Neural Probabilistic Logic Programming in Discrete-Continuous Domains

Lennert De Smet, Pedro Zuidberg Dos Martires, Robin Manhaeve, Giuseppe Marra, Angelika Kimmig, Luc De Raedt

Keywords: neural-symbolic AI, logic, probability, neural networks, probabilistic logic programming, neuro-symbolic integration, learning and reasoning

TL;DR: DeepSeaProbLog: a neural probabilistic logic programming language with discrete and continuous random variables.

Abstract: Neural-symbolic AI (NeSy) methods allow neural networks to exploit symbolic background knowledge. NeSy has been shown to aid learning in the limited data regime and to facilitate inference on out-of-distribution data. Neural probabilistic logic programming (NPLP) is a popular NeSy approach that integrates probabilistic models with neural networks and logic programming. A major limitation of current NPLP systems, such as DeepProbLog, is their restriction to discrete and finite probability distributions, e.g., binary random variables. To overcome this limitation, we introduce DeepSeaProbLog, an NPLP language that supports discrete and continuous random variables on (possibly) infinite and even uncountable domains. Our main contributions are 1) the introduction of DeepSeaProbLog and its semantics, 2) an implementation of DeepSeaProbLog that supports inference and gradient-based learning, and 3) an experimental evaluation of our approach.

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