Open-world query answering is the problem of deciding, given a set of facts, conjunction of constraints, and query, whether the facts and constraints imply the query. This amounts to reasoning over all instances that include the facts and satisfy the constraints. We study finite open-world query answering (FQA), which assumes that the underlying world is finite and thus only considers the finite completions of the instance. The major known decidable cases of FQA derive from the following: the guarded fragment of first-order logic, which can express referential constraints (data in one place points to data in another) but cannot express number restrictions such as functional dependencies; and the guarded fragment with number restrictions but on a signature of arity only two. In this article, we give the first decidability results for FQA that combine both referential constraints and number restrictions for arbitrary signatures: We show that, for unary inclusion dependencies and functional dependencies, the finiteness assumption of FQA can be lifted up to taking the finite implication closure of the dependencies. Our result relies on new techniques to construct finite universal models of such constraints for any bound on the maximal query size.

中文翻译：

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具有数量限制的有限开放世界查询回答

开放世界查询回答是在给定一组事实、约束的结合和查询的情况下确定事实和约束是否暗示查询的问题。这相当于对包含事实并满足约束的所有实例进行推理。我们学习有限开放世界查询回答（FQA），它假设底层世界是有限的，因此只考虑有限实例的完成。FQA 的主要已知可判定案例来源于以下几点： 一阶逻辑的保护片段，它可以表达引用约束（一个地方的数据指向另一个地方的数据），但不能表达函数依赖等数量限制；和带有数量限制但只有两个签名的受保护片段。在本文中，我们给出了 FQA 的第一个可判定性结果，它结合了任意签名的引用约束和数量限制：我们表明，对于一元包含依赖和函数依赖，FQA 的有限性假设可以提升为采用有限蕴涵关闭依赖项。