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IJCAI 2026

Injecting Qualitative Spatial Reasoning into World Models via Logic Tensor Networks

Ajay Ramachandra, Gesina Schwalbe, Zoe Falomir

World models (WM) learn predictive representations from high-dimensional sensory input. However, their internal knowledge is implicit and often inadequate for systematic reasoning about object structure. Qualitative Spatial Reasoning (QSR) models provide explicit human-readable object descriptions under transformations. This paper shows that these two forms of modeling can be combined by injecting a QSR model into a WM to improve the WM reasoning abilities. Using a cube rotation setting inspired by the cube comparison test used in mental rotation tasks as a case study, we use a QSR model that captures the geometric relationships and transformation rules describing how features move across faces under discrete rotations. We translate this QSR model into differentiable constraints using Logic Tensor Networks (LTNs) to guide gradient based learning. These constraints are injected into the WM loss function to regularize its latent dynamics to satisfy the spatial constraints of rotation. The results show that under an extreme data scarce regime (10%), baseline model's performance collapses to near zero, whereas our approach achieves above 90% better performance relative to baseline. Our method consistently maintains high scores across all data regimes (~80%), for both in-distribution and out-of-distribution observations. This paper proposes a novel framework to infuse QSR knowledge inside WM to make learned latent dynamics logical. Code is available at: https:// github.com/ajayrao80/LtnDreamer/

IJCAI 2026

Distance Between CP-theory Preferences

Zihao Qi, Erik Rauer, Samik Basu

Qualitative preferences specified in CP-theory define a partial order over outcomes based on induced dominance relations. We investigate the problem of measuring divergence between such induced orders. We introduce two formally equivalent distance metrics, each leveraging a distinct computational strategy based on different types of normalization. Preliminary empirical results support the soundness of the proposed methodologies and offer comparative insights into their computational properties. To the best of our knowledge, this is the first study to compute distance measures between qualitative preferences that jointly accounts for conditional dependencies and relative importance statements.

IJCAI 2026

A Foundation Model for Zero-Shot Logical Rule Induction

Yin Jun Phua

Inductive Logic Programming (ILP) learns interpretable logical rules from data. Existing methods are transductive: their learned parameters are bound to specific predicates and require retraining for each new task. We introduce Neural Rule Inducer (NRI), a pretrained model for zero-shot rule induction. Rather than encoding literal identities, NRI represents literals using domain-agnostic statistical properties such as class-conditional rates, entropy, and co-occurrence, which generalize across variable identities and counts without retraining. The model consists of a statistical encoder and a parallel slot-based decoder. Parallel decoding preserves the permutation invariance of logical disjunction; an autoregressive decoder would instead impose an arbitrary clause order. Product T-norm relaxation makes rule execution differentiable, allowing end-to-end training on prediction accuracy alone. We evaluate NRI on rule recovery, robustness to label noise and spurious correlations, and zero-shot transfer to real-world benchmarks, and we believe this work opens up the possibility of foundation models for symbolic reasoning. Code and the reference checkpoint are available at https://github.com/phuayj/neural-rule-inducer. An extended version with full appendices is available at https://arxiv.org/abs/2605.04916.

IJCAI 2026

Large Lemma Miners: Can LLMs Do Induction Proofs for Hardware?

Romy Peled, Daniel Kroening, Michael Tautschnig, Yakir Vizel

Large Language Models (LLMs) have shown potential for solving mathematical tasks. We show that LLMs can be utilized to generate proofs by induction for hardware verification and thereby replace some of the manual work %alleviating some of the manual effort done by Formal Verification engineers and deliver value to industry. We present a neurosymbolic approach that includes two prompting frameworks to generate candidate invariants, which are checked using a formal symbolic tool. Our results indicate that with sufficient reprompting, LLMs are able to generate inductive arguments for mid-size open-source RTL designs. For 90% of our problem set, at least one of the prompt setups succeeded in producing a provably correct inductive argument.

IJCAI 2026

Bounding Acceptability Degrees and Eliciting Initial Weights in Gradual Argumentation

Nir Oren, Bruno Yun

Many semantics for abstract weighted argumentation assume that each argument is associated with a numerical initial weight. Eliciting these initial weights poses several challenges: (1) accurately providing a specific numerical value is often difficult, and (2) individuals frequently confuse initial weights with acceptability degrees in the presence of other arguments. We therefore propose an elicitation pipeline that allows a user to specify their believed final acceptability degree intervals for each argument. We can determine which portion (if any) of these intervals are rational, refining the intervals, or restoring rationality when the intervals are irrational. This allows us to ultimately identify possible initial weights for each argument.

IJCAI 2026

A Versatile Framework for Formula-Based Enforcement and Synthesis in Abstract Argumentation

Andreas Niskanen, Jean-Guy Mailly, Yannis Dimopoulos, Pavlos Moraitis

Argumentation dynamics provides techniques for revising argumentation theories in real-world domains (e.g., an autonomous medical diagnostic agent). Within this context, enforcement in abstract argumentation has become a prominent topic. Enforcement aims to modify an argumentation framework to satisfy given acceptability conditions while minimizing change from the original framework. Motivated by the need to address both syntactic and semantic notions of change, we propose formula-based enforcement, a generic framework that strictly generalizes existing approaches, by additionally covering cases they cannot handle, including semantic change. We analyze its complexity under central argumentation semantics, obtaining results from NP-completeness to completeness for the third level of the polynomial hierarchy. For second-level complete variants, we present an exact procedure based on MaxSAT solving and counterexample-guided abstraction refinement (CEGAR), and evaluate it empirically.

IJCAI 2026

Harmonizing Federated Heterogeneous Optimization via Adaptive Objective Rectification

Jianrong Lu, Bangwei Li, Zhuoya Gu, Peng Fang, Ziming Zhao, Jianhai Chen

Federated optimization under data heterogeneity presents a significant challenge, often leading to suboptimal model performance. While numerous methods aim to replicate the ideal performance of centralized training, they frequently fall short in highly heterogeneous settings. In this paper, we introduce HaFedHo, an adaptive objective rectification method that harmonizes local training with the ideal data-centralized objective, requiring minimal modifications to the standard federated learning framework. HaFedHo operates by first decoupling the centralized objective and then employing a dynamic Taylor series expansion to accurately estimate the global objective for each client. Our theoretical analysis shows that the estimation error provably converges to zero as training progresses. Furthermore, extensive experiments on real-world datasets demonstrate that HaFedHo surpasses state-of-the-art methods, including SCAFFOLD, MimeLite, and FedDyn, in both test accuracy and communication efficiency. Notably, HaFedHo maintains its superior performance even with a client participation rate as low as $0.2\%$ in severely heterogeneous environments.

IJCAI 2026

Merging Beliefs and Counterfactuals

Emiliano Lorini, Dmitry Rozplokhas

We present a unified framework for modeling agents’ epistemic states and counterfactual conditionals. The novelty of our approach lies at the semantic level. We introduce a computationally grounded semantics in which an agent’s doxastic accessibility relation, needed to model the standard notion of deductively closed belief, is derived from the agent’s belief base, and in which the notion of comparative similarity between states, needed to interpret counterfactual conditionals, is computed from both the atomic formulas describing the agents’ belief bases and those describing the environment. We use this semantics to interpret a language of beliefs and counterfactuals. We demonstrate the expressiveness of our language and the flexibility of the semantics by formalizing a wide range of notions: counterfactual dependence, counterfactual notions of reason and knowledge, conditional belief. Furthermore, we show that our semantics illuminates the subtle interplay between belief change and counterfactuals. On the computational side, we provide a succinct formulation of model checking for our language and establish a PSPACE complexity result.

IJCAI 2026

Cross-Relational Preference Learning for Better LLM Instruction Following

Runsheng Li, Kai Sun, Bin Shi, Bo Dong

Large Language Models (LLMs) still exhibit limited capability in following complex instructions. While existing approaches often rely on preference learning to enhance this ability, they typically overlook the relationships between the permissible response spaces of different instructions, which restricts a model to align with subtle and diverse constraint variations. To address this, we propose Cross-Relational Preference Learning (CRPL), a novel framework for constructing preference data that explicitly models inter-instruction relationships through two key techniques: Cross-Relationship Perturbation and Cross-Region Pair Sampling. This enables the generation of more diverse preference data that captures a wide spectrum of constraint variations. Additionally, we introduce an atomic constraint-based verification mechanism to rigorously assess response satisfaction, ensuring high-quality preference pair construction. Extensive experiments across multiple preference learning methods (e.g., DPO, KTO), LLM backbones and four instruction-following benchmarks demonstrate that our approach achieves substantial improvements over prior baselines and exhibits strong generalization.

IJCAI 2026

Will My Favorite Chases Terminate If Evaluating Conjunctive Queries Does? One Does Not Simply Decide This

Lucas Larroque, Quentin Manière

Existential rules are a prominent formalism to enrich a database with knowledge from the domain of interest, but make even basic reasoning tasks on the resulting knowledge base undecidable. To circumvent this, several classes of rules offering various useful properties have been identified. One such class, for instance, contains all sets of rules on which the chase algorithm always terminates, which guarantees the existence of a finite universal model. However, these classes are often abstract rather than concrete: it may be undecidable to check whether a given set of rules belongs to them. Given that the most studied classes of existential rules are designed for reasoning on databases, thus ensuring decidable conjunctive query entailment, we ask: Within a class that supports decidable query entailment, do the usual abstract classes become concrete? We answer in the negative for classes based upon the termination of all classical chase variants and for the bts class.

IJCAI 2026

Learning Tree Automata with Term Rewriting

Jakub Kopystiański, Jan Otop

We present an extension of the Angluin-style learning algorithm for tree automata that incorporates deductive inference. The learning algorithm is provided with a term rewriting system that specifies properties of the target tree language (e.g., the order of subtrees under a symbol f is irrelevant). This term rewriting system is used to infer answers to some queries, which reduces the query complexity of the learning algorithm. We present examples of rewrite systems that express natural properties of tree-structured data, which yield a significant reduction in the number of queries.

IJCAI 2026

Fast Algorithms for Lexicographic Inference

Jonas Klein, Matthias Thimm

We present two new algorithms for the problem of lexicographic inference from conditional knowledge bases. These algorithms are based on SAT and MaxSAT encodings of the underlying problem of lexicographic comparisons of classical interpretations and require only a polynomial number of SAT solver calls. In our experimental evaluation we show that our new algorithms signficantly outperform the state of the art.

IJCAI 2026

ReSyn: A Generalized Recursive Regular Expression Synthesis Framework

Seongmin Kim, Hyunjoon Cheon, Su-Hyeon Kim, Yo-Sub Han, Sang-Ki Ko

Existing Programming-By-Example (PBE) systems often rely on simplified benchmarks that fail to capture the high structural complexity of real-world regexes, such as deeper nesting and frequent use of union operations. To overcome the resulting performance drop, we propose ReSyn, a synthesizer-agnostic divide-and-conquer framework that decomposes complex synthesis problem into manageable sub-problems. We also introduce Set2Regex, a parameter-efficient synthesizer capturing the permutation invariance of examples. Experimental results demonstrate that ReSyn significantly boosts accuracy across various synthesizers, and its combination with Set2Regex establishes a new state-of-the-art on challenging real-world benchmark. The complete source code, datasets, and pre-trained model checkpoints are publicly available at https://github.com/mrseongminkim/ReSyn.

IJCAI 2026

Synthesis and Verification of Transformer Programs

Hongjian Jiang, Matthew Hague, Philipp Rümmer, Anthony W. Lin

C-RASP is a simple programming language that was recently shown to capture concepts expressible by transformers. In this paper, we develop new algorithmic techniques for automatically verifying C-RASPs. To this end, we establish a connection to the verification of synchronous dataflow programs in Lustre, which enables us to exploit state-of-the-art model checkers utilizing highly optimized SMT-solvers. Our second contribution addresses learning a C-RASP program in the first place. To this end, we provide a new algorithm for learning a C-RASP from examples using local search. We demonstrate efficacy of our implementation for benchmarks of C-RASPs in the literature, in particular in connection to the following applications: (1) transformer program optimization, and (2) constrained learning of transformer programs (based on a partial specification).

IJCAI 2026

PAAL: Pattern-Anchor Alignment for Continual Knowledge Graph Embedding Under Structural Distribution Shift

Yue Jian, Lin Li, Kaize Shi, Junwei Zhou, Yu Yang

Continual knowledge graph embedding (CKGE) has gained popularity for managing dynamic knowledge graphs. Unlike general graph continual-learning approaches, CKGE focuses on retaining triple-level knowledge, thereby overcoming the inability of static models to accommodate continuously arriving facts. However, as new fact triples come in, real-world knowledge graphs often experience structural distribution shifts: the underlying topology and the way facts interconnect evolve over time. This presents a challenge that the structural distribution of historical data may diverge from that of emerging data, creating a distributional mismatch that complicates the adaptation to new trends. To address this, we propose Pattern-Anchor Alignment (PAAL), which introduces relation-level structural anchors to explicitly model these structural shifts. By quantifying the alignment between the structural distribution of emerging triples and historical anchors, PAAL implements an alignment-modulated optimization strategy. It utilizes a calibrated gating mechanism to precisely regulate the intensity of historical constraints based on structural stability. Experimental results indicate the effectiveness of PAAL, showing average H@1 improvements of 11.77% and 9.29% on pattern-shift and standard CKGE benchmarks, respectively. Our code is available at https://github.com/cangjie553/PAAL.

IJCAI 2026

Strikingness-Aware Evaluation for Temporal Knowledge Graph Reasoning

Rikui Huang, Shengzhe Zhang, Wei Wei

Temporal Knowledge Graph Reasoning (TKGR) aims at inferring missing (especially future) events from historical data. Current evaluation in TKGR uniformly weights all events, ignoring that most are trivial repetitions, which overestimate the true reasoning ability. Therefore, the rare outstanding events, whose prediction demands deeper reasoning, should be distinguished and emphasized. To this end, we propose a strikingness-aware evaluation framework, which introduces a rule-based strikingness measuring framework (RSMF) to quantify event strikingness by comparing its expected occurrence with peer events derived from temporal rules. Strikingness is then integrated as a weighting factor into metrics like weighted MRR and Hits@k. Experiments on four TKG benchmarks reveal: 1) All representative models perform worse as event strikingness increases, 2) Path-based methods excel on low-strikingness events and representation-based ones on high-strikingness events, 3) We design an ensemble method whose gains stem from fitting trivial events rather than reasoning improvement. Our framework provides a more rigorous evaluation, refocusing the field on predicting outstanding events.

IJCAI 2026

Unintended Consequences: Updating Causal Models

Joseph Y Halpern, Evan Piermont, Marie-Louise Vierø

We examine how causal beliefs affect an agent's choices and how feedback on those choices leads to updated causal beliefs. Building on the structural-equations framework for modeling causality, we first examine the general problem of updating causal beliefs in the face of novel (and possibly inexplicable) data. We model an agent who is uncertain of the true causal model, and therefore entertains a probabilistic belief over the set of possible models. We then consider how causal beliefs influence choices by building a model of agency and utility on top of the usual structural-equations framework. Using these two components, we propose a notion of steady state, where the feedback received from an agent's optimal action, given her current beliefs about the true causal model, can be rationalized by those beliefs.

IJCAI 2026

Tuple Inconsistency Measures: Toward Explaining Query Answers

Yurun Gu, Badran Raddaoui, Yue Ma, Aikaterini Tzompanaki, Nicole Bidoit

In this paper, we introduce novel tuple inconsistency measures that quantify the extent to which individual tuples contribute to violations of denial constraints in inconsistent databases. Then, we formally show that one of the proposed measures fully satisfies a set of well-motivated axiomatic properties. As an application, we lift tuple inconsistency to the level of query answers, obtaining a principled framework for measuring and explaining the inconsistency inherent in query results. We further investigate the computational complexity of tuple and answer inconsistency measures under denial constraints, identifying tractable cases that make their application to real-world data feasible. Finally, our experimental study on varying dataset- and inconsistency-settings demonstrates that, in comparison to existing methods, the proposed measures yield more fine-grained and informative assessments of inconsistency in databases.

IJCAI 2026

Bounded Fitting for Expressive Description Logics

Maurice Funk, Jean Christoph Jung, Tom Voellmer

Bounded fitting is an attractive paradigm for learning logical formulas from labeled data examples that offers PAC-style generalization guarantees and can often be implemented leveraging SAT solvers. It has been successfully applied to learning concepts of the description logic ALC. We study bounded fitting for learning concepts in expressive description logics that extend ALC with inverse roles, qualified number restrictions, and feature comparisons. We investigate under which conditions bounded fitting keeps its favorable theoretical properties in this setting, and implement is using a SAT solver. We compare our implementation against state-of-the-art concept learners with encouraging results, demonstrating that it is a practical approach to expressive concept learning.

IJCAI 2026

Diversity of Extensions in Abstract Argumentation

Johannes K. Fichte, Markus Hecher, Yasir Mahmood, Zhengjun Wang

Argumentation is an important topic of AI for modeling and reasoning about arguments. In abstract argumentation, we consider directed graphs, so-called argumentation frameworks (AF), that express conflicts between arguments. The semantics is defined by the notion of extensions, which are sets of arguments that satisfy particular relationship conditions in the AF. Usually, standard reasoning in argumentation do not reveal how far apart extensions are. We introduce a quantitative notion of diversity of extensions based on the symmetric-difference and provide a systematic complexity classification. Intuitively, diversity captures whether extensions of a framework (accepted viewpoints) differ only marginally or represent fundamentally incompatible sets of arguments. We study whether an AF admits k-diverse extensions, admits k-diverse extensions covering specific arguments, and to compute the largest k for which an AF admits k-diverse extensions. We outline a prototype and provide an evaluation for computing diversity levels.

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