To aggregate useful information among diversified sources, a hotspot research topic called truth discovery has emerged in recent years. Existing truth discovery methods attempt to infer the true attribute values for the entities by identifying and trusting reliable data sources. However, all these methods neglect the relations among different entities, which play important roles in truth discovery task. When reliable data sources cannot provide sufficient information of entities, the true attribute values of these entities can still be inferred by propagating trustworthy information from related entities. Motivated by this, in this paper, we introduce the constrained truth discovery problem. We incorporate denial constraints, a universally quantified first-order logic formalism, into the process of truth discovery. We formulate it as a constrained optimization problem and analyze its hardness. To address the problem, we propose algorithms to partition the entities into disjoint groups, and generate arithmetic constraints for each disjoint group separately. Then, the true attribute values of the entities in each disjoint group are derived by minimizing the objective function under the corresponding arithmetic constraints. Experimental results on both real-world and synthetic datasets demonstrate that the proposed approach achieves good performance even with very few constraints and reliable sources.

In the era of Big Data, integrating information from multiple sources has proven valuable in various fields. To ensure a high-quality supply of multi-source data, repairing different types of errors in the multi-source data becomes critical. This paper categorizes errors in multi-source data into entity information overlapping, attribute value conflicts, and attribute value inconsistencies. We first summarize existing repairing methods for these errors and then examine and review the study of the detection and repair of compound-type errors in multi-source data. Finally, we indicate further research directions in multi-source data repair.