论文标题
paracensistentGödel模态逻辑
Paraconsistent Gödel modal logic
论文作者
论文摘要
我们介绍了一个〜paraconsistent模态逻辑$ \ mathbf {k} \ Mathsf {g}^2 $，基于Gödel逻辑与CoImplication（Bi-Gödel逻辑），并随着de Morgan negation $ \ neg $ neg $的扩展。我们使用逻辑来通过分级，不完整和不一致的信息形式化推理。 $ \ Mathbf {K} \ Mathsf {G}^2 $的语义是二维的：我们解释了$ \ m arterbf {k} \ Mathsf {g}^2 $在清晰的框架上，带有两个值$ v_1 $和$ v_2 $，通过$ \ neg $ negal $ contect $ neach $ contect $ v_1 $和$ v_2 $ neach $ neack $ neact $ neact $ neact $ neact $ [0]第一个（分别，第二个）估值编码国家给出的正面信息（分别，负面）信息。我们获得了$ \ MathBf {K} \ Mathsf {G}^2 $严格表现得比经典的模态逻辑$ \ Mathbf {K K} $通过证明有限分支的框架是可以定义的，并且通过确定忠实的分支框架，并确定$ \ alsbf {k} $ a {k} $ \ nath $ \ mathbf {g {我们还为$ \ mathbf {k} \ mathsf {g}^2 $在有限分支框架上构造一个〜约束图表积分，建立了其可决定性并提供了〜复杂性评估。
We introduce a~paraconsistent modal logic $\mathbf{K}\mathsf{G}^2$, based on Gödel logic with coimplication (bi-Gödel logic) expanded with a De Morgan negation $\neg$. We use the logic to formalise reasoning with graded, incomplete and inconsistent information. Semantics of $\mathbf{K}\mathsf{G}^2$ is two-dimensional: we interpret $\mathbf{K}\mathsf{G}^2$ on crisp frames with two valuations $v_1$ and $v_2$, connected via $\neg$, that assign to each formula two values from the real-valued interval $[0,1]$. The first (resp., second) valuation encodes the positive (resp., negative) information the state gives to a~statement. We obtain that $\mathbf{K}\mathsf{G}^2$ is strictly more expressive than the classical modal logic $\mathbf{K}$ by proving that finitely branching frames are definable and by establishing a faithful embedding of $\mathbf{K}$ into $\mathbf{K}\mathsf{G}^2$. We also construct a~constraint tableau calculus for $\mathbf{K}\mathsf{G}^2$ over finitely branching frames, establish its decidability and provide a~complexity evaluation.
