Deep Probabilistic Logics

Introduction

Neurosymbolic AI (NeSy) is the 3rd wave in AI. It wants to answer the key open question in AI: how to combine learning (2nd wave) and reasoning (1st wave) by integrating logic-based AI with deep learning. However, there is only little understanding of the underlying principles, and there exist no widely used machine learning tools that support NeSy. This makes the development of learning and reasoning systems extremely hard.

Need for a Paradigm Shift

What is urgently needed is a paradigm shift in NeSy that focuses on foundations rather than on which system from the ‘alphabet-soup’ scores best on the latest benchmarks.

Proposed Development of Foundations

I propose to develop these foundations by identifying key building blocks and demonstrating that they support the integration of knowledge and reasoning into any neural network learning task. My methodology is based on the slogan that I have coined:

NeuroSymbolic AI = Neural + Probabilistic + Logical AI

This advocates that we need to integrate the two main paradigms for reasoning (logic and probability) with that for learning (neural networks).

Exploiting Similarities

I will exploit many similarities I have identified between statistical relational AI, which focuses on probabilistic logics, and NeSy. More specifically, I shall develop the foundations of NeSy.

Conceptual Level

At the conceptual level, I shall identify the building blocks of NeSy by designing primitives that integrate logical, probabilistic, and neural network representations.

Semantic Level

At the semantic level, I shall introduce the notion of NeSy networks (that encompass logic circuits, algebraic operators, and neural networks) as a semantic framework for NeSy.

Computational Level

At the computational level, I will show how to exploit NeSy networks for inference and learning.

DEEPLOG Framework

DEEPLOG is not 'yet another NeSy system', but rather a fundamental and operational framework in which a wide variety of NeSy systems and applications can be cast and implemented.

Open-Source Software Environment

We will develop an open-source software environment and evaluate DEEPLOG’s generality and applicability.