论文标题
线性空间中的基本逻辑
Elementary Logic in Linear Space
论文作者
论文摘要
一阶逻辑通常以基本量化的设置中的扣除研究表示。在本文中，我们提到了另一个有利的观点，并将一阶逻辑概念化为编码“合理性”的线性空间。而演绎的视角强调了（即过程）的方式，而空间视角则强调在哪里（即位置）。我们探讨了几种后果，即对“太空信号”的转变对一阶逻辑的转变，包括（1）基于正交分解的证明概念，（2）一种将概率分配给句子分配概率的方法，以反映逻辑不确定性的句子，以及（3）作为“边界”模型，将其与理论的模型相关联。
First-order logic is typically presented as the study of deduction in a setting with elementary quantification. In this paper, we take another vantage point and conceptualize first-order logic as a linear space that encodes "plausibility". Whereas a deductive perspective emphasizes how (i.e., process), a space perspective emphasizes where (i.e., location). We explore several consequences that a shift in perspective to "signals in space" has for first-order logic, including (1) a notion of proof based on orthogonal decomposition, (2) a method for assigning probabilities to sentences that reflects logical uncertainty, and (3) a "models as boundary" principle that relates the models of a theory to its "size".
