic with both Box and Diamond arising fromKripke models with a crisp accessibility and whose propositions are valued over the stan-dard Godel algebra [0,1]G. We provide an axiomatic system extending the one from [3]for models with a valued accessibility with Dunn axiom from positive modal logics, andshow it is strongly complete with respect to the intended semantics. The axiomatizationsof the most usual frame restrictions are given too. We also prove that in the studied logicit is not possible to get Box as an abbreviation of Diamond, nor vice-versa, showing that indeedthe axiomatic system we present does not coincide with any ofthe mono-modal fragmentspreviously axiomatized in the literature.
