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Advances in information extraction have enabled the automatic construction of large knowledge graphs (e.g., Yago, Wikidata or Google KG), which are widely used in many applications like semantic search or data analytics. However, due to their semi-automatic construction, KGs are often incomplete. Rule learning methods, concerned with the extraction of frequent patterns from KGs and casting them into rules, can be applied to predict potentially missing facts. A crucial step in this process is rule ranking. Ranking of rules is especially challenging over highly incomplete or biased KGs (e.g., KGs predominantly storing facts about famous people), as in this case biased rules might fit the data best and be ranked at the top based on standard statistical metrics like rule confidence. To address this issue, prior works proposed to rank rules not only relying on the original KG but also facts predicted by a KG embedding model. At the same time, with the recent rise of Language Models (LMs), several works have claimed that LMs can be used as alternative means for KG completion. In this work, our goal is to verify to which extent the exploitation of LMs is helpful for improving the quality of rule learning systems., Comment: proof of concept

This paper presents PROB-IRM, an approach that learns robust reward machines (RMs) for reinforcement learning (RL) agents from noisy execution traces. The key aspect of RM-driven RL is the exploitation of a finite-state machine that decomposes the agent's task into different subtasks. PROB-IRM uses a state-of-the-art inductive logic programming framework robust to noisy examples to learn RMs from noisy traces using the Bayesian posterior degree of beliefs, thus ensuring robustness against inconsistencies. Pivotal for the results is the interleaving between RM learning and policy learning: a new RM is learned whenever the RL agent generates a trace that is believed not to be accepted by the current RM. To speed up the training of the RL agent, PROB-IRM employs a probabilistic formulation of reward shaping that uses the posterior Bayesian beliefs derived from the traces. Our experimental analysis shows that PROB-IRM can learn (potentially imperfect) RMs from noisy traces and exploit them to train an RL agent to solve its tasks successfully. Despite the complexity of learning the RM from noisy traces, agents trained with PROB-IRM perform comparably to agents provided with handcrafted RMs., Comment: Preprint accepted for publication to the 21st International Conference on Principles of Knowledge Representation and Reasoning (KR 2024)

A popular method for modelling reactive systems is to use $\omega$-regular languages. These languages can be represented as nondeterministic B\"uchi automata (NBAs) or $\omega$-regular expressions. Existing methods synthesise expressions from state-based NBAs. Synthesis from transition-based NBAs is traditionally done by transforming transition-based NBAs into state-based NBAs. This transformation, however, can increase the complexity of the synthesised expressions. This paper proposes a novel method for directly synthesising $\omega$-regular expressions from transition-based NBAs. We prove that the method is sound and complete. Our empirical results show that the $\omega$-regular expressions synthesised from transition-based NBAs are more compact than those synthesised from state-based NBAs. This is particularly the case for NBAs computed from obligation, reactivity, safety and recurrence-type LTL formulas, reporting in the latter case an average reduction of over 50%. We also show that our method successfully synthesises $\omega$-regular expressions from more LTL formulas when using a transition-based instead of a state-based NBA.

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., Comment: Pre-print

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.

Symbolic rule learners generate interpretable solutions, however they require the input to be encoded symbolically. Neuro-symbolic approaches overcome this issue by mapping raw data to latent symbolic concepts using a neural network. Training the neural and symbolic components jointly is difficult, due to slow and unstable learning, hence many existing systems rely on hand-engineered rules to train the network. We introduce NeuralFastLAS, a scalable and fast end-to-end approach that trains a neural network jointly with a symbolic learner. For a given task, NeuralFastLAS computes a relevant set of rules, proved to contain an optimal symbolic solution, trains a neural network using these rules, and finally finds an optimal symbolic solution to the task while taking network predictions into account. A key novelty of our approach is learning a posterior distribution on rules while training the neural network to improve stability during training. We provide theoretical results for a sufficient condition on network training to guarantee correctness of the final solution. Experimental results demonstrate that NeuralFastLAS is able to achieve state-of-the-art accuracy in arithmetic and logical tasks, with a training time that is up to two orders of magnitude faster than other jointly trained neuro-symbolic methods., Comment: Pre-print, work in progress

This volume contains the Technical Communications presented at the 39th International Conference on Logic Programming (ICLP 2023), held at Imperial College London, UK from July 9 to July 15, 2023. Technical Communications included here concern the Main Track, the Doctoral Consortium, the Application and Systems/Demo track, the Recently Published Research Track, the Birds-of-a-Feather track, the Thematic Tracks on Logic Programming and Machine Learning, and Logic Programming and Explainability, Ethics, and Trustworthiness.

In this work, following the intuition that adverbs describing scene-sequences are best identified by reasoning over high-level concepts of object-behavior, we propose the design of a new framework that reasons over object-behaviours extracted from raw-video-clips to recognize the clip's corresponding adverb-types. Importantly, while previous works for general scene adverb-recognition assume knowledge of the clips underlying action-types, our method is directly applicable in the more general problem setting where the action-type of a video-clip is unknown. Specifically, we propose a novel pipeline that extracts human-interpretable object-behaviour-facts from raw video clips and propose novel symbolic and transformer based reasoning methods that operate over these extracted facts to identify adverb-types. Experiment results demonstrate that our proposed methods perform favourably against the previous state-of-the-art. Additionally, to support efforts in symbolic video-processing, we release two new datasets of object-behaviour-facts extracted from raw video clips - the MSR-VTT-ASP and ActivityNet-ASP datasets.

Clinical decision-making is a fundamental stage in delivering appropriate care to patients. In recent years several decision-making systems designed to aid the clinician in this process have been developed. However, technical solutions currently in use are based on simple regression models and are only able to take into account simple pre-defined multiple-choice features, such as patient age, pre-existing conditions, smoker status, etc. One particular source of patient data, that available decision-making systems are incapable of processing is the collection of patient consultation GP notes. These contain crucial signs and symptoms - the information used by clinicians in order to make a final decision and direct the patient to the appropriate care. Extracting information from GP notes is a technically challenging problem, as they tend to include abbreviations, typos, and incomplete sentences. This paper addresses this open challenge. We present a framework that performs knowledge graph construction from raw GP medical notes written during or after patient consultations. By relying on support phrases mined from the SNOMED ontology, as well as predefined supported facts from values used in the RECAP (REmote COVID-19 Assessment in Primary Care) patient risk prediction tool, our graph generative framework is able to extract structured knowledge graphs from the highly unstructured and inconsistent format that consultation notes are written in. Our knowledge graphs include information about existing patient symptoms, their duration, and their severity. We apply our framework to consultation notes of COVID-19 patients in the UK COVID-19 Clinical Assesment Servcie (CCAS) patient dataset. We provide a quantitative evaluation of the performance of our framework, demonstrating that our approach has better accuracy than traditional NLP methods when answering questions about patients.

Large pre-trained language models such as BERT have been widely used as a framework for natural language understanding (NLU) tasks. However, recent findings have revealed that pre-trained language models are insensitive to word order. The performance on NLU tasks remains unchanged even after randomly permuting the word of a sentence, where crucial syntactic information is destroyed. To help preserve the importance of word order, we propose a simple approach called Forced Invalidation (FI): forcing the model to identify permuted sequences as invalid samples. We perform an extensive evaluation of our approach on various English NLU and QA based tasks over BERT-based and attention-based models over word embeddings. Our experiments demonstrate that Forced Invalidation significantly improves the sensitivity of the models to word order., Comment: EACL 2023

Neuro-symbolic rule learning has attracted lots of attention as it offers better interpretability than pure neural models and scales better than symbolic rule learning. A recent approach named pix2rule proposes a neural Disjunctive Normal Form (neural DNF) module to learn symbolic rules with feed-forward layers. Although proved to be effective in synthetic binary classification, pix2rule has not been applied to more challenging tasks such as multi-label and multi-class classifications over real-world data. In this paper, we address this limitation by extending the neural DNF module to (i) support rule learning in real-world multi-class and multi-label classification tasks, (ii) enforce the symbolic property of mutual exclusivity (i.e. predicting exactly one class) in multi-class classification, and (iii) explore its scalability over large inputs and outputs. We train a vanilla neural DNF model similar to pix2rule's neural DNF module for multi-label classification, and we propose a novel extended model called neural DNF-EO (Exactly One) which enforces mutual exclusivity in multi-class classification. We evaluate the classification performance, scalability and interpretability of our neural DNF-based models, and compare them against pure neural models and a state-of-the-art symbolic rule learner named FastLAS. We demonstrate that our neural DNF-based models perform similarly to neural networks, but provide better interpretability by enabling the extraction of logical rules. Our models also scale well when the rule search space grows in size, in contrast to FastLAS, which fails to learn in multi-class classification tasks with 200 classes and in all multi-label settings., Comment: Accepted at AAAI-MAKE 2023

This paper presents a novel approach to Multi-Agent Reinforcement Learning (MARL) that combines cooperative task decomposition with the learning of reward machines (RMs) encoding the structure of the sub-tasks. The proposed method helps deal with the non-Markovian nature of the rewards in partially observable environments and improves the interpretability of the learnt policies required to complete the cooperative task. The RMs associated with each sub-task are learnt in a decentralised manner and then used to guide the behaviour of each agent. By doing so, the complexity of a cooperative multi-agent problem is reduced, allowing for more effective learning. The results suggest that our approach is a promising direction for future research in MARL, especially in complex environments with large state spaces and multiple agents., Comment: Neuro-symbolic AI for Agent and Multi-Agent Systems Workshop at AAMAS'23

We investigate the composability of soft-rules learned by relational neural architectures when operating over object-centric (slot-based) representations, under a variety of sparsity-inducing constraints. We find that increasing sparsity, especially on features, improves the performance of some models and leads to simpler relations. Additionally, we observe that object-centric representations can be detrimental when not all objects are fully captured; a failure mode to which CNNs are less prone. These findings demonstrate the trade-offs between interpretability and performance, even for models designed to tackle relational tasks., Comment: ICML 2022, DyNN Workshop

Recent efforts in interpretable deep learning models have shown that concept-based explanation methods achieve competitive accuracy with standard end-to-end models and enable reasoning and intervention about extracted high-level visual concepts from images, e.g., identifying the wing color and beak length for bird-species classification. However, these concept bottleneck models rely on a necessary and sufficient set of predefined concepts-which is intractable for complex tasks such as video classification. For complex tasks, the labels and the relationship between visual elements span many frames, e.g., identifying a bird flying or catching prey-necessitating concepts with various levels of abstraction. To this end, we present CoDEx, an automatic Concept Discovery and Extraction module that rigorously composes a necessary and sufficient set of concept abstractions for concept-based video classification. CoDEx identifies a rich set of complex concept abstractions from natural language explanations of videos-obviating the need to predefine the amorphous set of concepts. To demonstrate our method's viability, we construct two new public datasets that combine existing complex video classification datasets with short, crowd-sourced natural language explanations for their labels. Our method elicits inherent complex concept abstractions in natural language to generalize concept-bottleneck methods to complex tasks., Comment: 10 pages, Appendix: 2 pages

Reward machines (RMs) are a recent formalism for representing the reward function of a reinforcement learning task through a finite-state machine whose edges encode subgoals of the task using high-level events. The structure of RMs enables the decomposition of a task into simpler and independently solvable subtasks that help tackle long-horizon and/or sparse reward tasks. We propose a formalism for further abstracting the subtask structure by endowing an RM with the ability to call other RMs, thus composing a hierarchy of RMs (HRM). We exploit HRMs by treating each call to an RM as an independently solvable subtask using the options framework, and describe a curriculum-based method to learn HRMs from traces observed by the agent. Our experiments reveal that exploiting a handcrafted HRM leads to faster convergence than with a flat HRM, and that learning an HRM is feasible in cases where its equivalent flat representation is not., Comment: Preprint accepted for publication to the 40th International Conference on Machine Learning (ICML-23)

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, Comment: Accepted to IJCAI 2023

Numerical reasoning based machine reading comprehension is a task that involves reading comprehension along with using arithmetic operations such as addition, subtraction, sorting, and counting. The DROP benchmark (Dua et al., 2019) is a recent dataset that has inspired the design of NLP models aimed at solving this task. The current standings of these models in the DROP leaderboard, over standard metrics, suggest that the models have achieved near-human performance. However, does this mean that these models have learned to reason? In this paper, we present a controlled study on some of the top-performing model architectures for the task of numerical reasoning. Our observations suggest that the standard metrics are incapable of measuring progress towards such tasks., Comment: to appear at EMNLP 2021

Logic-based machine learning aims to learn general, interpretable knowledge in a data-efficient manner. However, labelled data must be specified in a structured logical form. To address this limitation, we propose a neural-symbolic learning framework, called Feed-Forward Neural-Symbolic Learner (FFNSL), that integrates a logic-based machine learning system capable of learning from noisy examples, with neural networks, in order to learn interpretable knowledge from labelled unstructured data. We demonstrate the generality of FFNSL on four neural-symbolic classification problems, where different pre-trained neural network models and logic-based machine learning systems are integrated to learn interpretable knowledge from sequences of images. We evaluate the robustness of our framework by using images subject to distributional shifts, for which the pre-trained neural networks may predict incorrectly and with high confidence. We analyse the impact that these shifts have on the accuracy of the learned knowledge and run-time performance, comparing FFNSL to tree-based and pure neural approaches. Our experimental results show that FFNSL outperforms the baselines by learning more accurate and interpretable knowledge with fewer examples., Comment: Pre-print, work in progress

Humans have the ability to seamlessly combine low-level visual input with high-level symbolic reasoning often in the form of recognising objects, learning relations between them and applying rules. Neuro-symbolic systems aim to bring a unifying approach to connectionist and logic-based principles for visual processing and abstract reasoning respectively. This paper presents a complete neuro-symbolic method for processing images into objects, learning relations and logical rules in an end-to-end fashion. The main contribution is a differentiable layer in a deep learning architecture from which symbolic relations and rules can be extracted by pruning and thresholding. We evaluate our model using two datasets: subgraph isomorphism task for symbolic rule learning and an image classification domain with compound relations for learning objects, relations and rules. We demonstrate that our model scales beyond state-of-the-art symbolic learners and outperforms deep relational neural network architectures., Comment: IJCLR-NeSy, 41 pages. Minor correction to Lukasiewicz logic

The Credal semantics is a probabilistic extension of the answer set semantics which can be applied to programs that may or may not be stratified. It assigns to atoms a set of acceptable probability distributions characterised by its lower and upper bounds. Performing exact probabilistic inference in the Credal semantics is computationally intractable. This paper presents a first solver, based on sampling, for probabilistic inference under the Credal semantics called PASOCS (Parallel Approximate SOlver for the Credal Semantics). PASOCS performs both exact and approximate inference for queries given evidence. Approximate solutions can be generated using any of the following sampling methods: naive sampling, Metropolis-Hastings and Gibbs Markov Chain Monte-Carlo. We evaluate the fidelity and performance of our system when applied to both stratified and non-stratified programs. We perform a sanity check by comparing PASOCS to available systems for stratified programs, where the semantics agree, and show that our system is competitive on unstratified programs.

Reasoning about information from multiple parts of a passage to derive an answer is an open challenge for reading-comprehension models. In this paper, we present an approach that reasons about complex questions by decomposing them to simpler subquestions that can take advantage of single-span extraction reading-comprehension models, and derives the final answer according to instructions in a predefined reasoning template. We focus on subtraction-based arithmetic questions and evaluate our approach on a subset of the DROP dataset. We show that our approach is competitive with the state-of-the-art while being interpretable and requires little supervision, Comment: Published at EACL 2021 SRW

The task of Video Question Answering (VideoQA) consists in answering natural language questions about a video and serves as a proxy to evaluate the performance of a model in scene sequence understanding. Most methods designed for VideoQA up-to-date are end-to-end deep learning architectures which struggle at complex temporal and causal reasoning and provide limited transparency in reasoning steps. We present the HySTER: a Hybrid Spatio-Temporal Event Reasoner to reason over physical events in videos. Our model leverages the strength of deep learning methods to extract information from video frames with the reasoning capabilities and explainability of symbolic artificial intelligence in an answer set programming framework. We define a method based on general temporal, causal and physics rules which can be transferred across tasks. We apply our model to the CLEVRER dataset and demonstrate state-of-the-art results in question answering accuracy. This work sets the foundations for the incorporation of inductive logic programming in the field of VideoQA., Comment: Preprint accepted by the 35th AAAI Conference on Artificial Intelligence (AAAI-21) Workshop on Hybrid Artificial Intelligence (HAI)

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., Comment: This article has been replaced with arXiv:2106.13103

We propose a new model for relational VAE semi-supervision capable of balancing disentanglement and low complexity modelling of relations with different symbolic properties. We compare the relative benefits of relation-decoder complexity and latent space structure on both inductive and transductive transfer learning. Our results depict a complex picture where enforcing structure on semi-supervised representations can greatly improve zero-shot transductive transfer, but may be less favourable or even impact negatively the capacity for inductive transfer.