We study consistent query answering via different graph representations. First, we introduce solution-conflict hypergraphs in which nodes represent facts and edges represent either conflicts or query solutions. Considering a monotonic query and a set of antimonotonic constraints, we present an explicit algorithm for counting the number of repairs satisfying the query based on a tree decomposition of the solution-conflict hypergraph. The algorithm not only provides fixed-parameter tractability results for data complexity over expressive query and constraint classes, but also introduces a novel and potentially implementable approach to repair counting. Second, we consider the Gaifman graphs arising from MSO descriptions of consistent query answering. Using a generalization of Courcelle's theorem, we then present fixed-parameter tractability results for combined complexity over expressive query and constraint classes.

翻译：本研究通过不同图表示方法探讨相容查询应答问题。首先，我们提出解-冲突超图结构，其中节点表示事实，边表示冲突或查询解。针对单调查询与反单调约束集，基于解-冲突超图的树分解，我们提出显式算法以计算满足查询的修复数量。该算法不仅为表达性查询与约束类的数据复杂度提供了固定参数可解性结果，同时提出了一种新颖且具备潜在可实施性的修复计数方法。其次，我们考察由相容查询应答的MSO描述所产生的盖夫曼图。通过推广库塞勒定理，我们进一步为表达性查询与约束类的组合复杂度提供了固定参数可解性结果。