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Despite the emergence of probabilistic logic programming (PLP) languages for data driven applications, there are currently no debugging tools based on provenance for PLP programs. In this paper, we propose a novel provenance model and system, called P3 (Provenance for Probabilistic logic Programs) for analyzing PLP programs. P3 enables four types of provenance queries: traditional explanation queries, queries for finding the set of most important derivations within an approximate error, top-K most influential queries, and modification queries that enable us to modify tuple probabilities with fewest modifications to program or input data. We apply these queries into real-world scenarios and present theoretical analysis and practical algorithms for such queries. We have developed a prototype of P3, and our evaluation on real-world data demonstrates that the system can support a wide-range of provenance queries with explainable results. Moreover, the system maintains provenance and execute queries efficiently with low overhead.