Deep Probabilistic Logics

Neurosymbolic AI (NeSy) is the 3rd wave in AI.

It wants to answer the key open question in AI as 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.

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.I propose to develop these foundations by identifying key building blocks and demonstrate 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 AIThis advocates that we need to integrate the two main paradigms for reasoning (logic and probability), with that for learning (neural networks).

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.

At the conceptual level, I shall identify the building blocks of NeSy by designing primitives that integrate logical, probabilistic and neural networks representations; 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; at the computational level, I will show how to exploit NeSy networks for inference and learning.

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