Martin Grohe ; Peter Lindner - Infinite Probabilistic Databases

lmcs:6945 - Logical Methods in Computer Science, February 25, 2022, Volume 18, Issue 1 - https://doi.org/10.46298/lmcs-18(1:34)2022
Infinite Probabilistic Databases

Authors: Martin Grohe ; Peter Lindner

    Probabilistic databases (PDBs) model uncertainty in data in a quantitative way. In the established formal framework, probabilistic (relational) databases are finite probability spaces over relational database instances. This finiteness can clash with intuitive query behavior (Ceylan et al., KR 2016), and with application scenarios that are better modeled by continuous probability distributions (Dalvi et al., CACM 2009). We formally introduced infinite PDBs in (Grohe and Lindner, PODS 2019) with a primary focus on countably infinite spaces. 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. We argue that finite point processes are an appropriate model from probability theory for dealing with general probabilistic databases. This 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.


    Volume: Volume 18, Issue 1
    Published on: February 25, 2022
    Accepted on: November 24, 2021
    Submitted on: December 1, 2020
    Keywords: Computer Science - Databases

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