Empirical Probabilities in Monadic Deductive Databases

TL;DR

This paper introduces a model-theoretic framework and algorithms for incorporating empirical probabilities into monadic logic databases, enabling statistical reasoning within deductive database systems.

Contribution

It provides the first formal semantics and algorithms for integrating empirical probabilities into monadic logic databases, bridging logic programming and statistical data.

Findings

Developed a model-theoretic characterization for probabilistic logic databases.

Designed a correct algorithm for consistency checking of probabilistic databases.

Created a sound and complete query processing procedure for these databases.

Abstract

We address the problem of supporting empirical probabilities in monadic logic databases. Though the semantics of multivalued logic programs has been studied extensively, the treatment of probabilities as results of statistical findings has not been studied in logic programming/deductive databases. We develop a model-theoretic characterization of logic databases that facilitates such a treatment. We present an algorithm for checking consistency of such databases and prove its total correctness. We develop a sound and complete query processing procedure for handling queries to such databases.