Neuro-symbolic Models for Logic

Context of the Research
Machine learning has exploded in popularity and success in recent years, as it has proved to be a powerful tool for approximating functions in many different
domains. Neural networks, in particular, are robust against noisy data, can learn insightful relationships, and scale well to working with massive amounts
of data. On the other hand, symbolic artificial intelligence has built-in explainability, can perform systematic generalisation, lends itself well to structured data, and makes it easy to incorporate expert knowledge. These are all properties which neural networks typically lack.
If these two paradigms could be combined, it would unlock the benefits provided by both approaches, as they have complementary strengths and weaknesses. Furthermore, the research communities of these sub-fields of artificial intelligence are largely disconnected from each other, and there are mutual insights which can be gained from one another.
Aims and Objectives
My research aims can be broadly summarised as trying to bring together the fields of symbolic and neural artificial intelligence: such models are commonly
referred to as neuro-symbolic models. I am particularly aiming to create neuro-symbolic models for logic, instead of other kinds of structures (such as graphs).
The main application area that I will focus on is knowledge base completion: trying to predict missing facts or entries in existing knowledge bases. With that
in mind, here is a brief list of some of the main objectives of my research:
Create neuro-symbolic models which faithfully capture the semantics of the underlying logic, thus utilizing good structural inductive biases.
Make existing techniques for neuro-symbolic logic more robust and interpretable by equating their operations to operations in symbolic logic.
Use my created neuro-symbolic models to perform knowledge base completion, creation, and curation on real-world knowledge bases.
Novelty of the Research Method
While there are existing works on neuro-symbolic logic, they still fail to compete well with purely neural approaches in terms of performance and scalability, and
fail to compete with purely symbolic approaches in terms of robustness and explainability.
Through my work, I hope to overcome these limitations by better incorporating the structural inductive biases of logic into my models, thus yielding
better explainability and performance simultaneously.
Alignment to EPSRC Research Area
This project falls within the EPSRC Artificial Intelligence Technologies research area.
Companies and Collaborators Involved
The research will be performed at and through the University of Oxford, in the Computer Science department. I will be supervised by Ian Horrocks and am
aiming to collaborate with Bernardo Cuenca Grau and David Tena Cucala.