Parameterised Complexity of Consistent Query Answering via Graph Representations Hankala, Teemu Hannula, Miika Mahmood, Yasir Meier, Arne 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. 2024 info:eu-repo/semantics/preprint doc-type:preprint text http://purl.org/coar/resource_type/c_816b https://ris.uni-paderborn.de/record/57814 Hankala T, Hannula M, Mahmood Y, Meier A. Parameterised Complexity of Consistent Query Answering via Graph  Representations. <i>arXiv:241208324</i>. Published online 2024. eng info:eu-repo/semantics/altIdentifier/arxiv/2412.08324 info:eu-repo/semantics/closedAccess