Despite the popularity of reinforcement learning (RL) in wireless networks, existing approaches that rely on model-free RL (MFRL) and model-based RL (MBRL) are data inefficient and short-sighted. Such RL-based solutions cannot generalize to novel network states since they capture only statistical patterns rather than the underlying physics and logic from wireless data. These limitations become particularly challenging in complex wireless networks with high dynamics and long-term planning requirements. To address these limitations, in this paper, a novel dual-mind world model-based learning framework is proposed with the goal of optimizing completeness-weighted age of information (CAoI) in a challenging mmWave V2X scenario. Inspired by cognitive psychology, the proposed dual-mind world model encompasses a pattern-driven System 1 component and a logic-driven System 2 component to learn dynamics and logic of the wireless network, and to provide long-term link scheduling over reliable imagined trajectories. Link scheduling is learned through end-to-end differentiable imagined trajectories with logical consistency over an extended horizon rather than relying on wireless data obtained from environment interactions. Moreover, through imagination rollouts, the proposed world model can jointly reason network states and plan link scheduling. During intervals without observations, the proposed method remains capable of making efficient decisions. Extensive experiments are conducted on a realistic simulator based on Sionna with real-world physical channel, ray-tracing, and scene objects with material properties. Simulation results show that the proposed world model achieves a significant improvement in data efficiency and achieves strong generalization and adaptation to unseen environments, compared to the state-of-the-art RL baselines, and the world model approach with only System 1.

We introduce the Agent GPA (Goal-Plan-Action) framework: an evaluation paradigm based on an agent's operational loop of setting goals, devising plans, and executing actions. The framework includes five evaluation metrics: Goal Fulfillment, Logical Consistency, Execution Efficiency, Plan Quality, and Plan Adherence. Logical Consistency checks that an agent's actions are consistent with its prior actions. Execution Efficiency checks whether the agent executes in the most efficient way to achieve its goal. Plan Quality checks whether an agent's plans are aligned with its goals; Plan Adherence checks if an agent's actions are aligned with its plan; and Goal Fulfillment checks that agent's final outcomes match the stated goals. Our experimental results on two benchmark datasets - the public TRAIL/GAIA dataset and an internal dataset for a production-grade data agent - show that this framework (a) provides a systematic way to cover a broad range of agent failures, including all agent errors on the TRAIL/GAIA benchmark dataset; (b) supports LLM-judges that exhibit strong agreement with human annotation, covering 80% to over 95% errors; and (c) localizes errors with 86% agreement to enable targeted improvement of agent performance.

Large Language Models (LLMs) often exhibit factual inconsistencies and logical decay in extended, multi-turn dialogues, a challenge stemming from their reliance on static, pre-trained knowledge and an inability to reason adaptively over the dialogue history. Prevailing mitigation strategies, such as Retrieval-Augmented Generation (RAG) and agentic working memories, improve information recall but still engage with fundamentally static knowledge sources and follow pre-defined single reasoning path. This hinders their ability to preserve factual and logical consistency of their responses in multi-turn dialogues while the context evolves over time. To address this issue, we propose D-SMART, a model-agnostic framework designed to maintain multi-turn dialogue consistency by enabling LLMs to build and reason over a dynamic, structured representation of the conversational context. This is achieved via two synergistic components: (1) a Dynamic Structured Memory (DSM), which incrementally constructs and maintains an authoritative, OWL-compliant knowledge graph of the conversation; and (2) a Reasoning Tree (RT), which executes inferences as an explicit and traceable multi-step search over the graph. As the popular-used quality score (judged by GPT -4) can overlook logical flaws, we introduce new NLI-based metrics to better measure multi-turn dialogue consistency. Comprehensive experiments on the MT -Bench-101 benchmark show that D-SMART significantly outperforms state-of-the-art baselines, elevating the dialogue consistency score by over 48% for both proprietary and open-source models, and notably improves the quality score of the latter by up to 10.1%.

The emergence of large language models has enabled sophisticated multi-agent systems, yet coordinating their reasoning capabilities through prompt engineering remains challenging. We present a theoretically-grounded framework for dynamic prompt orchestration that enhances reasoning across multiple specialized agents. This framework addresses three core challenges: logical consistency preservation during agent transitions, reasoning-aware prompt adaptation, and scalable coordination of distributed inference. Our approach formalizes agent states using prompt templates, reasoning context vectors, and capability matrices. We prove system convergence to stable coordination patterns when step sizes satisfy $α< \frac{1}{2L}$ where $L$ is the Lipschitz constant of the state transition function. We implement this through a distributed architecture that dynamically routes reasoning tasks while maintaining semantic coherence. Experimental results on 1,000 synthetic multi-agent conversations demonstrate a 42% reduction in reasoning latency, a 23% improvement in logical consistency measured by ROUGE-L score, and an 89% success rate for task completion without context loss across agent transitions. Ablation studies identify the consensus mechanism as the primary performance driver, while revealing limitations: performance degrades beyond 10 agent transitions, and the system requires 76.5GB memory for 1,000 concurrent agents. These findings establish a new paradigm for scalable reasoning in multi-agent systems, providing theoretical foundations for understanding reasoning emergence across coordinated language models.

If two experts disagree on a test, we may conclude both cannot be 100 per cent correct. But if they completely agree, no possible evaluation can be excluded. This asymmetry in the utility of agreements versus disagreements is explored here by formalizing a logic of unsupervised evaluation for classifiers. Its core problem is computing the set of group evaluations that are logically consistent with how we observe them agreeing and disagreeing in their decisions. Statistical summaries of their aligned decisions are inputs into a Linear Programming problem in the integer space of possible correct or incorrect responses given true labels. Obvious logical constraints, such as, the number of correct responses cannot exceed the number of observed responses, are inequalities. But in addition, there are axioms, universally applicable linear equalities that apply to all finite tests. The practical and immediate utility of this approach to unsupervised evaluation using only logical consistency is demonstrated by building no-knowledge alarms that can detect when one or more LLMs-as-Judges are violating a minimum grading threshold specified by the user.

If we use LLMs as judges to evaluate the complex decisions of other LLMs, who or what monitors the judges? Infinite monitoring chains are inevitable whenever we do not know the ground truth of the decisions by experts and we do not want to trust them. One way to ameliorate our evaluation uncertainty is to exploit the use of logical consistency between disagreeing experts. By observing how LLM judges agree and disagree while grading other LLMs, we can compute the only possible evaluations of their grading ability. For example, if two LLM judges disagree on which tasks a third one completed correctly, they cannot both be 100\% correct in their judgments. This logic can be formalized as a Linear Programming problem in the space of integer response counts for any finite test. We use it here to develop no-knowledge alarms for misaligned LLM judges. The alarms can detect, with no false positives, that at least one member or more of an ensemble of judges are violating a user specified grading ability requirement.

While significant progress has been made with dual- and bi-encoder dense retrievers, they often struggle on queries with logical connectives, a use case that is often overlooked yet important in downstream applications. Current dense retrievers struggle with such queries, such that the retrieved results do not respect the logical constraints implied in the queries. To address this challenge, we introduce LogiCoL, a logically-informed contrastive learning objective for dense retrievers. LogiCoL builds upon in-batch supervised contrastive learning, and learns dense retrievers to respect the subset and mutually-exclusive set relation between query results via two sets of soft constraints expressed via t-norm in the learning objective. We evaluate the effectiveness of LogiCoL on the task of entity retrieval, where the model is expected to retrieve a set of entities in Wikipedia that satisfy the implicit logical constraints in the query. We show that models trained with LogiCoL yield improvement both in terms of retrieval performance and logical consistency in the results. We provide detailed analysis and insights to uncover why queries with logical connectives are challenging for dense retrievers and why LogiCoL is most effective.

Large language models (LLMs) have demonstrated impressive performance in various natural language processing tasks, yet their ability to perform multi-step logical reasoning remains an open challenge. Although Chain-of-Thought prompting has improved logical reasoning by enabling models to generate intermediate steps, it lacks mechanisms to assess the coherence of these logical transitions. In this paper, we propose a novel, lightweight evaluation strategy for logical reasoning that uses query-key alignments inside transformer attention heads. By computing a single forward pass and extracting a "QK-score" from carefully chosen heads, our method reveals latent representations that reliably separate valid from invalid inferences, offering a scalable alternative to traditional ablation-based techniques. We also provide an empirical validation on multiple logical reasoning benchmarks, demonstrating improved robustness of our evaluation method against distractors and increased reasoning depth. The experiments were conducted on a diverse set of models, ranging from 1.5B to 70B parameters.

Large language models (LLMs) have achieved remarkable successes on various natural language tasks. However, recent studies have found that there are still significant challenges to the logical reasoning abilities of LLMs. This paper summarizes and categorizes the main challenges into two aspects: (1) Logical question answering, LLMs often fail to generate the correct answer within complex logical problem which requires sophisticated deductive, inductive or abductive reasoning given a collection of premises and constrains. (2) Logical consistency, LLMs are prone to producing responses contradicting themselves across different questions. For example, a state-of-the-art Macaw question-answering LLM answers Yes to both questions Is a magpie a bird? and Does a bird have wings? but answers No to Does a magpie have wings?. To facilitate this research direction, we comprehensively investigate the most cutting-edge methods and propose detailed taxonomies of these methods. Specifically, to accurately answer complex logic questions, previous methods can be categorized based on reliance on external solvers, prompts, pretraining, and fine-tuning. To avoid logical contradictions, we discuss concepts and solutions of various logical consistencies, including implication, negation, transitivity, factuality consistency, and their composites. In addition, we review commonly used benchmark datasets and evaluation metrics, and discuss promising research directions, such as extensions to modal logic to account for uncertainty, and efficient algorithms satisfying multiple logical consistencies simultaneously.

Recent methodologies utilizing synthetic datasets have aimed to address inconsistent hallucinations in large language models (LLMs); however,these approaches are primarily tailored to specific tasks, limiting their generalizability. Inspired by the strong performance of code-trained models in logic-intensive domains, we propose a novel framework that leverages event-based text to generate corresponding code and employs cyclic training to transfer the logical consistency of code to natural language effectively. Our method significantly reduces inconsistent hallucinations across three leading LLMs and two categories of natural language tasks while maintaining overall performance. This framework effectively alleviates hallucinations without necessitating adaptation to downstream tasks, demonstrating generality and providing new perspectives to tackle the challenge of inconsistent hallucinations.