清晰哥德尔模态逻辑的公理化
Axiomatization of crisp Godel modal logic
摘要：
本文研究了由具有清晰可达性的Kripke模型产生的同时具有Box和Diamond的模态逻辑，其命题取值于标准Godel代数[0，1]G上.本文从正模态逻辑出发，利用Dunn公理，对[3]中的公理系统进行了扩充，得到了一个关于可达性的公理系统，并证明了它在语义上是强完备的.对最常见的框架限制也给出了公理化。我们还证明了在所研究的逻辑中不可能得到Box作为Diamond的缩写，反之亦然，这表明我们所提出的公理系统实际上与文献中任意一个被公理化的单峰片段都不一致。
英文摘要：
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.
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。
