Abductive Reasoning

A major question in cognitive modeling concerns the behavioral alignment between large language models and humans across linguistic and non-linguistic tasks. Unlike standard LLMs, large reasoning models (LRMs) are optimized with reinforcement learning from verifiable rewards, encouraging correct solutions to reasoning tasks rather than preference-aligned responses. Recent work (de Varda et al., 2025) investigates the cost of thinking in humans and LRMs by comparing human reaction times with model reasoning traces across a range of reasoning tasks. We isolate this alignment by turning to abductive reasoning: unlike deductive tasks, its difficulty cannot be inferred from formal structure and offers no shortcuts a model could exploit to mimic effort without genuine search, providing firmer ground for empirical claims of shared effort. We find further evidence of alignment between LRM and human reasoning effort, as well as evidence that models and humans tend to make similar errors. Finally, we show that decoding methods that let models explore multiple reasoning paths increase alignment in reasoning cost between humans and LRMs across the three models tested.

First-order concept synthesis asks a system to infer one formula that classifies labeled objects consistently across several finite relational structures. Every candidate can be evaluated exactly, but quantified first-order formulas form a vast search space, and LLM outputs are often semantically promising without being fully correct. We introduce Hypothesis Frontier, a verifier-guided neurosymbolic framework that evaluates each LLM formula on every training object, retains the strongest verified hypothesis across rounds, and uses its remaining errors to guide subsequent generation. Symbolic processing repairs invalid formulas while remaining anchored to the LLM-generated hypothesis, and simplifies train-valid formulas without changing any training prediction. Under matched models, problem sets, and LLM-round budgets, Hypothesis Frontier solves substantially more problems than repeated original-prompt generation. After the final formulas are selected, exact simplification shortens many train-valid formulas while preserving every training prediction. Exact symbolic reasoning therefore helps both to solve more induction problems and to compress many of the resulting formulas.

Standard approaches to abductive reasoning can retain multiple candidate explanations, but they do not generally combine explicit compositional cross-hypothesis interaction with an internal, rival-sensitive commitment judgment. This paper argues that in risk-sensitive domains -- where premature commitment carries asymmetric downside costs -- the timing of commitment is itself a governed decision that the inferential apparatus should formally represent. We present a minimal $κ$--$τ$ logical framework built on two primitives: epistemic interaction among hypotheses ($κ$) and a normative commitment threshold ($τ$). Hypotheses may coexist, reinforce or inhibit one another, and form emergent composite explanations, while collapse into committed conclusions is regulated by governance constraints rather than forced by inference alone. The logic is developed in two complementary modes sharing the interaction relation and the governance apparatus: a synthetic mode, in which atomic hypotheses are composed upward into emergent explanations, and an analytic mode, in which complex observed states of affairs are decomposed into causal clusters of latent factors, with commitment governed at both the cluster and the factor level. The framework provides formal machinery for domains in which the distinction between highly likely and commit-worthy is operationally consequential. The $κ$--$τ$ logic is positioned as the symbolic governance layer of a neurosymbolic architecture: its epistemic parameters are naturally estimated by neural components -- semantic embeddings and generative models, as demonstrated in existing computational realizations -- while its normative parameters remain under explicit human governance, yielding transparent and auditable abductive reasoning for deployment in high-stakes settings.

Abductive reasoning requires forming hypotheses that explain observed evidence and revising them as new evidence becomes available. While large language models (LLMs) are often evaluated on whether they solve abductive reasoning tasks correctly, less is known about how they acquire evidence, update their hypotheses, and decide when to stop. We introduce Alien Abduction game, an interactive probe for studying these behaviours under different interaction modes. The modes vary in whether evidence is provided upfront or across turns, and whether queries are selected by the model or examples are provided by the oracle. Across models, providing evidence upfront leads to higher success rates than distributing it across turns. In multi-turn settings, some models commit before using the available evidence, while others exhaust the turn budget without converging. Models also achieve higher success rates when examples are provided by the oracle than when they select their own queries, although their final hypotheses are more consistent with the evidence they selected. These findings suggest that models may form hypotheses that fit self-selected evidence without sufficiently distinguishing them from alternatives, and may struggle to validate and refine their hypotheses or determine when to stop.

Can scientific abduction occur without continuous sensorimotor embodiment? Recent arguments in AI and philosophy of science hold that genuine hypothesis generation requires an agent continuously coupled to the physical world. We defend a narrower claim: online embodiment is not necessary for every abductive scientific act. Our focus is identity abduction: the inference that two independently developed structures are one object under an explicit correspondence, reached through representational grounding rather than bodily interaction. An agent may acquire new inferential affordances not through physical interaction but through transformations into representations that expose latent invariants. Scientific diagrams are a practical substrate because they embody independently evolved conventions that partially canonicalize symmetry, topology, and operator structure across disciplines - a property we develop as convention space, which answers a hard retrieval problem: finding mathematically related work when two fields share no discriminating vocabulary. We operationalize the mechanism as an architecture, the Abduction Loop: representation generation, motif extraction, convention-space canonicalization, cross-domain retrieval, identity-hypothesis generation, and adversarial verification, with abstention as the designed default. A documented episode, in which a multimodal model given a figure of a gravitational-memory transport model generated and then verified the hypothesis that its central differential complex is equivalent to the spherical Kaiser-Squires mass-mapping complex of weak-lensing cosmology, serves as a motivating possibility witness from which the architecture is abstracted, not as evidence of general capability. We close with a falsifiable evaluation program, the DAB-30 benchmark. The contribution is a mechanistic proposal, an architecture, and a test program.

Planning over Temporal Dynamic Knowledge Graphs (TDKGs) presents theoretical challenges in open-world environments with incomplete information. Existing action formalisms often face decidability issues and the Ramification Problem, while structural abduction requires expansive combinatorial search spaces. We introduce a unified framework with two modules--PIE-Abducer (incremental direct-derivation abduction) and PIE-APT (Abductive Planning for TDKGs)--operating natively on the expressive SROIQ Description Logic. Modeling state transitions as non-monotonic updates to deductively closed DL theories, we represent actions natively in OWL. This leverages an incremental reasoner to preserve decidability and natively bypass the Ramification Problem. To address incomplete knowledge, PIE-Abducer circumvents Minimal Hitting Set (MHS) enumeration. Instead of combinatorial search, it injects the logical negation of a goal into a consistent DL branch and synthesizes missing premises via direct refutation consequences. PIE-APT employs a recursive Generate-and-Test architecture, interleaving backward-chaining A* search with PIE-Abducer to synthesize both action sequences and abductive assumptions. Candidates undergo strict validation via forward-chaining Temporal Projection to evaluate logical trajectories. We evaluate four OWL benchmarks targeting semantic abilities missing from classical planning: parameterized goals with witness search, mid-search DL entailment, open-world assumption injection, and adversarial plan synthesis. Results show qualitative superiority over classical planners and prove our direct-derivation approach significantly outperforms an MHS-faithful baseline in abductive enrichment.

We present MiSS, a black-box, query-based framework for explaining 3D point cloud classifiers through perturbation-relative sufficiency reasoning. MiSS treats a superpoint partition as an interpretable abstraction layer and asks whether the original prediction can be certified from a minimal coalition of geometric regions under a specified perturbation distribution. Unlike abductive explainers that require Boolean feature spaces or white-box logical encodings of the predictor, MiSS separates candidate proposal from verification: a weighted MaxSAT procedure proposes coalitions using a heuristic adaptive cardinality floor, certified exact-size fallback, a safely tightened upper bound, blocking clauses, and a surrogate acquisition heuristic learned from previous oracle evaluations, while a blackbox statistical oracle decides sufficiency from prediction queries. The system returns a statistically verified sufficient coalition as a binary attribution, with minimum cardinality guaranteed when certified search completes. Experiments on ModelNet40 and ShapeNet with PointNet and PointMLP classifiers show higher precision and coverage than rule-based baselines in most settings, with lower explanation time than exhaustive search.

The propositional abduction problem is a well-known form of non-monotonic reasoning where we are asked to find an explanation of a given manifestation. Recently, there has been an influx of results asking more refined questions about the solution space rather than only individual solutions. For example, we might be interested in finding two solutions that are sufficiently far from each other (diverse solutions) in the solution space. In this paper we consider a related representation question where we ask if a given set of explanations S can represent any other explanation (that is, whether their symmetric difference is smaller than a given k). We first study this problem from a classical complexity perspective and obtain a complete classification. While only a handful of cases are tractable, the increase in complexity compared to classical abduction is often smaller than expected. We then study the parameterized complexity for several parameters and obtain new tractable and hard cases. Interestingly, a full parameterized complexity classification would require resolving the parameterized complexity of the covering radius problem from coding theory. To the best of our knowledge, no useful relationship between coding theory and non-monotonic reasoning has previously been established, but such connections seemingly become important when asking more complex questions about solution spaces.

OWL ontologies provide a formal knowledge representation framework that enables semantic reasoning, and have been widely adopted across domains such as healthcare and bioinformatics. In practice, however, real-world ontologies are often incomplete, which pose challenges for reasoning. In this work, we focus on a fundamental subsumption reasoning problem: given an incomplete ontology and a candidate (non-entailed) subsumption, determine whether the subsumption is semantically plausible and, if so, providing a logically sound explanation containing potential missing axioms. This task unifies subsumption verification with ontology abduction, and generalizes the latter by removing the need for a predefined candidate set of missing axioms. To address this subsumption reasoning problem, we propose NeurOWL, an end-to-end neuro-symbolic framework that jointly performs verification and abduction, leveraging both formally defined semantics and textual semantics through Large Language Models and ontology embeddings. We evaluate NeurOWL on real-world ontologies across multiple domains, demonstrating strong and robust performance across different domains.

Abductive reasoning operates in two directions. The synthetic mode builds explanations from available hypotheses; the analytic mode, conversely, identifies the latent factors whose interaction accounts for a complex observed state. This paper develops the analytic mode as a non-greedy, risk-sensitive discipline of commitment, in which candidate factors coexist and interact, resolving into committed conclusions only when explicit governance conditions are met. The formal core is the $κ$-$τ$ apparatus: $κ$ encodes the epistemic interaction among hypotheses, and $τ$ sets a commitment threshold calibrated to the decision's stakes. The central contribution is the causal cluster, a structured object recording which latent factors participate in a decomposition, with what weights and interaction structure, together with a two-level architecture (intra-cluster $κ^*$, inter-cluster $κ^{**}$) that guards against causal misattribution. Demonstrated in epidemiological crisis decomposition and adversarial cyber threat analysis, the framework's contribution to human-AI reasoning is the legibility of suspended decomposition as a shared coordination object, providing structural resistance to premature convergence. In practice, the decision-maker is handed not a single imposed answer but the competing explanatory scenarios, weighted by plausibility and paired with the evidence that would resolve between them, so that sound action is possible even before the ambiguity is resolved.

This paper addresses Carl Hempel's longstanding problem of statistical ambiguity in inductive-statistical inference, in which contradictory predictions are derived from statistical laws. To avoid such predictions, Carl Hempel proposed the Requirement of Maximal Specificity (RMS) for the statistical laws used in the inference. An analysis of the RMS refinements made by Wesley Salmon, Alberto Coffa, and James Fetzer led to the following definition of maximally specific statistical laws: "the lawlike premises of an adequate explanation must specify all and only those properties whose presence or absence made a difference to the occurrence of its explanandum-phenomenon." However, there was no proof of a solution to the statistical ambiguity problem based on this definition. We use Nancy Cartwright's definition of causes that raise probabilities across background contexts, and then introduce the concept of Causal Rules. Then we define a special semantic probabilistic inference procedure that incrementally refines these causal rules by incorporating all statistically relevant information. This procedure yields Maximally Specific Causal Relationships (MSCRs), for which we prove (Theorem 1) that predictions derived from them are consistent. This resolves the statistical ambiguity problem. The semantic probabilistic inference procedure provides a probabilistic causal learning system, which may be used in such new areas as Causal AI and Causal Machine Learning. They fundamentally explore causal inference as a tool for understanding cause-and-effect relationships within complex systems. Properties similar to RMS remain under discussion. Several notions related to RMS are considered: invariant feature learning, invariant causal prediction, and spurious association.

Large language models (LLMs) excel at pattern recognition and text generation, but their capacity for abductive inference - inferring latent hypotheses that explain observed behavior - remains poorly understood. Here, we introduce Elenchos (named after the Socratic method of cross-examination), a generative evaluation framework that measures abductive reasoning as a structural inverse problem. Given a reference formal system, such as the lambda-calculus, and a potentially mutated counterpart, agents must determine whether a mutation has occurred and infer the rule modifications responsible for the resulting behavioral differences. Evaluating frontier and mid-tier LLMs reveals a consistent detection-attribution dissociation: models often recognize that a system has been altered but struggle to identify the latent mutations causing the observed discrepancies. Performance degrades substantially under interacting mutations, where models frequently recover only a subset of the underlying mutations. Preliminary evidence also suggests diminishing returns from increased inference-time reasoning, with only modest improvements under larger reasoning budgets, though this finding requires further validation.

We extend, in Isabelle/HOL, the deep-and-shallow embedding methodology of our prior work from propositional to first-order modal logic (FML) with constant-domain Kripke semantics. Three embeddings of FML into classical higher-order logic (HOL) are provided side by side: a deep embedding, a heavyweight maximal-shallow embedding, and a lightweight minimal-shallow embedding. The minimal-shallow embedding is presented as an Isabelle/HOL locale, parametrised by an accessibility relation, a world-indexed interpretation, a universe of worlds, and a variable assignment; the locale form admits a global faithfulness theorem, stating that quantifying over all minimal-shallow interpretations recovers exactly deep validity. A central technical contribution is a mechanisation, for FML under constant-domain Kripke semantics, of the (countable) downward Löwenheim-Skolem theorem, which underpins the automation of our faithfulness proof between the deep and minimal-shallow embeddings. Deploying it inside an extension of the minimal-shallow locale resolves the surjectivity problem that arises against an uncountable domain of individuals -- where the locale's variable assignment, having countable domain V = nat, cannot be surjective onto the domain -- and thereby yields faithfulness over the full domain. Since prior work treats only the propositional fragment, we develop here the substitution machinery (free/bound-variable predicates, the fresh-variable function, capture-avoiding substitution, alphabetic renaming, the substitutability predicate, the substitution lemma, and size-based induction principles) needed for the first-order quantifiers.

Neuro-symbolic AI based on $IFOL_B$ is a way to combine neural learning and symbolic reasoning to overcome limitations of purely neural systems (like lack of interpretability and logical structure) with formal logical machinery for self-reference. In this paper we expand the cognitive power of $IFOL_B$ by using the probability computation for the currently unknown sentences, based on Nilsson's probability structure for the $IFOL_B$. We introduce the global symmetry transformation that preserves the current knowledge database and logical deduction, and the local one used for real-time decisions about concrete (sub)problems that involve only a very strict subset of $IFOL_B$ predicates. The computation of probability density function $KI$ in both cases, based on the Shannon's maximum information entropy, is provided by neural networks of this probabilistic neuro-symbolic AGI.

Understanding how artworks are created requires reasoning about the iterative decisions, material operations, and contextual influences that shape artistic production. While recent generative AI systems can synthesize artworks with high fidelity, they primarily model distributions over finished artifacts rather than the creative processes underlying their creation. In practice, artistic workflows are only partially documented through fragmented sources such as archival records, preparatory studies, correspondence, etc., making process-level understanding difficult to formalize computationally. In this work, we introduce ArtMine, a framework for discovering and formalizing artistic processes from heterogeneous historical evidence. Our approach synthesizes heterogeneous artwork evidence into a structured repository, from which a Peircean abductive agent infers evidence-grounded production steps. These steps are converted into a compositional graph and rendering prompt, then optimized through self-reflection over deviations between the generated and reference artworks. We provide a preliminary proof-of-concept case study using open-domain historical sources across multiple artists and artistic movements, demonstrating that fragmented documentary evidence can support coherent, interpretable, and auditable representations of artistic workflows. By modeling creative processes rather than only final artifacts, our work moves toward process-centred human-AI co-creativity systems that can support artistic interpretation, creative education, reflective collaboration, and computational studies of cultural production.

Large language models (LLMs) have emerged as important tools in healthcare, showing growing potential for clinical reasoning and patient care. This survey examines recent progress in medical LLMs, focusing on reasoning applications and requirements. We present a dual-view approach that connects clinical practice with computational methods. On the clinical side, we establish a five-level competency scheme following Miller's Pyramid, progressing from knowledge recall to dynamic case management. On the computational side, we link deductive, inductive, and abductive reasoning patterns to common medical goals and tasks. We also introduce a benchmark dataset spanning five levels of medical reasoning capability and report results on 18 state-of-the-art models, revealing that medical specialist models excel in diagnosis-centric tasks while general models lead in decision support and dialogue. We conclude by discussing current progress and open challenges, including data limitations, hallucination, and grounding issues, and outline directions toward safer, more reliable, and workflow-ready systems.

Artificial Intelligence (AI) models, at their core, apply general learnings from broad datasets to individual circumstances using probabilistic behaviour. This inductive approach stands in contrast to deductive reasoning approaches which seek to prove conclusions from their premises. However, research has shown that deductive reasoning with AI models is a challenging problem and in the real-world it may not always be feasible. An alternative way forward is to leverage abductive reasoning, seeking to corroborate the output of multiple approaches to identify the most likely conclusion from the factual matrix. We apply this to synthetic media detection in forensic settings, and find we are able to disproportionately lower the risk of false positives to true positive recall. We also provide the first empirical evaluation of OpenAI's rollout of SynthID on synthetic images and evaluate how complementary different synthetic media detection approaches are.

Predicate invention (PI), the creation of new predicates to extend the hypothesis space, remains a critical bottleneck in Inductive Logic Programming (ILP). Existing methods rely on domain expertise and produce semantically opaque predicates, hindering adaptation to unfamiliar domains and cross-task reuse. We present ADVENT, an LLM-driven PI mechanism for ILP. ADVENT pairs LLM abductive generation with Prolog deductive verification, forming an iterative loop in which concrete execution results guide the LLM to refine candidate predicates. The mechanism leverages Large Language Models to identify implicit patterns in structured relational data and invent auxiliary predicates with meaningful names and definitions. Invented predicates and learned rules accumulate in a knowledge pool for cross-task reuse. Experiments on nine poker-hand concepts across seven LLMs show that LLM-driven PI achieves 58% success rate where ILP alone fails entirely, formal verification raises this to 80%, and the knowledge pool yields gains up to +31 percentage points, while producing human-interpretable rules. These results suggest that ADVENT offers a promising direction for automating predicate invention and enabling cross-task knowledge reuse in ILP.

In his 1996 doctoral thesis, Maurice Pagnucco created the first AGM-like abductive expansion operation. Taking his operation as a basis, as well as a taxonomy -- inspired by Atocha Aliseda -- responsible for highlighting and formalizing the main components of abductive reasoning, the main aim of this paper is to present a new paraconsistent AGM-like abductive expansion operation -- capable of assimilating contradictory explanatory hypotheses without trivialization and the consequent absurd epistemic state -- with its postulates and its transitively relational partial meet construction. To a large extent, the formal development presented in this paper was only made possible by the recent creation of the paraconsistent logic RCbr, an LFI (Logics of Formal Inconsistencies) that establishes properties especially relevant to belief revision contexts, in particular, the ability to be self-extensional -- i.e., to satisfy the replacement property. This is the first of two papers: the paraconsistent abductive expansion operation announced here -- which is part of a new system called AGMpabd -- despite bringing many interesting features, does not assign any relevant epistemic role to the paraconsistent operators of negation and consistency. Only in a second paper will an analogous paraconsistent abductive expansion operation -- which is part of another new system, AGMcircabd -- be enhanced in this direction. Nevertheless, to the best of my knowledge, the operation developed in this paper is the first of its kind in the AGM literature.

Large Language Models (LLMs) offer a promising path to automate Clinical Trial Matching (CTM), but still struggle with the deterministic verification required for complex eligibility criteria. Conversely, purely symbolic methods provide formal rigour but break down when faced with incomplete patient records and noisy clinical evidence. To bridge this gap, we investigate a hybrid framework for CTM combining LLMs with logical verification. In particular, we introduce an abductive neurosymbolic CTM framework (αNeSy-CTM), which leverages the linguistic and world knowledge in LLMs to support reasoning over noisy and underspecified clinical text. Extensive evaluation demonstrates that αNeSy-CTM substantially outperforms standalone LLM baselines, achieving up to 30% relative improvement over zero-shot baselines. In addition, our analyses confirm the impact of abductive reasoning on CTM, with αNeSy-CTM exhibiting improved accuracy, specificity, and robustness over a non-abductive neurosymbolic setting. Furthermore, αNeSy-CTM and Chain-of-Thought (CoT) reasoning prove highly complementary, highlighting the potential for a hybrid routing policy. Ultimately, this paper demonstrates the impact of neurosymbolic methods for automating CTM, providing a path toward the next generation of auditable, LLM-driven clinical applications.

Abduction is a central approach to explain missing entailments from a knowledge base by providing a hypothesis, that would, if added to the knowledge base, make the missing entailment become true. Abduction under repair semantics has recently been investigated in detail, where several desirable properties and optimality criteria were considered, such as signature-restrictions and minimality in size and of introduced conflicts. Naturally, hypotheses that satisfy more than one of these properties or combine a property with an optimality criterion would be even more desirable for applications. So far, such hypotheses have not been investigated in the literature. In the present paper, we consider the ABox abduction problem for hypotheses satisfying more than one property or additional optimality criteria, for EL_bot under brave and AR semantics. Our main observation is that often requiring additional properties for hypotheses does not lead to an increase of complexity.

A rule-based logic solver resolves every instance in our benchmark in under 50 microseconds with 100% accuracy; the best frontier language model reaches 65% at best and drops to 23.5% under rendering-robust evaluation (worst case over four surface renderings). We introduce DeFAb (Defeasible Abduction Benchmark), a dataset and generation pipeline that converts four decades of publicly funded knowledge bases into formally grounded instances for defeasible abduction: constructing hypotheses that explain anomalies by overriding defaults while preserving unrelated expectations. Because every hypothesis must pass polynomial-time checks for valid derivation, conservativity, and minimality, DeFAb makes logical rigor the instrument for measuring creativity and theoretical reasoning, scoring the disciplined construction of theory revisions rather than fluent but theory-destroying prose. The pipeline pairs taxonomic hierarchies (OpenCyc, YAGO, Wikidata) with behavioral property graphs (ConceptNet, UMLS) to produce 372,648+ instances across 33.75M materialized rules from 18 sources, in three levels with polynomial-time verifiable gold standards. Four frontier models do not reliably internalize defeasible reasoning: rendering-robust Level 2 accuracy is 7.8-23.5%; chain-of-thought variance (~36 pp) exceeds any inter-model gap; and a matched contamination control isolates a +19.4 pp Level 3 gap. We further release DeFAb-Hard (a 235-instance Level 3 difficulty variant; best model 53.3% vs 100% symbolic) and CONJURE (a kernel-verified transformative-creativity variant of 560 Lean 4/Mathlib instances whose gold answers are definitions the proof kernel did not previously contain, judge-free verifier; a pilot finds zero novel concepts). The same verifier doubles as an exact reward for preference optimization (DPO, RLVR/GRPO). Released under MIT at https://huggingface.co/datasets/PatrickAllenCooper/DeFAb.

A long-standing finding in the causal learning literature is that adults struggle to identify conjunctive causal rules, where an effect requires the simultaneous presence of multiple causes, while performing better in disjunctive settings. However, most demonstrations of this conjunctive handicap'' rely on passive observation paradigms with limited evidence, where learners have no control over evidence generation. This paper asks whether this bias persists when adults are granted agency through active exploration. Using a modified blicket detector'' task, adult participants freely intervened to identify causal objects under conjunctive or disjunctive rule structures. We show that active exploration substantially improves adults' conjunctive causal reasoning, although conjunctive rules still require more tests to infer than disjunctive rules. We further compare human performance to a range of large language models in the same setting. While some state-of-the-art models approach human-level performance on hypothesis inference accuracy, they often exhibit less efficient exploration strategies and similar conjunctive-disjunctive performance gaps.

Proof assistants based on expressive logics suffer limited automation for proof search, raising the cost of formal verification based on proof assistants. We address this problem by introducing the Abduction Prover for Isabelle/HOL. Given a challenging proof goal, the Abduction Prover constructs a proof script for the goal by identifying useful conjectures using abductive reasoning.

Abductive reasoning over knowledge graphs aims to generate logical hypotheses that explain observed entities or facts. Existing controllable hypothesis generation methods allow users to guide this process with explicit conditions, but they remain limited in interactive settings: they struggle to ground evolving natural-language intents across multi-turn dialogues and provide little fine-grained diagnosis when generated hypotheses fail. To address these limitations, we propose HypoAgent, an Agentic framework for interactive abductive Hypothesis Generation over knowledge graphs. HypoAgent integrates three agents: an Intent Recognition Agent that grounds user utterances and dialogue history into executable KG conditions, a Hypothesis Generation Agent that performs controllable hypothesis generation according to the extracted user intention, and a Root Cause Analysis Agent that diagnoses unreliable hypothesis fragments and leverages KG neighborhood probing to identify supported refinements. Experiments on commonsense and biomedical domain-specific knowledge graphs demonstrate that HypoAgent achieves state-of-the-art semantic similarity under single-turn, multi-turn, and unconditional settings. Our code is available at https://github.com/HKUST-KnowComp/HypoAgent.

We highlight a failure mode of large reasoning models on questions with insufficient information: models may recognize that a problem is under-specified, yet still continue reasoning and produce unsupported final answers instead of abstaining. We formalize this mismatch as the detection-to-abstention gap, where detected insufficiency fails to translate into final abstention. This gap is especially concerning in high-risk domains such as medical AI, where answers based on incomplete evidence can be more harmful than refusal. To close this gap, we propose Judge-Then-Solve (JTS), a trajectory-level reasoning-control framework that trains models to make an explicit answerability commitment before solution generation. Rather than treating abstention as a final-answer style, JTS casts it as a control decision: the model either proceeds to solve or terminates early based on its answerability judgment. We instantiate this policy through supervised warm-up and missing-premise reinforcement learning with consistency and length-shaping rewards. Experiments on dense and MoE reasoning models show that JTS substantially improves reliable abstention across datasets and pushes Abstention@Detection (A@D) to near-saturation, indicating that models not only detect missing information but also act on that detection. By terminating unanswerable trajectories immediately after the answerability judgment, JTS reduces unnecessary reasoning and improves inference efficiency when continued deliberation would amplify unsupported assumptions. We also observe that missing-premise training can alter reasoning behavior on difficult but answerable problems, reducing unproductive self-reflection. These results suggest that abstention under insufficient information is a key form of reasoning control for deploying reasoning models safely and efficiently.

Reinforcement learning with verifiable rewards (RLVR) has become central to post-training reasoning models, yet a key limitation of existing studies is their narrow view of the reasoning space: difficulty is treated as reasoning depth alone, and reward is concentrated on forward deductive state tracking. We instead characterize the reasoning space along two dimensions. Difficulty. Beyond reasoning depth, we study environment complexity, where models must identify the correct path amid distractors and interacting structures. Rewarded reasoning form. We consider four abilities core to real-world reasoning: deductive state tracking, abductive recovery of hidden events or facts, inductive rule induction, and analogical transfer. To disentangle these factors, we construct a synthetic knowledge-graph environment with controlled pre- and post-training distributions, where each instance varies along depth, complexity, and task family. Three findings emerge: joint depth-complexity coverage outperforms single-axis recipes; reasoning families respond non-uniformly, with abductive reasoning degrading outside the RL-covered region and task correlations clustering into deductive-abductive and inductive-analogy pairs; and uniform mixing outperforms staged curricula under a fixed budget. We also find that recent off-the-shelf models exhibit the same deductive-over-abductive asymmetry, suggesting that this gap is not merely an artifact of our controlled setup.

In a long conversation, an LLM can produce a plausible continuation that rests on premises the conversation has already abandoned. No runtime check ties its output to what the conversation has established, a gap that context-manipulation attacks on deployed agents exploit. We close this gap with a runtime verifier: an LLM Interpreter classifies each utterance into one of eight epistemic operations, and a symbolic engine applies them to a dependency map that records what every claim rests on and whether it still stands. Whether a continuation is grounded reduces to a walk over the map, linear in its size, with no LLM call. Retraction propagates through the same map with a conflict-free guarantee, flagging exactly the conclusions that lose support. On ReviseQA for belief revision and MemoryAgentBench's fact-consolidation split, two third-party benchmarks where earlier premises are superseded, the verifier leads a budget-matched retrieval baseline across five QA models and lifts MemoryAgentBench single-hop accuracy from 0.46--0.95 to 0.93--0.98. With the verifier, even the 7B model overtakes unaided GPT-4o. These runs feed the engine the benchmarks' own structured updates. When a GPT-4o Interpreter extracts every update from raw text instead, accuracy is statistically unchanged. Per-query cost is flat in conversation length, prompts staying near 0.8k tokens where full context reaches 114k and retraction queries under a microsecond at 2000 turns.

Recent efforts to improve the reasoning abilities of Large Language Models (LLMs) have focused on integrating formal logic solvers within neurosymbolic frameworks. A key challenge is that formal solvers lack commonsense world knowledge, preventing them from making reasoning steps that humans find obvious. Prior methods address this by using LLMs to supply missing commonsense assumptions, but these approaches implicitly assume universal agreement on such commonsense facts. In reality, commonsense beliefs vary across individuals. We propose a probabilistic framework for abductive commonsense reasoning that explicitly models this variation, aiming to determine whether most people would judge a statement as true or false. We introduce Probabilistic Abductive CommonSense (PACS), a novel algorithm that uses an LLM and a formal solver to sample proofs as observations of individuals' distinct commonsense beliefs, and aggregates conclusions across these samples. Empirically, PACS outperforms chain-of-thought reasoning, prior neurosymbolic methods, and search-based approaches across multiple benchmarks.

There has been a growing interest in explaining entailments over description logic (DL) knowledge bases. The existing explanation formalisms focus on justifications to explain true axioms, and abductive reasoning to explain missing axioms in a knowledge base. However, these formalisms only point out the reasoning steps behind a (missing) entailment and lack a user-centered approach as they do not consider an inquirer's needs, level of understanding, or prior knowledge. We propose contrastive explanations, aiming at answering "why an axiom P (fact) is true instead of another axiom Q (foil)" over description logic knowledge bases. The motivation arises from the observation that when a user discovers that P has occurred, they are often surprised because they anticipated the occurrence of another similar event Q. Furthermore, individual explanations for "why P" and "why not Q" are unsatisfactory since a user expects to see the difference between P and Q. In this work, we first present formal foundations of contrasting questions and then define contrastive explanations within description logics. To this end, facts include ABox assertions of the form C(x) for a concept C and individual x. Possible foils for such facts are assertions C(y) (contrasting against an individual y), or D(x) (contrasting against a concept D). Additionally, we explore the properties of contrastive explanations in the DL EL and ALC. We also provide an implementation of our definition and an experimental evaluation on KBs of varying sizes.

Given a knowledge base (KB) with a non-entailed fact, the ABox abduction problem asks for possible extensions of the KB that would entail this fact. This problem has many applications, ranging from diagnosis to explainability and repair. ABox abduction has been well-investigated for consistent KBs and classical semantics, but little is known for the case of inconsistent KBs, which can be caused by erroneous data. In this paper we define suitable notions of abduction in this setting and propose criteria that guide abduction towards "useful" hypotheses. To regain meaningful reasoning in the presence of inconsistencies, we use well-established repair semantics. We provide a comprehensive landscape of the complexity of ABox abduction under repair semantics, treating different variants of the abduction problem for the light-weight description logics DL-Lite and EL_bot.

Logical reasoning serve as a central capability in LLMs and includes three main forms: deductive, inductive, and abductive reasoning. In this work, we study the knowledge representations of these reasoning types in LLMs and analyze the correlations among them. Our analysis shows that each form of logical reasoning can be captured as a reasoning-specific knowledge vector in a linear representation space, yet these vectors are largely independent of each other. Motivated by cognitive science theory that these subforms of logical reasoning interact closely in the human brain, as well as our observation that the reasoning process for one type can benefit from the reasoning chain produced by another, we further propose to refine the knowledge representations of each reasoning type in LLMs to encourage complementarity between them. To this end, we design a complementary subspace-constrained refinement framework, which introduces a complementary loss that enables each reasoning vector to leverage auxiliary knowledge from the others, and a subspace constraint loss that prevents erasure of their unique characteristics. Through steering experiments along reasoning vectors, we find that refined vectors incorporating complementary knowledge yield consistent performance gains. We also conduct a mechanism-interpretability analysis of each reasoning vector, revealing insights into the shared and specific features of different reasoning in LLMs.

In active learning, membership queries (MQs) allow a learner to pose questions to a teacher, such as ''Is every apple a fruit?'', to which the teacher responds correctly with yes or no. These MQs can be viewed as subsumption tests with respect to the target ontology. Inspired by the standard reduction of subsumption to satisfiability in description logics, we reformulate each candidate axiom into its corresponding counter-concept and verbalise it in controlled natural language before presenting it to Large Language Models (LLMs). We introduce LLMs as a third component that provides real-world examples approximating an instance of the counter-concept. This design property ensures that only Type II errors may occur in ontology modelling; in the worst case, these errors merely delay the construction process without introducing inconsistencies. Experimental results on 13 commercial LLMs show that recall, corresponding to Type II errors in our framework, remains stable across several well-established ontologies.

Large language models exhibit systematic limitations in structured logical reasoning: they conflate hypothesis generation with verification, cannot distinguish conjecture from validated knowledge, and allow weak reasoning steps to propagate unchecked through inference chains. We present a symbolic reasoning scaffold that operationalizes Peirce's tripartite inference -- abduction, deduction, and induction -- as an explicit protocol for LLM-assisted reasoning. The framework enforces logical consistency through five algebraic invariants (the Gamma Quintet), the strongest of which -- the Weakest Link bound -- ensures that no conclusion in a reasoning chain can exceed the reliability of its least-supported premise. This principle, independently grounded as weakest link resolution in possibilistic logic and empirically validated for chain-of-thought reasoning, prevents logical inconsistencies from accumulating across multi-step inference. We verify all invariants through a property-based testing suite of 100 properties and 16 fuzz tests over 10^5+ generated cases, providing a verified reference implementation of the invariants suitable as a foundation for future reasoning benchmarks.

Knowledge representation formalisms are aimed to represent general conceptual information and are typically used in the construction of the knowledge base of reasoning agent. A knowledge base can be thought of as representing the beliefs of such an agent. Like a child, a strong-AI (AGI) robot would have to learn through input and experiences, constantly progressing and advancing its abilities over time. Both with statistical AI generated by neural networks we need also the concept of \textsl{causality} of events traduced into directionality of logic entailments and deductions in order to give to robots the emulation of human intelligence. Moreover, by using the axioms we can guarantee the \textsl{controlled security} about robot's actions based on logic inferences. For AGI robots we consider the 4-valued Belnap's bilattice of truth-values with knowledge ordering as well, where the value "unknown" is the bottom value, the sentences with this value are indeed unknown facts, that is, the missed knowledge in the AGI robots. Thus, these unknown facts are not part of the robot's knowledge database, and by learn through input and experiences, the robot's knowledge would be naturally expanded over time. Consequently, this phenomena can be represented by the Closed Knowledge Assumption and Logic Inference provided by this paper. Moreover, the truth-value "inconsistent", which is the top value in the knowledge ordering of Belnap's bilattice, is necessary for strong-AI robots to be able to support such inconsistent information and paradoxes, like Liar paradox, during deduction processes.

Large language models (LLMs) have developed rapidly, and their reasoning capabilities have become a hot research topic. However, there is still limited exploration of abductive reasoning. The multi-perspective and multi-level of causes is one of the core challenges of abductive reasoning, which cannot be solved well by existing methods. We construct a specialized dataset named DeepAbduction, which is designed for tracing the causes of pollution and disease, addressing the lack of datasets in this field. We propose \textsc{Inverse-Forward Abductive Reasoning} (IFAR) framework for LLMs multi-perspective and multi-level abductive reasoning. IFAR is zero-shot and combines generalized backward reasoning with relation-by-relation forward verification. Experimental results show that IFAR achieves an improvement of approximately 40% in the F1 score compared to other methods under mainstream LLMs, while maintaining a balance between recall and precision. Furthermore, IFAR enhances the performance of non-reasoning LLMs to surpass LLMs which have been trained for reasoning, and remains effective when applied to the latter. Code will be released after the acceptance of our work.

Modern language models (LMs) can learn to perform new tasks in different ways: in instruction following, the target task is described explicitly in natural language; in few-shot prompting, the task is specified implicitly with a small number of examples; in instruction inference, LMs are presented with in-context examples and are then prompted to generate a natural language task description before making predictions. Each of these procedures may be thought of as invoking a different form of reasoning: instruction following involves deductive reasoning, few-shot prompting involves inductive reasoning, and instruction inference involves abductive reasoning. How do these different capabilities relate? Across four LMs (from the gpt and llama families) and two learning problems (involving arithmetic functions and machine translation) we find a strong dissociation between the different types of reasoning: LMs can sometimes learn effectively from few-shot prompts even when they are unable to explain their own prediction rules; conversely, they sometimes infer useful task descriptions while completely failing to learn from human-generated descriptions of the same task. Our results highlight the non-systematic nature of reasoning even in some of today's largest LMs, and underscore the fact that very different learning mechanisms may be invoked by seemingly similar prompting procedures.