Abstract Inferring linear temporal logic over finite traces ($\text{LTL}_{\text{f}}$) formulas from a set of example traces, known as passive learning, presents significant challenges due to its combinatorial nature. In this paper, we introduce a novel approach to $\text{LTL}_{\text{f}}$ passive learning based on inductive logic programming (ILP), leveraging the inductive learning of answer set programs framework. Our ILP-based method effectively exploits the set of example traces to guide the learning process, and experimental results demonstrate that it o ffers a more efficient solution compared to traditional techniques based on propositional satisfiability.

The ability to efficiently solve hard combinatorial optimization problems is a key prerequisite to various applications of declarative programming paradigms. Symmetries in solution candidates pose a significant challenge to modern optimization algorithms since the enumeration of such candidates might substantially reduce their performance. This paper proposes a novel approach using Inductive Logic Programming (ILP) to lift symmetry-breaking constraints for optimization problems modeled in Answer Set Programming (ASP). Given an ASP encoding with optimization statements and a set of small representative instances, our method augments ground ASP programs with auxiliary normal rules enabling the identification of symmetries using existing tools, like SBASS. Then, the obtained symmetries are lifted to first-order constraints with ILP. We prove the correctness of our method and evaluate it on real-world optimization problems from the domain of automated configuration. Our experiments show significant improvements of optimization performance due to the learned first-order constraints.

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.

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

Abstract 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.

Abstract 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 article 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.

In the past decade, several systems for learning Answer Set Programs (ASP) have been proposed, including the recent FastLAS system. Compared to other state-of-the-art approaches to learning ASP, FastLAS is more scalable, as rather than computing the hypothesis space in full, it computes a much smaller subset relative to a given set of examples that is nonetheless guaranteed to contain an optimal solution to the task (called an OPT-sufficient subset). On the other hand, like many other Inductive Logic Programming (ILP) systems, FastLAS is designed to be run on a fixed learning task meaning that if new examples are discovered after learning, the whole process must be run again. In many real applications, data arrives in a stream. Rerunning an ILP system from scratch each time new examples arrive is inefficient. In this paper we address this problem by presenting IncrementalLAS, a system that uses a new technique, called hypothesis space expansion, to enable a FastLAS-like OPT-sufficient subset to be expanded each time new examples are discovered. We prove that this preserves FastLAS's guarantee of finding an optimal solution to the full task (including the new examples), while removing the need to repeat previous computations. Through our evaluation, we demonstrate that running IncrementalLAS on tasks updated with sequences of new examples is significantly faster than re-running FastLAS from scratch on each updated task.

Abstract Many industrial applications require finding solutions to challenging combinatorial problems. Efficient elimination of symmetric solution candidates is one of the key enablers for high-performance solving. However, existing model-based approaches for symmetry breaking are limited to problems for which a set of representative and easily solvable instances is available, which is often not the case in practical applications. This work extends the learning framework and implementation of a model-based approach for Answer Set Programming to overcome these limitations and address challenging problems, such as the Partner Units Problem. In particular, we incorporate a new conflict analysis algorithm in the Inductive Logic Programming system ILASP, redefine the learning task, and suggest a new example generation method to scale up the approach. The experiments conducted for different kinds of Partner Units Problem instances demonstrate the applicability of our approach and the computational benefits due to the first-order constraints learned.

Recently, novel ILP systems under the answer set semantics have been proposed, some of which are robust to noise and scalable over large hypothesis spaces. One such system is FastLAS, which is significantly faster than other state-of-the-art ASP-based ILP systems. FastLAS is, however, only capable of Observational Predicate Learning (OPL), where the learned hypothesis defines predicates that are directly observed in the examples. It cannot learn knowledge that is indirectly observable, such as learning causes of observed events. This class of problems, known as non-OPL, is known to be difficult to handle in the context of non-monotonic semantics. Solving non-OPL learning tasks whilst preserving scalability is a challenging open problem. We address this problem with a new abductive method for translating examples of a non-OPL task to a set of examples, called possibilities, such that the original example is covered iff at least one of the possibilities is covered. This new method allows an ILP system capable of performing OPL tasks to be "upgraded" to solve non-OPL tasks. In particular, we present our new FastNonOPL system, which upgrades FastLAS with the new possibility generation. We compare it to other state-of-the-art ASP-based ILP systems capable of solving non-OPL tasks, showing that FastNonOPL is significantly faster, and in many cases more accurate, than these other systems.

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 gridworld 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 performance in terms of the traces, the symmetry 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.

In this work we present ISA, a novel approach for learning and exploiting subgoals in reinforcement learning (RL). 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 have on the learner's performance.

Inductive Logic Programming (ILP) systems aim to find a set of logical rules, called a hypothesis, that explain a set of examples. In cases where many such hypotheses exist, ILP systems often bias towards shorter solutions, leading to highly general rules being learned. In some application domains like security and access control policies, this bias may not be desirable, as when data is sparse more specific rules that guarantee tighter security should be preferred. This paper presents a new general notion of a scoring function over hypotheses that allows a user to express domain-specific optimisation criteria. This is incorporated into a new ILP system, called FastLAS, that takes as input a learning task and a customised scoring function, and computes an optimal solution with respect to the given scoring function. We evaluate the accuracy of FastLAS over real-world datasets for access control policies and show that varying the scoring function allows a user to target domain-specific performance metrics. We also compare FastLAS to state-of-the-art ILP systems, using the standard ILP bias for shorter solutions, and demonstrate that FastLAS is significantly faster and more scalable.

Abstract General game playing (GGP) is a framework for evaluating an agent’s general intelligence across a wide range of tasks. In the GGP competition, an agent is given the rules of a game (described as a logic program) that it has never seen before. The task is for the agent to play the game, thus generating game traces. The winner of the GGP competition is the agent that gets the best total score over all the games. In this paper, we invert this task: a learner is given game traces and the task is to learn the rules that could produce the traces. This problem is central toinductive general game playing(IGGP). We introduce a technique that automatically generates IGGP tasks from GGP games. We introduce an IGGP dataset which contains traces from 50 diverse games, such asSudoku,Sokoban, andCheckers. We claim that IGGP is difficult for existing inductive logic programming (ILP) approaches. To support this claim, we evaluate existing ILP systems on our dataset. Our empirical results show that most of the games cannot be correctly learned by existing systems. The best performing system solves only 40% of the tasks perfectly. Our results suggest that IGGP poses many challenges to existing approaches. Furthermore, because we can automatically generate IGGP tasks from GGP games, our dataset will continue to grow with the GGP competition, as new games are added every year. We therefore think that the IGGP problem and dataset will be valuable for motivating and evaluating future research.

In this paper we introduce an extension of context-free grammars called answer set grammars (ASGs). These grammars allow annotations on production rules, written in the language of Answer Set Programming (ASP), which can express context-sensitive constraints. We investigate the complexity of various classes of ASG with respect to two decision problems: deciding whether a given string belongs to the language of an ASG and deciding whether the language of an ASG is non-empty. Specifically, we show that the complexity of these decision problems can be lowered by restricting the subset of the ASP language used in the annotations. To aid the applicability of these grammars to computational problems that require context-sensitive parsers for partially known languages, we propose a learning task for inducing the annotations of an ASG. We characterise the complexity of this task and present an algorithm for solving it. An evaluation of a (prototype) implementation is also discussed.

To facilitate information sharing between systems and devices in a distributed environment, unstructured data from various sensors must be analysed accordingly. Recent work has developed the notion of a context-dependant generative policy framework capable of learning generative policy models from strings and text-based data in a tabular format. However, it is vital that unstructured contextual information can be analysed alongside tabular data, potentially at the edge of the network to enable generative policy models to be applied to more complex tasks. This paper performs a deep-dive into the field of neuralsymbolic machine learning with a view towards enabling future neural-symbolic generative policy models that are capable of analysing both structured and unstructured data, whilst providing full transparency and enabling edge of network reasoning capability. Firstly, an existing technique called DeepProbLog is investigated and applied to a policy inferencing task based on unstructured data and secondly, a recent inductive logic programming technique currently used for learning generative policy models is evaluated with respect to a policy learning task also based on unstructured data. Finally, the results of both tasks are discussed to provide a platform for future research into enabling neural-symbolic generative policy models.

Policy systems are critical for managing missions and collaborative activities carried out by coalitions involving different organizations. Conventional policy-based management approaches are not suitable for next-generation coalitions that will involve not only humans, but also autonomous computing devices and systems. It is critical that those parties be able to generate and customize policies based on contexts and activities. This paper introduces a novel approach for the autonomic generation of policies by autonomous parties. The framework combines context free grammars, answer set programs, and inductionbased learning. It allows a party to generate its own policies, based on a grammar and some semantic constraints, by learning from examples. The paper also outlines initial experiments in the use of such a symbolic approach and outlines relevant research challenges, ranging from explainability to quality assessment of policies.

Generative Policy Models (GPMs) have been proposed as a method for future autonomous decision making in a distributed, collaborative environment. To learn a GPM, previous policy examples that contain policy features and the corresponding policy decisions are used. Recently, GPMs have been constructed using both symbolic and statistical learning algorithms. In either case, the goal of the learning process is to create a model across a wide range of contexts from which specific policies may be generated in a given context. Empirically, we expect each learning approach to provide certain advantages over the other. This paper assesses the relative performance of each learning approach in order to examine these advantages and disadvantages. Several carefully prepared data sets are used to train a variety of models across different learning algorithms, where models for each learning algorithm are trained with varying amounts of labelled examples. The performance of each model is evaluated across a variety of metrics which indicates the strength of each learning algorithm for the different scenarios presented and the amount of training data provided. Finally, future research directions are outlined to fully realise GPMs in a distributed, collaborative environment.

Generative policies have recently been researched to provide a method for next generation security policies. They are created using either traditional machine learning techniques or, more recently, inductive learning of answer set programs. The latter method is targeted to the learning of Answer Set Grammars (ASG), a new notion of generative policy model for security policies that has the benefit of transparent explainability of the learned outcomes. This paper proposes a military scenario based on logistical resupply from a military base to coalition forces located in a nearby urban area or city. We describe the scenario and accompanying policy such that the context of the resupply missions (and therefore the policy) changes over time. The set of policies and related changes over time have been manually defined using a set of human created rules to replicate how security policies would currently be created by humans in such scenarios. We show how inductive learning of answer set programs can successfully learn ASG generative policy models that capture the human-driven rules from just example traces and decisions made at different time points and with respect to different contextual situations that can arise during the resupply mission. These results demonstrate the utility of ASG generative policy as a method for modelling human-driven policy rules.

Traditionally most of the work in the field of Inductive Logic Programming (ILP) has addressed the problem of learning Prolog programs. On the other hand, Answer Set Programming is increasingly being used as a powerful language for knowledge representation and reasoning, and is also gaining increasing attention in industry. Consequently, the research activity in ILP has widened to the area of Answer Set Programming, witnessing the proposal of several new learning frameworks that have extended ILP to learning answer set programs. In this paper, we investigate the theoretical properties of these existing frameworks for learning programs under the answer set semantics. Specifically, we present a detailed analysis of the computational complexity of each of these frameworks with respect to the two decision problems of deciding whether a hypothesis is a solution of a learning task and deciding whether a learning task has any solutions. We introduce a new notion of generality of a learning framework, which enables us to define a framework to be more general than another in terms of being able to distinguish one ASP hypothesis solution from a set of incorrect ASP programs. Based on this notion, we formally prove a generality relation over the set of existing frameworks for learning programs under answer set semantics. In particular, we show that our recently proposed framework, Context-dependent Learning from Ordered Answer Sets, is more general than brave induction, induction of stable models, and cautious induction, and maintains the same complexity as cautious induction, which has the highest complexity of these frameworks.

Abstract In recent years, several frameworks and systems have been proposed that extend Inductive Logic Programming (ILP) to the Answer Set Programming (ASP) paradigm. In ILP, examples must all be explained by a hypothesis together with a given background knowledge. In existing systems, the background knowledge is the same for all examples; however, examples may be context-dependent. This means that some examples should be explained in the context of some information, whereas others should be explained in different contexts. In this paper, we capture this notion and present a context-dependent extension of theLearning from Ordered Answer Setsframework. In this extension, contexts can be used to further structure the background knowledge. We then propose a new iterative algorithm, ILASP2i, which exploits this feature to scale up the existing ILASP2 system to learning tasks with large numbers of examples. We demonstrate the gain in scalability by applying both algorithms to various learning tasks. Our results show that, compared to ILASP2, the newly proposed ILASP2i system can be two orders of magnitude faster and use two orders of magnitude less memory, whilst preserving the same average accuracy.

Abstract This paper contributes to the area of inductive logic programming by presenting a new learning framework that allows the learning of weak constraints in Answer Set Programming (ASP). The framework, calledLearning from Ordered Answer Sets, generalises our previous work on learning ASP programs without weak constraints, by considering a new notion of examples asorderedpairs of partial answer sets that exemplify which answer sets of a learned hypothesis (together with a given background knowledge) arepreferredto others. In this new learning task inductive solutions are searched within a hypothesis space of normal rules, choice rules, and hard and weak constraints. We propose a new algorithm, ILASP2, which is sound and complete with respect to our new learning framework. We investigate its applicability to learning preferences in an interview scheduling problem and also demonstrate that when restricted to the task of learning ASP programs without weak constraints, ILASP2 can be much more efficient than our previously proposed system.