文章基本信息

标题：Infinite Probabilistic Databases
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作者：Martin Grohe ; Peter Lindner
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：155
页码：16:1-16:20
DOI：10.4230/LIPIcs.ICDT.2020.16
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：Probabilistic databases (PDBs) are used to model uncertainty in data in a quantitative way. In the standard formal framework, PDBs are finite probability spaces over relational database instances. It has been argued convincingly that this is not compatible with an open-world semantics (Ceylan et al., KR 2016) and with application scenarios that are modeled by continuous probability distributions (Dalvi et al., CACM 2009). We recently introduced a model of PDBs as infinite probability spaces that addresses these issues (Grohe and Lindner, PODS 2019). While that work was mainly concerned with countably infinite probability spaces, our focus here is on uncountable spaces. Such an extension is necessary to model typical continuous probability distributions that appear in many applications. However, an extension beyond countable probability spaces raises nontrivial foundational issues concerned with the measurability of events and queries and ultimately with the question whether queries have a well-defined semantics. It turns out that so-called finite point processes are the appropriate model from probability theory for dealing with probabilistic databases. This model allows us to construct suitable (uncountable) probability spaces of database instances in a systematic way. Our main technical results are measurability statements for relational algebra queries as well as aggregate queries and Datalog queries.
关键词：Probabilistic Databases; Possible Worlds Semantics; Query Measurability; Relational Algebra; Aggregate Queries