Extensions and Applications of Probabilistic Logic Programming

By Damiano Azzolini,
Dipartimento di Ingegneria, Università di Ferrara
February 2022


Symbolic Artificial Intelligence has been considered “Good Old-Fashioned Artificial Intelligence” since it usually represents knowledge through explicit symbols, such as first-order logic predicates and constants, instead of through large numeric matrices, as happens for sub-symbolic solutions, namely, neural networks. Despite the recent predominance of neural networks, considered almost a silver bullet for solving every machine learning problem, there is still an ever-growing field of research called Statistical Relational Artificial Intelligence, where the goal is to combine logic and uncertainty to represent and reason over complex domains. Among all the several possible formalisms, Probabilistic Logic Programming (PLP) is gaining traction thanks to its ability to integrate logical and probabilistic reasoning.

The work presented in this dissertation is structured in two parts. In the first, we present several extensions of PLP to widen the possible application scenarios. In particular, we review hybrid probabilistic logic programs, where continuous and discrete random variables coexist, and provide a new well-defined semantics. After this, we introduce probabilistic abductive logic programs, where we extend PLP with the possibility to reason with incomplete data, and probabilistic optimizable and reducible logic programs, where we leverage constraint programming to learn the parameters and the structure of probabilistic logic programs subject to constraints. The definition of these new classes is motivated by real-world examples discussed in the correspondent chapters. For all of these proposals, we formally introduce the task to solve and provide practical inference algorithms.

The second part is focused on the adoption of PLP and hybrid probabilistic logic programs to model several blockchain-related scenarios. We discuss models to analyse transaction fees, smart contracts, double spending, and the Lightning Network.