Inspired by Hintikka's treatment of question embedding verbs in [8] and thevariations of noncontingency operator, we propose a logic with strongnoncontingency operator $lacktriangle$ as the only primitive modality. Aproposition is strongly noncontingent, if no matter whether it is true orfalse, it does it necessarily; otherwise, it is weakly contingent. This logicis not a normal modal logic, since$lacktriangle(phiopsi)o(lacktrianglephiolacktrianglepsi)$ isinvalid. We compare the relative expressivity of this logic and other logics,such as standard modal logic, noncontingency logic, and logic of essence andaccident, and investigate its frame definability. Apart from these results, wealso propose a suitable notion of bisimulation for the logic of strongnoncontingency, based on which we characterize this logic within modal logicand within first-order logic. We also axiomatize the logic of strongnoncontingency over various frame classes. Our work is also related to thetreatment of agreement operator in [10].
展开▼
机译：通过辛提卡的处理问题[8]中嵌入动词和noncontingency运营商的thevariations的启发，我们提出用strongnoncontingency操作$ $ blacktriangle作为唯一的原始形式逻辑。 4月份是强烈的，如果无论是真正的orfalse，它都是如此;否则，它是弱偶然的。这个逻辑不是一个正常的模态逻辑，自$ 黑色riangle（ phi to psi） to（ blacktriangle phi to blacktriangle psi）$ IsInvalid。我们比较此逻辑和其他逻辑的相对表征性，例如标准模态逻辑，非强制逻辑和精华逻辑和逻辑，并调查其框架可定定性。除了这些结果之外，Wealso提出了对强度逻辑的逻辑的合适概念，基于该逻辑，基于该逻辑，基于该逻辑，我们在一阶逻辑中在模态逻辑中表征了这种逻辑。我们还在各种框架类上公开了强度强调的逻辑。我们的工作也与[10]中的协议运营商进行了关系。
展开▼
