Neuro-Symbolic AI (NeSy) holds promise to ensure the safe deployment of AI systems, as interpretable symbolic techniques provide formal behaviour guarantees. The challenge is how to effectively integrate neural and symbolic computation, to enable learning and reasoning from raw data. Existing pipelines that train the neural and symbolic components sequentially require extensive labelling, whereas end-to-end approaches are limited in terms of scalability, due to the combinatorial explosion in the symbol grounding problem. In this paper, we leverage the implicit knowledge within foundation models to enhance the performance in NeSy tasks, whilst reducing the amount of data labelling and manual engineering. We introduce a new architecture, called NeSyGPT, which fine-tunes a vision-language foundation model to extract symbolic features from raw data, before learning a highly expressive answer set program to solve a downstream task. Our comprehensive evaluation demonstrates that NeSyGPT has superior accuracy over various baselines, and can scale to complex NeSy tasks. Finally, we highlight the effective use of a large language model to generate the programmatic interface between the neural and symbolic components, significantly reducing the amount of manual engineering required.

Argumentation is a very active research field of Artificial Intelligence concerned with the representation and evaluation of arguments used in dialogues between humans and/or artificial agents. Acceptability semantics of formal argumentation systems define the criteria for the acceptance or rejection of arguments. Several software systems, known as argumentation solvers, have been developed to compute the accepted/rejected arguments using such criteria. These include systems that learn to identify the accepted arguments using non-interpretable methods. In this paper we present a novel framework, which uses an Inductive Logic Programming approach to learn the acceptability semantics for several abstract and structured argumentation frameworks in an interpretable way. Through an empirical evaluation we show that our framework outperforms existing argumentation solvers, thus opening up new future research directions in the area of formal argumentation and human-machine dialogues.

One of the ultimate goals of Artificial Intelligence is to assist humans in complex decision making. A promising direction for achieving this goal is Neuro-Symbolic AI, which aims to combine the interpretability of symbolic techniques with the ability of deep learning to learn from raw data. However, most current approaches require manually engineered symbolic knowledge, and where end-to-end training is considered, such approaches are either restricted to learning definite programs, or are restricted to training binary neural networks. In this paper, we introduce Neuro-Symbolic Inductive Learner (NSIL), an approach that trains a general neural network to extract latent concepts from raw data, whilst learning symbolic knowledge that maps latent concepts to target labels. The novelty of our approach is a method for biasing the learning of symbolic knowledge, based on the in-training performance of both neural and symbolic components. We evaluate NSIL on three problem domains of different complexity, including an NP-complete problem. Our results demonstrate that NSIL learns expressive knowledge, solves computationally complex problems, and achieves state-of-the-art performance in terms of accuracy and data efficiency. Code and technical appendix: https://github.com/DanCunnington/NSIL

Hierarchical reinforcement learning (HRL; Barto & Mahadevan, 2003) frameworks, such as options (Sutton et al., Reward machines (RMs) are a recent formalism 1999), have been used to exploit RMs by learning policies for representing the reward function of a reinforcement at two levels of abstraction: (i) select a formula (i.e., subgoal) learning task through a finite-state machine from a given RM state, and (ii) select an action to whose edges encode subgoals of the task using (eventually) satisfy the chosen formula (Toro Icarte et al., high-level events. The structure of RMs enables 2018; Furelos-Blanco et al., 2021). The subtask decomposition the decomposition of a task into simpler and independently powered by HRL enables learning at multiple scales solvable subtasks that help tackle longhorizon simultaneously, and eases the handling of long-horizon and and/or sparse reward tasks. We propose sparse reward tasks. In addition, several works have considered a formalism for further abstracting the subtask the problem of learning the RMs themselves from structure by endowing an RM with the ability to interaction (e.g., Toro Icarte et al., 2019; Xu et al., 2020; call other RMs, thus composing a hierarchy of Furelos-Blanco et al., 2021; Hasanbeig et al., 2021).

Logic-based machine learning [1, 2] learns interpretable knowledge expressed in the form of a logic program, called a hypothesis, that explains labelled examples in the context of (optional) background knowledge. Recent logic-based machine learning systems have demonstrated the ability to learn highly complex and noise-tolerant hypotheses in a data efficient manner (e.g., Learning from Answer Sets (LAS) [2]). However, they require labelled examples to be specified in a structured logical form, which limits their applicability to many real-world problems. On the other hand, differentiable learning systems, such as (deep) neural networks, are able to learn directly from unstructured data, but they require large amounts of training data and their learned models are difficult to interpret [3]. Within neural-symbolic artificial intelligence, many approaches aim to integrate neural and symbolic systems with the goal of preserving the benefits of both paradigms [4, 5]. Most neural-symbolic integrations assume the existence of pre-defined knowledge expressed symbolically, or logically, and focus on training a neural network to extract symbolic features from raw unstructured data [6-10]. In this paper, we introduce Feed-Forward Neural-Symbolic Learner (FFNSL), a neural-symbolic learning framework that assumes the opposite. Given a pre-trained neural network, FFNSL uses a logic-based machine learning system robust to noise to learn a logic-based hypothesis whose symbolic features are constructed from neural network predictions.

The goal of Inductive Logic Programming (ILP) is to learn a program that explains a set of examples. Until recently, most research on ILP targeted learning Prolog programs. The ILASP system instead learns Answer Set Programs (ASP). Learning such expressive programs widens the applicability of ILP considerably; for example, enabling preference learning, learning common-sense knowledge, including defaults and exceptions, and learning non-deterministic theories. Early versions of ILASP can be considered meta-level ILP approaches, which encode a learning task as a logic program and delegate the search to an ASP solver. More recently, ILASP has shifted towards a new method, inspired by conflict-driven SAT and ASP solvers. The fundamental idea of the approach, called Conflict-driven ILP (CDILP), is to iteratively interleave the search for a hypothesis with the generation of constraints which explain why the current hypothesis does not cover a particular example. These coverage constraints allow ILASP to rule out not just the current hypothesis, but an entire class of hypotheses that do not satisfy the coverage constraint. This paper formalises the CDILP approach and presents the ILASP3 and ILASP4 systems for CDILP, which are demonstrated to be more scalable than previous ILASP systems, particularly in the presence of noise.

Inductive Logic Programming (ILP) systems learn generalised, interpretable rules in a data-efficient manner utilising existing background knowledge. However, current ILP systems require training examples to be specified in a structured logical format. Neural networks learn from unstructured data, although their learned models may be difficult to interpret and are vulnerable to data perturbations at run-time. This paper introduces a hybrid neural-symbolic learning framework, called NSL, that learns interpretable rules from labelled unstructured data. NSL combines pre-trained neural networks for feature extraction with FastLAS, a state-of-the-art ILP system for rule learning under the answer set semantics. Features extracted by the neural components define the structured context of labelled examples and the confidence of the neural predictions determines the level of noise of the examples. Using the scoring function of FastLAS, NSL searches for short, interpretable rules that generalise over such noisy examples. We evaluate our framework on propositional and first-order classification tasks using the MNIST dataset as raw data. Specifically, we demonstrate that NSL is able to learn robust rules from perturbed MNIST data and achieve comparable or superior accuracy when compared to neural network and random forest baselines whilst being more general and interpretable.

In this paper we present ISA, an approach for learning and exploiting subgoals in episodic reinforcement learning (RL) tasks. ISA interleaves reinforcement learning with the induction of a subgoal automaton, an automaton whose edges are labeled by the task's subgoals expressed as propositional logic formulas over a set of high-level events. A subgoal automaton also consists of two special states: a state indicating the successful completion of the task, and a state indicating that the task has finished without succeeding. A state-of-the-art inductive logic programming system is used to learn a subgoal automaton that covers the traces of high-level events observed by the RL agent. When the currently exploited automaton does not correctly recognize a trace, the automaton learner induces a new automaton that covers that trace. The interleaving process guarantees the induction of automata with the minimum number of states, and applies a symmetry breaking mechanism to shrink the search space whilst remaining complete. We evaluate ISA in several grid-world and continuous state space problems using different RL algorithms that leverage the automaton structures. We provide an in-depth empirical analysis of the automaton learning process performance in terms of the traces, the symmetric breaking and specific restrictions imposed on the final learnable automaton. For each class of RL problem, we show that the learned automata can be successfully exploited to learn policies that reach the goal, achieving an average reward comparable to the case where automata are not learned but handcrafted and given beforehand.

The goal of Inductive Logic Programming (ILP) is to learn a program that explains a set of examples in the context of some pre-existing background knowledge. Until recently, most research on ILP targeted learning Prolog programs. Our own ILASP system instead learns Answer Set Programs, including normal rules, choice rules and hard and weak constraints. Learning such expressive programs widens the applicability of ILP considerably; for example, enabling preference learning, learning common-sense knowledge, including defaults and exceptions, and learning non-deterministic theories. In this paper, we first give a general overview of ILASP's learning framework and its capabilities. This is followed by a comprehensive summary of the evolution of the ILASP system, presenting the strengths and weaknesses of each version, with a particular emphasis on scalability.

Our method relies on inducing an automaton whose transitions are subgoals expressed as propositional formulas over a set of observable events. A state-of-the-art inductive logic programming system is used to learn the automaton from observation traces perceived by the RL agent. The reinforcement learning and automaton learning processes are interleaved: a new refined automaton is learned whenever the RL agent generates a trace not recognized by the current automaton. We evaluate ISA in several gridworld problems and show that it performs similarly to a method for which automata are given in advance. We also show that the learned automata can be exploited to speed up convergence through reward shaping and transfer learning across multiple tasks. Finally, we analyze the running time and the number of traces that ISA needs to learn an automata, and the impact that the number of observable events has on the learner's performance.