We study the complexity of answer counting for ontology-mediated queries and for querying under constraints, considering conjunctive queries and unions thereof (UCQs) as the query language and guarded TGDs as the ontology and constraint language, respectively. Our main result is a classification according to whether answer counting is fixed-parameter tractable (FPT), W[1]-equivalent, #W[1]-equivalent, #W[2]-hard, or #A[2]-equivalent, lifting a recent classification for UCQs without ontologies and constraints due to Dell et al. The classification pertains to various structural measures, namely treewidth, contract treewidth, starsize, and linked matching number. Our results rest on the assumption that the arity of relation symbols is bounded by a constant and, in the case of ontology-mediated querying, that all symbols from the ontology and query can occur in the data (so-called full data schema). We also study the meta-problems for the mentioned structural measures, that is, to decide whether a given ontology-mediated query or constraint-query specification is equivalent to one for which the structural measure is bounded.

中文翻译：

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受保护的TGD下的答案计数

我们研究了联合介导的查询和约束下查询的应答计数的复杂性，分别将联合查询及其联合（UCQs）作为查询语言，将受保护的TGD作为本体和约束语言。我们的主要结果是根据答案计数是固定参数易处理（FPT），W [1]等效，＃W [1]等效，＃W [2] -hard还是#A [2]-分类等效，取消了由于戴尔等人而没有本体和约束的UCQ的最新分类。该分类涉及各种结构度量，即树宽，合同树宽，星号和链接的匹配数。我们的结果基于这样的假设：关系符号的有限性受一个常数限制，并且在本体介导的查询的情况下，本体和查询中的所有符号都可以出现在数据中（所谓的完整数据模式）。我们还研究了上述结构度量的元问题，即决定给定的本体介导查询或约束查询规范是否等同于结构度量受其约束的规范。