向量逻辑允许通过NOT的平方根进行反事实虚拟化
Vector logic allows counterfactual virtualization by The Square Root of NOT
摘要：
在这项工作中，我们调查的表示使用向量逻辑，矩阵向量形式主义的逻辑函数和真值的反事实条件。在这种形式主义中，反事实可以被转换成复矩阵，用NOT的平方根之一（复矩阵）预处理蕴涵矩阵。这种数学方法证明了反事实的虚拟性。这是因为这种表示产生了一个反事实的估值，即由两个复共轭系数分别加权的两个相反真值的叠加。这一结果表明，该过程给出了一个不确定的评估投射在复杂的域。在这个基本表征之后，对给定反事实的可接受性的判断允许我们将决定转向接受或拒绝。这个移位是第二次应用NOT的两个平方根之一的结果。
英文摘要：
In this work we investigate the representation of counterfactual conditionals using the vector logic, a matrix-vectors formalism for logical functions and truth values. Inside this formalism, the counterfactuals can be transformed in complex matrices preprocessing an implication matrix with one of the square roots of NOT, a complex matrix. This mathematical approach puts in evidence the virtual character of the counterfactuals. This happens because this representation produces a valuation of a counterfactual that is the superposition of the two opposite truth values weighted, respectively, by two complex conjugated coefficients. This result shows that this procedure gives an uncertain evaluation projected on the complex domain. After this basic representation, the judgment of the plausibility of a given counterfactual allows us to shift the decision towards an acceptance or a refusal. This shift is the result of applying for a second time one of the two square roots of NOT.
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