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Matching natural language sentences is central for many applications such as information retrieval and question answering. Existing deep models rely on a single sentence representation or multiple granularity representations for matching. However, such methods cannot well capture the contextualized local information in the matching process. To tackle this problem, we present a new deep architecture to match two sentences with multiple positional sentence representations. Specifically, each positional sentence representation is a sentence representation at this position, generated by a bidirectional long short term memory (Bi-LSTM). The matching score is finally produced by aggregating interactions between these different positional sentence representations, through k-Max pooling and a multi-layer perceptron. Our model has several advantages: (1) By using Bi-LSTM, rich context of the whole sentence is leveraged to capture the contextualized local information in each positional sentence representation; (2) By matching with multiple positional sentence representations, it is flexible to aggregate different important contextualized local information in a sentence to support the matching; (3) Experiments on different tasks such as question answering and sentence completion demonstrate the superiority of our model.