Generative Datalog with Stable Negation

TL;DR

This paper extends generative Datalog, a probabilistic logic programming language, with stable negation to enhance expressiveness while ensuring a robust probabilistic semantics.

Contribution

It introduces a novel approach to incorporate stable negation into generative Datalog, providing a well-defined probabilistic semantics for the extended language.

Findings

Defined a probabilistic semantics for generative Datalog with stable negation

Demonstrated the increased expressiveness of the extended language

Ensured robustness of the probabilistic interpretation with negation

Abstract

Extending programming languages with stochastic behaviour such as probabilistic choices or random sampling has a long tradition in computer science. A recent development in this direction is a declarative probabilistic programming language, proposed by Barany et al. in 2017, which operates on standard relational databases. In particular, Barany et al. proposed generative Datalog, a probabilistic extension of Datalog that allows sampling from discrete probability distributions. Intuitively, the output of a generative Datalog program P on an input database D is a probability space over the minimal models of D and P, the so-called possible outcomes. This is a natural generalization of the (deterministic) semantics of Datalog, where the output of a program on a database is their unique minimal model. A natural question to ask is how generative Datalog can be enriched with the useful feature of negation, which in turn leads to a strictly more expressive declarative probabilistic programming language. In particular, the challenging question is how the probabilistic semantics of generative Datalog with negation can be robustly defined. Our goal is to provide an answer to this question by interpreting negation according to the stable model semantics.