Liu et al. (2009) use the product of inside and outside probabilities as the fractional count of a phrase pair. Liu et al. (2009) define that inside probability indicates the probability that at least one word in source phrase is aligned to a word in target phrase, and outside probability indicates the chance that no words in one phrase are aligned to a word outside the other phrase. The fractional count is calculated: where α(·) and β(·) denote the inside and outside probabilities respectively, which can be calculated as Here in(·) denotes the inside area, which includes elements that fall inside the phrase pair, while out(·) denotes the outside area including elements that fall outside the phrase pair while fall in the same row or the same column.