arXiv subjects

Katsumi Inoue

Publications and source records attributed to Katsumi Inoue.

At least 19 recordsLinked to original sources

arXiv2026

Differentiable Logic Programming to Mitigate Reasoning Shortcuts in Neurosymbolic Systems

Neurosymbolic (NeSy) systems integrate neural networks with logical reasoning to achieve both generalization and interpretability, but recent work has shown they are susceptible to shortcut reasoning behaviors. We propose a novel method using matrix-based differentiable logic programming to mitigate reasoning shortcuts in two phenomena: constraint satisfaction shortcuts, where constraints are satisfied without achieving the intended task, and cognition shortcuts, where biased data leads to semantically incorrect concept mappings despite logically sound inference. Building on recent matrix-based logic programming semantics, we introduce design elements to mitigate shortcuts, including a unified encoding of rules and constraints in a single matrix. We also identify connections to fuzzy logic t-norms and empirically compare their gradient flow properties. Through carefully designed experiments on MNIST variants, we show that one-to-one grounding of neural outputs to logical atoms significantly reduces both shortcut types compared to previous methods that rely on soft probability distributions. We then confirm that architectural choices in coupling symbolic knowledge with neural learning play a critical role in shortcut mitigation.

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arXiv2026

Can Transformers Learn to Verify During Backtracking Search?

Backtracking search underlies classical constraint solvers, planners, and theorem provers. Recent transformer-based reasoning systems explore search trees over their own intermediate steps. A common training recipe fits an autoregressive next-token loss on offline solver traces. The model's input at each step is a cumulative trace of all prior decisions. The optimal continue-or-backtrack predictor depends only on the current search state, since two trajectories reaching the same state admit the same viable continuations. We show that decoder-only transformers trained on cumulative traces fail this requirement in two ways: the trace can scatter state features across many positions (scattered retrieval), and the predictor can condition on the trajectory rather than the state (history entanglement). We address scattered retrieval with localization, a trace-level fix that rewrites each decision block to expose state features locally. We address history entanglement with Selective State Attention (SSA), a fixed attention mask that enforces state-based decisions structurally without modifying training data, objective, or parameters. We focus on reactive verification, after propagation has exposed a contradiction. We test SSA on 3-SAT, graph coloring, Blocks World, and backtracking parsing. On same-state pairs that differ only in prior history, SSA emits identical decisions while a cumulative-trained causal baseline does not. Our contribution is a diagnostic of transformer behavior on serialized trajectory data, paired with a structural fix. Pretrained language models that search over their own reasoning steps may face the same failure. Our analysis opens up inference-time context clearing as a candidate way to apply the same isolation without retraining.

cs.LG↗

arXiv2026

Neural Decision-Propagation for Answer Set Programming

Integration of Answer Set Programming (ASP) with neural networks has emerged as a promising tool in Neuro-symbolic AI. While existing approaches extend the capabilities of ASP to real world domains, their reasoning pipelines depend on classical solvers, which is a bottleneck for scalability. To tackle this problem, we propose a new method to compute stable models, called decision-propagation (DProp), which alternates falsity decisions and truth propagations. Successful DProp computations are shown to capture the stable model semantics. We then develop Neural DProp (NDProp), a differentiable extension of DProp with neural computation for decisions and fuzzy evaluation for propagations. We evaluate the capabilities of NDProp for learning decision heuristics as well as neuro-symbolic integration, and compare it with existing neuro-symbolic approaches. The results show that NDProp can learn to efficiently compute stable models, and it improves accuracy and scalability on neuro-symbolic benchmarks.

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arXiv2026

Constraint-Based Analysis of Reasoning Shortcuts in Neurosymbolic Learning

Neurosymbolic systems can satisfy logical constraints during learning without achieving the intended concept-label correspondence; this is a problem known as reasoning shortcuts. We formalize reasoning shortcuts as a constraint satisfaction problem and investigate under which conditions concept mappings are uniquely determined by the constraints. We prove that a discrimination property (requiring that no valid concept mapping can be transformed into another valid mapping by swapping two concept values) is necessary for shortcut-freeness under bijective mappings, but demonstrate via a counterexample that it is insufficient even when the constraint graph is connected. We develop an ASP-based algorithm that verifies whether a given constraint set uniquely determines the intended concept mapping, with proven soundness and completeness. When shortcuts are detected, a greedy repair algorithm eliminates them by augmenting the constraint set, converging in at most $k$ iterations, where $k$ is the number of alternative valid mappings. We further provide a complexity classification: deciding shortcut-freeness is coNP-complete, counting shortcuts is #P-complete, and finding minimal repairs is NP-hard. We also establish sample complexity bounds showing that logarithmically many label queries suffice for disambiguation in favorable cases, while querying all ambiguous positions suffices in the worst case. Experiments across eight benchmark domains validate our approach.

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arXiv2026

Inferring High-Level Events from Timestamped Data: Complexity and Medical Applications

In this paper, we develop a novel logic-based approach to detecting high-level temporally extended events from timestamped data and background knowledge. Our framework employs logical rules to capture existence and termination conditions for simple temporal events and to combine these into meta-events. In the medical domain, for example, disease episodes and therapies are inferred from timestamped clinical observations, such as diagnoses and drug administrations stored in patient records, and can be further combined into higher-level disease events. As some incorrect events might be inferred, we use constraints to identify incompatible combinations of events and propose a repair mechanism to select preferred consistent sets of events. While reasoning in the full framework is intractable, we identify relevant restrictions that ensure polynomial-time data complexity. Our prototype system implements core components of the approach using answer set programming. An evaluation on a lung cancer use case supports the interest of the approach, both in terms of computational feasibility and positive alignment of our results with medical expert opinions. While strongly motivated by the needs of the healthcare domain, our framework is purposely generic, enabling its reuse in other areas.

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arXiv2026

Probabilistic Abduction in a Fuzzy Logic Framework

We study the problem of explaining observations about the probabilities of events, such as "it rains $20\%$ of the time", "rain and snow are equally likely", etc. We explain these statements with a probability distribution or a statement about probabilities of (other) events that are consistent with our knowledge and entail the observation. We formalise this problem in a fuzzy probabilistic logic $\mathsf{FP}$. We define and motivate the notions of abduction problems and their solutions. Our main technical contribution is a comprehensive study of the complexity of solution recognition and existence for a given abduction problem in $\mathsf{FP}$ for the case of full language and its disjunctive-clause fragments. We also obtain a translation of classical probabilistic abduction (finding the most likely explanation of a given event) to $\mathsf{FP}$.

cs.LO↗

arXiv2026

Visual Perceptual to Conceptual First-Order Rule Learning Networks

Learning rules plays a crucial role in deep learning, particularly in explainable artificial intelligence and enhancing the reasoning capabilities of large language models. While existing rule learning methods are primarily designed for symbolic data, learning rules from image data without supporting image labels and automatically inventing predicates remains a challenge. In this paper, we tackle these inductive rule learning problems from images with a framework called {\gamma}ILP, which provides a fully differentiable pipeline from image constant substitution to rule structure induction. Extensive experiments demonstrate that {\gamma}ILP achieves strong performance not only on classical symbolic relational datasets but also on relational image data and pure image datasets, such as Kandinsky patterns.

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arXiv2026

Differentiable Rule Induction from Raw Sequence Inputs

Rule learning-based models are widely used in highly interpretable scenarios due to their transparent structures. Inductive logic programming (ILP), a form of machine learning, induces rules from facts while maintaining interpretability. Differentiable ILP models enhance this process by leveraging neural networks to improve robustness and scalability. However, most differentiable ILP methods rely on symbolic datasets, facing challenges when learning directly from raw data. Specifically, they struggle with explicit label leakage: The inability to map continuous inputs to symbolic variables without explicit supervision of input feature labels. In this work, we address this issue by integrating a self-supervised differentiable clustering model with a novel differentiable ILP model, enabling rule learning from raw data without explicit label leakage. The learned rules effectively describe raw data through its features. We demonstrate that our method intuitively and precisely learns generalized rules from time series and image data.

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arXiv2026

Formally Explaining Decision Tree Models with Answer Set Programming

Decision tree models, including random forests and gradient-boosted decision trees, are widely used in machine learning due to their high predictive performance. However, their complex structures often make them difficult to interpret, especially in safety-critical applications where model decisions require formal justification. Recent work has demonstrated that logical and abductive explanations can be derived through automated reasoning techniques. In this paper, we propose a method for generating various types of explanations, namely, sufficient, contrastive, majority, and tree-specific explanations, using Answer Set Programming (ASP). Compared to SAT-based approaches, our ASP-based method offers greater flexibility in encoding user preferences and supports enumeration of all possible explanations. We empirically evaluate the approach on a diverse set of datasets and demonstrate its effectiveness and limitations compared to existing methods.

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arXiv2025

Predicate Renaming via Large Language Models

In this paper, we address the problem of giving names to predicates in logic rules using Large Language Models (LLMs). In the context of Inductive Logic Programming, various rule generation methods produce rules containing unnamed predicates, with Predicate Invention being a key example. This hinders the readability, interpretability, and reusability of the logic theory. Leveraging recent advancements in LLMs development, we explore their ability to process natural language and code to provide semantically meaningful suggestions for giving a name to unnamed predicates. The evaluation of our approach on some hand-crafted logic rules indicates that LLMs hold potential for this task.

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arXiv2025

A Rule-Based Approach to Specifying Preferences over Conflicting Facts and Querying Inconsistent Knowledge Bases

Repair-based semantics have been extensively studied as a means of obtaining meaningful answers to queries posed over inconsistent knowledge bases (KBs). While several works have considered how to exploit a priority relation between facts to select optimal repairs, the question of how to specify such preferences remains largely unaddressed. This motivates us to introduce a declarative rule-based framework for specifying and computing a priority relation between conflicting facts. As the expressed preferences may contain undesirable cycles, we consider the problem of determining when a set of preference rules always yields an acyclic relation, and we also explore a pragmatic approach that extracts an acyclic relation by applying various cycle removal techniques. Towards an end-to-end system for querying inconsistent KBs, we present a preliminary implementation and experimental evaluation of the framework, which employs answer set programming to evaluate the preference rules, apply the desired cycle resolution techniques to obtain a priority relation, and answer queries under prioritized-repair semantics.

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arXiv2025

Neural Logic Networks for Interpretable Classification

Traditional neural networks have an impressive classification performance, but what they learn cannot be inspected, verified or extracted. Neural Logic Networks on the other hand have an interpretable structure that enables them to learn a logical mechanism relating the inputs and outputs with AND and OR operations. We generalize these networks with NOT operations and biases that take into account unobserved data and develop a rigorous logical and probabilistic modeling in terms of concept combinations to motivate their use. We also propose a novel factorized IF-THEN rule structure for the model as well as a modified learning algorithm. Our method improves the state-of-the-art in Boolean networks discovery and is able to learn relevant, interpretable rules in tabular classification, notably on examples from the medical and industrial fields where interpretability has tangible value.

cs.LG↗

arXiv2025

Complexity of Abduction in \L{}ukasiewicz Logic

We explore the problem of explaining observations in contexts involving statements with truth degrees such as `the lift is loaded', `the symptoms are severe', etc. To formalise these contexts, we consider infinitely-valued {\L}ukasiewicz fuzzy logic. We define and motivate the notions of abduction problems and explanations in the language of {\L}ukasiewicz logic expanded with `interval literals' of the form $p\geq\mathbf{c}$, $p\leq\mathbf{c}$, and their negations that express the set of values a variable can have. We analyse the complexity of standard abductive reasoning tasks (solution recognition, solution existence, and relevance / necessity of hypotheses) in {\L}ukasiewicz logic for the case of the full language and for the case of theories containing only disjunctive clauses and show that in contrast to classical propositional logic, the abduction in the clausal fragment has lower complexity than in the general case.

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arXiv2025

Disentangling Neural Disjunctive Normal Form Models

Neural Disjunctive Normal Form (DNF) based models are powerful and interpretable approaches to neuro-symbolic learning and have shown promising results in classification and reinforcement learning settings without prior knowledge of the tasks. However, their performance is degraded by the thresholding of the post-training symbolic translation process. We show here that part of the performance degradation during translation is due to its failure to disentangle the learned knowledge represented in the form of the networks' weights. We address this issue by proposing a new disentanglement method; by splitting nodes that encode nested rules into smaller independent nodes, we are able to better preserve the models' performance. Through experiments on binary, multiclass, and multilabel classification tasks (including those requiring predicate invention), we demonstrate that our disentanglement method provides compact and interpretable logical representations for the neural DNF-based models, with performance closer to that of their pre-translation counterparts. Our code is available at https://github.com/kittykg/disentangling-ndnf-classification.

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arXiv2025

Neuro-Symbolic Contrastive Learning for Cross-domain Inference

Pre-trained language models (PLMs) have made significant advances in natural language inference (NLI) tasks, however their sensitivity to textual perturbations and dependence on large datasets indicate an over-reliance on shallow heuristics. In contrast, inductive logic programming (ILP) excels at inferring logical relationships across diverse, sparse and limited datasets, but its discrete nature requires the inputs to be precisely specified, which limits their application. This paper proposes a bridge between the two approaches: neuro-symbolic contrastive learning. This allows for smooth and differentiable optimisation that improves logical accuracy across an otherwise discrete, noisy, and sparse topological space of logical functions. We show that abstract logical relationships can be effectively embedded within a neuro-symbolic paradigm, by representing data as logic programs and sets of logic rules. The embedding space captures highly varied textual information with similar semantic logical relations, but can also separate similar textual relations that have dissimilar logical relations. Experimental results demonstrate that our approach significantly improves the inference capabilities of the models in terms of generalisation and reasoning.

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arXiv2024

Transformers Use Causal World Models in Maze-Solving Tasks

Recent studies in interpretability have explored the inner workings of transformer models trained on tasks across various domains, often discovering that these networks naturally develop highly structured representations. When such representations comprehensively reflect the task domain's structure, they are commonly referred to as "World Models" (WMs). In this work, we identify WMs in transformers trained on maze-solving tasks. By using Sparse Autoencoders (SAEs) and analyzing attention patterns, we examine the construction of WMs and demonstrate consistency between SAE feature-based and circuit-based analyses. By subsequently intervening on isolated features to confirm their causal role, we find that it is easier to activate features than to suppress them. Furthermore, we find that models can reason about mazes involving more simultaneously active features than they encountered during training; however, when these same mazes (with greater numbers of connections) are provided to models via input tokens instead, the models fail. Finally, we demonstrate that positional encoding schemes appear to influence how World Models are structured within the model's residual stream.

cs.LG↗

arXiv2024

Generating Global and Local Explanations for Tree-Ensemble Learning Methods by Answer Set Programming

We propose a method for generating rule sets as global and local explanations for tree-ensemble learning methods using Answer Set Programming (ASP). To this end, we adopt a decompositional approach where the split structures of the base decision trees are exploited in the construction of rules, which in turn are assessed using pattern mining methods encoded in ASP to extract explanatory rules. For global explanations, candidate rules are chosen from the entire trained tree-ensemble models, whereas for local explanations, candidate rules are selected by only considering rules that are relevant to the particular predicted instance. We show how user-defined constraints and preferences can be represented declaratively in ASP to allow for transparent and flexible rule set generation, and how rules can be used as explanations to help the user better understand the models. Experimental evaluation with real-world datasets and popular tree-ensemble algorithms demonstrates that our approach is applicable to a wide range of classification tasks. Under consideration in Theory and Practice of Logic Programming (TPLP).

cs.AI↗

arXiv2024

Differentiable Logic Programming for Distant Supervision

We introduce a new method for integrating neural networks with logic programming in Neural-Symbolic AI (NeSy), aimed at learning with distant supervision, in which direct labels are unavailable. Unlike prior methods, our approach does not depend on symbolic solvers for reasoning about missing labels. Instead, it evaluates logical implications and constraints in a differentiable manner by embedding both neural network outputs and logic programs into matrices. This method facilitates more efficient learning under distant supervision. We evaluated our approach against existing methods while maintaining a constant volume of training data. The findings indicate that our method not only matches or exceeds the accuracy of other methods across various tasks but also speeds up the learning process. These results highlight the potential of our approach to enhance both accuracy and learning efficiency in NeSy applications.

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