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Katsumi Inoue

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Published work

11 published item(s)

preprint2026arXiv

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.

preprint2026arXiv

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.

preprint2022arXiv

Learning First-Order Rules with Differentiable Logic Program Semantics

Learning first-order logic programs (LPs) from relational facts which yields intuitive insights into the data is a challenging topic in neuro-symbolic research. We introduce a novel differentiable inductive logic programming (ILP) model, called differentiable first-order rule learner (DFOL), which finds the correct LPs from relational facts by searching for the interpretable matrix representations of LPs. These interpretable matrices are deemed as trainable tensors in neural networks (NNs). The NNs are devised according to the differentiable semantics of LPs. Specifically, we first adopt a novel propositionalization method that transfers facts to NN-readable vector pairs representing interpretation pairs. We replace the immediate consequence operator with NN constraint functions consisting of algebraic operations and a sigmoid-like activation function. We map the symbolic forward-chained format of LPs into NN constraint functions consisting of operations between subsymbolic vector representations of atoms. By applying gradient descent, the trained well parameters of NNs can be decoded into precise symbolic LPs in forward-chained logic format. We demonstrate that DFOL can perform on several standard ILP datasets, knowledge bases, and probabilistic relation facts and outperform several well-known differentiable ILP models. Experimental results indicate that DFOL is a precise, robust, scalable, and computationally cheap differentiable ILP model.

preprint2020arXiv

Enhancing Linear Algebraic Computation of Logic Programs Using Sparse Representation

Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation in order to perform logical inference in large scale knowledge bases. This paper proposes further improvement by using sparse matrices to embed logic programs in vector spaces. We show its great power of computation in reaching the fixpoint of the immediate consequence operator from the initial vector. In particular, performance for computing the least models of definite programs is dramatically improved in this way. We also apply the method to the computation of stable models of normal programs, in which the guesses are associated with initial matrices, and verify its effect when there are small numbers of negation. These results show good enhancement in terms of performance for computing consequences of programs and depict the potential power of tensorized logic programs.

preprint2015arXiv

Characterization of Logic Program Revision as an Extension of Propositional Revision

We address the problem of belief revision of logic programs, i.e., how to incorporate to a logic program P a new logic program Q. Based on the structure of SE interpretations, Delgrande et al. adapted the well-known AGM framework to logic program (LP) revision. They identified the rational behavior of LP revision and introduced some specific operators. In this paper, a constructive characterization of all rational LP revision operators is given in terms of orderings over propositional interpretations with some further conditions specific to SE interpretations. It provides an intuitive, complete procedure for the construction of all rational LP revision operators and makes easier the comprehension of their semantic and computational properties. We give a particular consideration to logic programs of very general form, i.e., the generalized logic programs (GLPs). We show that every rational GLP revision operator is derived from a propositional revision operator satisfying the original AGM postulates. Interestingly, the further conditions specific to GLP revision are independent from the propositional revision operator on which a GLP revision operator is based. Taking advantage of our characterization result, we embed the GLP revision operators into structures of Boolean lattices, that allow us to bring to light some potential weaknesses in the adapted AGM postulates. To illustrate our claim, we introduce and characterize axiomatically two specific classes of (rational) GLP revision operators which arguably have a drastic behavior. We additionally consider two more restricted forms of logic programs, i.e., the disjunctive logic programs (DLPs) and the normal logic programs (NLPs) and adapt our characterization result to DLP and NLP revision operators.

preprint2015arXiv

Modeling of Resilience Properties in Oscillatory Biological Systems using Parametric Time Petri Nets, Supplementary Information

Automated verification of living organism models allows us to gain previously unknown knowledge about underlying biological processes. In this paper, we show the benefits to use parametric time Petri nets in order to analyze precisely the dynamic behavior of biological oscillatory systems. In particular, we focus on the resilience properties of such systems. This notion is crucial to understand the behavior of biological systems (e.g. the mammalian circadian rhythm) that are reactive and adaptive enough to endorse major changes in their environment (e.g. jet-lags, day-night alternating work-time). We formalize these properties through parametric TCTL and demonstrate how changes of the environmental conditions can be tackled to guarantee the resilience of living organisms. In particular, we are able to discuss the influence of various perturbations, e.g. artificial jet-lag or components knock-out, with regard to quantitative delays. This analysis is crucial when it comes to model elicitation for dynamic biological systems. We demonstrate the applicability of this technique using a simplified model of circadian clock.

preprint2013arXiv

Aspartame: Solving Constraint Satisfaction Problems with Answer Set Programming

Encoding finite linear CSPs as Boolean formulas and solving them by using modern SAT solvers has proven to be highly effective, as exemplified by the award-winning sugar system. We here develop an alternative approach based on ASP. This allows us to use first-order encodings providing us with a high degree of flexibility for easy experimentation with different implementations. The resulting system aspartame re-uses parts of sugar for parsing and normalizing CSPs. The obtained set of facts is then combined with an ASP encoding that can be grounded and solved by off-the-shelf ASP systems. We establish the competitiveness of our approach by empirically contrasting aspartame and sugar.

preprint2013arXiv

Encoding Higher Level Extensions of Petri Nets in Answer Set Programming

Answering realistic questions about biological systems and pathways similar to the ones used by text books to test understanding of students about biological systems is one of our long term research goals. Often these questions require simulation based reasoning. To answer such questions, we need formalisms to build pathway models, add extensions, simulate, and reason with them. We chose Petri Nets and Answer Set Programming (ASP) as suitable formalisms, since Petri Net models are similar to biological pathway diagrams; and ASP provides easy extension and strong reasoning abilities. We found that certain aspects of biological pathways, such as locations and substance types, cannot be represented succinctly using regular Petri Nets. As a result, we need higher level constructs like colored tokens. In this paper, we show how Petri Nets with colored tokens can be encoded in ASP in an intuitive manner, how additional Petri Net extensions can be added by making small code changes, and how this work furthers our long term research goals. Our approach can be adapted to other domains with similar modeling needs.

preprint2013arXiv

Encoding Petri Nets in Answer Set Programming for Simulation Based Reasoning

One of our long term research goals is to develop systems to answer realistic questions (e.g., some mentioned in textbooks) about biological pathways that a biologist may ask. To answer such questions we need formalisms that can model pathways, simulate their execution, model intervention to those pathways, and compare simulations under different circumstances. We found Petri Nets to be the starting point of a suitable formalism for the modeling and simulation needs. However, we need to make extensions to the Petri Net model and also reason with multiple simulation runs and parallel state evolutions. Towards that end Answer Set Programming (ASP) implementation of Petri Nets would allow us to do both. In this paper we show how ASP can be used to encode basic Petri Nets in an intuitive manner. We then show how we can modify this encoding to model several Petri Net extensions by making small changes. We then highlight some of the reasoning capabilities that we will use to accomplish our ultimate research goal.

preprint2013arXiv

Post-Proceedings of the First International Workshop on Learning and Nonmonotonic Reasoning

Knowledge Representation and Reasoning and Machine Learning are two important fields in AI. Nonmonotonic logic programming (NMLP) and Answer Set Programming (ASP) provide formal languages for representing and reasoning with commonsense knowledge and realize declarative problem solving in AI. On the other side, Inductive Logic Programming (ILP) realizes Machine Learning in logic programming, which provides a formal background to inductive learning and the techniques have been applied to the fields of relational learning and data mining. Generally speaking, NMLP and ASP realize nonmonotonic reasoning while lack the ability of learning. By contrast, ILP realizes inductive learning while most techniques have been developed under the classical monotonic logic. With this background, some researchers attempt to combine techniques in the context of nonmonotonic ILP. Such combination will introduce a learning mechanism to programs and would exploit new applications on the NMLP side, while on the ILP side it will extend the representation language and enable us to use existing solvers. Cross-fertilization between learning and nonmonotonic reasoning can also occur in such as the use of answer set solvers for ILP, speed-up learning while running answer set solvers, learning action theories, learning transition rules in dynamical systems, abductive learning, learning biological networks with inhibition, and applications involving default and negation. This workshop is the first attempt to provide an open forum for the identification of problems and discussion of possible collaborations among researchers with complementary expertise. The workshop was held on September 15th of 2013 in Corunna, Spain. This post-proceedings contains five technical papers (out of six accepted papers) and the abstract of the invited talk by Luc De Raedt.