 Intuitively, an event in the past is relevant to our making predictions if taking the past event into account makes a difference to our predictions, or more specifically if it lowers or raises the probability for a future event. In other words, \(p(A^t \mid B_{1}^{t_1}) - p(A^t)\) is a measure of the relevance of \(B^{t_1}\) to predicting \(A^t : B^{t_1}\) is positively relevant if the \(p(A^t \mid B_{1}^{t_1}) - p(A^t) \gt 0\), negatively relevant if \(p(A^t \mid B_{1}^{t_1}) - p(A^t) \lt 0\), and irrelevant if \(p(A^t \mid B_{1}^{t_1}) - p(A^t) = 0\). For technical reasons it turns out to be easier to work with a slightly different but equivalent notion of relevance, which is obtained from the above by multiplying both sides of the equation by \(p(B^{t_1})\). Therefore we adopt the following definition. The relevance of \(B^{t_1}\) for \(A^t\) is