Knowledge refactoring compresses a logic program by introducing new rules. Current approaches struggle to scale to large programs. To overcome this limitation, we introduce a constrained optimisation refactoring approach. Our first key idea is to encode the problem with decision variables based on literals rather than rules. Our second key idea is to focus on linear invented rules. Our empirical results on multiple domains show that our approach can refactor programs quicker and with more compression than the previous state-of-the-art approach, sometimes by 60%.

We propose a stable model semantics for higher-order logic programs. Our semantics is developed using Approximation Fixpoint Theory (AFT), a powerful formalism that has successfully been used to give meaning to diverse non-monotonic formalisms. The proposed semantics generalizes the classical two-valued stable model semantics of (Gelfond and Lifschitz 1988) as-well-as the three-valued one of (Przymusinski 1990), retaining their desirable properties. Due to the use of AFT, we also get for free alternative semantics for higher-order logic programs, namely supported model, Kripke-Kleene, and well-founded. Additionally, we define a broad class of stratified higher-order logic programs and demonstrate that they have a unique two-valued higher-order stable model which coincides with the well-founded semantics of such programs. We provide a number of examples in different application domains, which demonstrate that higher-order logic programming under the stable model semantics is a powerful and versatile formalism, which can potentially form the basis of novel ASP systems. This work is under consideration for acceptance in TPLP.

Abstract argumentation is a popular toolkit for modeling, evaluating, and comparing arguments. Relationships between arguments are specified in argumentation frameworks (AFs), and conditions are placed on sets (extensions) of arguments that allow AFs to be evaluated. For more expressiveness, AFs are augmented with \emph{acceptance conditions} on directly interacting arguments or a constraint on the admissible sets of arguments, resulting in dialectic frameworks or constrained argumentation frameworks. In this paper, we consider flexible conditions for \emph{rejecting} an argument from an extension, which we call rejection conditions (RCs). On the technical level, we associate each argument with a specific logic program. We analyze the resulting complexity, including the structural parameter treewidth. Rejection AFs are highly expressive, giving rise to natural problems on higher levels of the polynomial hierarchy.

Learning from interpretation transition (LFIT) is a framework for learning rules from observed state transitions. LFIT has been implemented in purely symbolic algorithms, but they are unable to deal with noise or generalize to unobserved transitions. Rule extraction based neural network methods suffer from overfitting, while more general implementation that categorize rules suffer from combinatorial explosion. In this paper, we introduce a technique to leverage variable permutation invariance inherent in symbolic domains. Our technique ensures that the permutation and the naming of the variables would not affect the results. We demonstrate the effectiveness and the scalability of this method with various experiments.

We apply logic-based machine learning techniques to facilitate cellular engineering and drive biological discovery, based on comprehensive databases of metabolic processes called genome-scale metabolic network models (GEMs). Predicted host behaviours are not always correctly described by GEMs. Learning the intricate genetic interactions within GEMs presents computational and empirical challenges. To address these, we describe a novel approach called Boolean Matrix Logic Programming (BMLP) by leveraging boolean matrices to evaluate large logic programs. We introduce a new system, $BMLP_{active}$, which efficiently explores the genomic hypothesis space by guiding informative experimentation through active learning. In contrast to sub-symbolic methods, $BMLP_{active}$ encodes a state-of-the-art GEM of a widely accepted bacterial host in an interpretable and logical representation using datalog logic programs. Notably, $BMLP_{active}$ can successfully learn the interaction between a gene pair with fewer training examples than random experimentation, overcoming the increase in experimental design space. $BMLP_{active}$ enables rapid optimisation of metabolic models and offers a realistic approach to a self-driving lab for microbial engineering.

Assumption-based Argumentation (ABA) is advocated as a unifying formalism for various forms of non-monotonic reasoning, including logic programming. It allows capturing defeasible knowledge, subject to argumentative debate. While, in much existing work, ABA frameworks are given up-front, in this paper we focus on the problem of automating their learning from background knowledge and positive/negative examples. Unlike prior work, we newly frame the problem in terms of brave reasoning under stable extensions for ABA. We present a novel algorithm based on transformation rules (such as Rote Learning, Folding, Assumption Introduction and Fact Subsumption) and an implementation thereof that makes use of Answer Set Programming. Finally, we compare our technique to state-of-the-art ILP systems that learn defeasible knowledge.

Parameter learning is a crucial task in the field of Statistical Relational Artificial Intelligence: given a probabilistic logic program and a set of observations in the form of interpretations, the goal is to learn the probabilities of the facts in the program such that the probabilities of the interpretations are maximized. In this paper, we propose two algorithms to solve such a task within the formalism of Probabilistic Answer Set Programming, both based on the extraction of symbolic equations representing the probabilities of the interpretations. The first solves the task using an off-the-shelf constrained optimization solver while the second is based on an implementation of the Expectation Maximization algorithm. Empirical results show that our proposals often outperform existing approaches based on projected answer set enumeration in terms of quality of the solution and in terms of execution time. The paper has been accepted at the ICLP2024 conference and is under consideration in Theory and Practice of Logic Programming (TPLP).

Argument mining is natural language processing technology aimed at identifying arguments in text. Furthermore, the approach is being developed to identify the premises and claims of those arguments, and to identify the relationships between arguments including support and attack relationships. In this paper, we assume that an argument map contains the premises and claims of arguments, and support and attack relationships between them, that have been identified by argument mining. So from a piece of text, we assume an argument map is obtained automatically by natural language processing. However, to understand and to automatically analyse that argument map, it would be desirable to instantiate that argument map with logical arguments. Once we have the logical representation of the arguments in an argument map, we can use automated reasoning to analyze the argumentation (e.g. check consistency of premises, check validity of claims, and check the labelling on each arc corresponds with thw logical arguments). We address this need by using classical logic for representing the explicit information in the text, and using default logic for representing the implicit information in the text. In order to investigate our proposal, we consider some specific options for instantiation.

This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t. rule dependency structure, allowing quantification of specific inference challenges on LLM performance. Integrating LLMs with formal methods is a promising frontier in the Natural Language Processing field, as an important avenue for improving model inference control and explainability. In particular, inductive learning over complex sets of facts and rules, poses unique challenges for current autoregressive models, as they lack explicit symbolic grounding. While they can be complemented by formal systems, the properties delivered by LLMs regarding inductive learning, are not well understood and quantified. Empirical results indicate that the largest LLMs can achieve competitive results against a SOTA Inductive Logic Programming (ILP) system baseline, but also that tracking long predicate relationship chains is a more difficult obstacle than theory complexity for the LLMs.

We present a novel approach to querying classical inconsistent description logic (DL) knowledge bases by adopting a~paraconsistent semantics with the four Belnapian values: exactly true ($\mathbf{T}$), exactly false ($\mathbf{F}$), both ($\mathbf{B}$), and neither ($\mathbf{N}$). In contrast to prior studies on paraconsistent DLs, we allow truth value operators in the query language, which can be used to differentiate between answers having contradictory evidence and those having only positive evidence. We present a reduction to classical DL query answering that allows us to pinpoint the precise combined and data complexity of answering queries with values in paraconsistent $\mathcal{ALCHI}$ and its sublogics. Notably, we show that tractable data complexity is retained for Horn DLs. We present a comparison with repair-based inconsistency-tolerant semantics, showing that the two approaches are incomparable.