Katsumi Inoue

We explore abductive reasoning in contexts involving fuzzy statements (statements with truth degrees) such as ‘the lift is heavily loaded’ (meaning, e.g., that the lift is carrying more than 70% of its maximal load), ‘the symptoms are severe’, ‘it is cold outside’, etc. Such statements are both used to express observations and to explain observed events. That is, both the observed event and our explanation of it may have truth degrees. To formalise these contexts, we use infinitely-valued Łukasiewicz fuzzy logic Ł with semantics defined over the real-valued interval [0,1]. Here, 0 and 1 are interpreted as ‘absolutely false’ and ‘absolutely true’, respectively, and the remaining values as degrees of truth. We consider two standard entailment relations for Ł: the ‘truth-preserving’ one (if the premise is absolutely true, then the conclusion is absolutely true) and the ‘degree-preserving’ (the truth degree of the premise should be at most as high as the truth degree of the conclusion). For each of these entailment relations, we define and motivate the notions of abduction problems and explanations in the language of Ł expanded with ‘interval literals’ of the form p≥c, p≤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 Ł 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.

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.

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.

In this paper, we explore the problem of explaining observations starting from a classically inconsistent theory by adopting a paraconsistent framework. More precisely, we consider theories formulated in the well-known Belnap–Dunn paraconsistent four-valued logic BD and its implicative expansion BD⊃. Abductive solutions are then given in one of the two further expansions of BD: BD∘, which introduces formulas of the form ∘φ (‘the information on φ is reliable’), and BD△, which augments the language with formulas of the form △φ (‘there is information that φ is true’). We show that explanations in BD∘ and BD△ are not reducible to one another. We analyse the complexity of standard abductive reasoning tasks (solution recognition, solution existence, and relevance/necessity of hypotheses) depending on the language of the solution (BD∘ or BD△) and on the language of the theory (BD or BD⊃). In addition, we consider the complexity of abductive reasoning in the Horn fragment of BD⊃. By showing how to reduce abduction in BD and its expansions to abduction in classical propositional logic, we enable the reuse of existing abductive reasoning procedures.

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.

We propose an end-to-end approach for Answer Set Programming (ASP) and linear algebraically compute stable models satisfying given constraints. The idea is to implement Lin-Zhao’s theorem together with constraints directly in vector spaces as numerical minimization of a cost function constructed from a matricized normal logic program, loop formulas in Lin-Zhao’s theorem and constraints, thereby no use of symbolic ASP or SAT solvers involved in our approach. We also propose precomputation that shrinks the program size and heuristics for loop formulas to reduce computational difficulty. We empirically test our approach with programming examples including the three-coloring and Hamiltonian cycle problems.

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 Łukasiewicz fuzzy logic Ł. We define and motivate the notions of abduction problems and explanations in the language of Ł expanded with 'interval literals' of the form p ≥ c, p ≤ 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 Ł 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.

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.