## 1 Introduction  
Data have become an important asset, and how to explore the value of personal data has become a hot topic. The term \"personal data\" refers to personal privacy data generated in the daily life or work of individuals, and individuals have ownership of the data [1]. With the further development of the mobile Internet, personal data as a valuable asset are growing exponentially [2]. A much effort has been made to define computing and resource-based pricing models [3]. [PERSON] et al. [4] presented a user-centered model in which individuals can collect, manage, use, and share their own data to discover their potential value. Personal data have different values for different objects. For example, personal data have different values for data owners and data analysis institutions. In [5], an effective method was designed to explore this competitive benefit distribution. [PERSON] et al. [6] turned individuals into providers and co-creators of data services and products in the economy. However, only recently, [PERSON] et al. [7] studied some major pricing models of current data trading services and found that buyers can only purchase data through volume or predefined views. In the study of pricing models, arbitrage-free is an important economic attribute, but many pricing models have arbitrage phenomenon. Here, arbitrage refers to the strategy adopted for the purchase of data for greater benefits. For instance, it is more expensive to issue a single query than to issue several and combine their results. Because of the current data trading market, there is little transparency between buyers and sellers, resulting in uncertainty about how data are collected, how they are handled before sales, and how they are used after sales. This may be the competitive strategy of some institutions, but it preventsthe healthy development of the data market and creates information asymmetry. Therefore, it is necessary to trace the source tuples that produce the query results, and data provenance is a good solution to this problem. In [8], a data provenance trust model was proposed to evaluate the reliability of data and data providers according to various factors affecting the reliability. [PERSON] et al. [9] constructed a heterogeneous data source provenance model based on the origin and evolution of data sources. [PERSON] et al. [10] believed data provenance can be used to track query results, audit cloud computing data, and interpret big data analysis output. In this paper, a pricing model with a tuple granularity is devised. The model leverages and extends the concept of data provenance, that is a set of source tuples that contributes to query results. When designing a personal data pricing model based on data provenance, there will be three difficulties. The first major difficulty is how can source tuples that contribute to query results be compensated reasonably. Furthermore, personal data have different values for data owners and data analysis institutions. The second difficulty concerns designing a robust personal data pricing mechanism. The current personal data pricing mechanism is very simple, that is buyers can only choose explicit views, and each view has a specific price. Buyers can only purchase data through data volume or predefined views. The complex arbitrage behavior brings great challenges to the design of the pricing model. The third difficulty is how to calculate the exact price of the query in an acceptable time. Personal data can be viewed as an information commodity with significant original investment costs, but the marginal cost of copying is negligible. As a result, value-based pricing models may be more suitable for personal data transactions. The main contributions of this paper are as follows. * A more rigorous personal data provenance model than the existing ones (e.g., [11; 12; 13]) is devised. In this model, even if a source tuple contributes to a query result multiple times, it is paid only once. A new provenance for a set of source tuples rather than a single source tuple is proposed.