Forgetting as a knowledge management operation deliberately ignores parts of the knowledge and beliefs of an agent, for various reasons. Forgetting has many facets, one may want to forget parts of the syntax, a proposition, or a conditional. In the literature, two main operators suitable for performing forgetting have been proposed and investigated in depth: First, variable elimination is a syntactical method that blends out certain atomic variables to focus on the rest of the language. It has been mainly used in the area of logic programming and answer set programming. Second, contraction in AGM belief revision theory effectively removes propositions from belief sets under logical deduction. Both operations rely mainly on classical logics. In this article, we take an epistemic perspective and study forgetting operations in epistemic states with richer semantic structures, but with clear links to propositional logic. This allows us to investigate what forgetting in the epistemic background means, thereby lifting well-known and novel forgetting operations to the epistemic level. We present five general types of epistemic forgetting and instantiate them with seven concrete forgetting operations for Spohn's ranking functions. We take inspiration from postulates of forgetting both from logic programming and AGM theory to propose a rich landscape of axioms for evaluating forgetting operations. Finally, we evaluate all concrete forgetting operations according to all postulates, leading to a novel comprehensive overview highlighting differences and commonalities among the forgetting operators.

We propose a framework for probability aggregation based on propositional probability logic. Unlike conventional judgment aggregation, which focuses on static rationality, our model addresses dynamic rationality by ensuring that collective beliefs update consistently with new information. We show that any consensus-compatible and independent aggregation rule on a non-nested agenda is necessarily linear. Furthermore, we provide sufficient conditions for a fair learning process, where individuals initially agree on a specified subset of propositions known as the common ground, and new information is restricted to this shared foundation. This guarantees that updating individual judgments via Bayesian conditioning--whether performed before or after aggregation--yields the same collective belief. A distinctive feature of our framework is its treatment of sequential decision-making, which allows new information to be incorporated progressively through multiple stages while maintaining the established common ground. We illustrate our findings with a running example in a political scenario concerning healthcare and immigration policies.

Robot swarms require cohesive collective behaviour to address diverse challenges, including shape formation and decision-making. Existing approaches often treat consensus in discrete and continuous decision spaces as distinct problems. We present DANCeRS, a unified, distributed algorithm leveraging Gaussian Belief Propagation (GBP) to achieve consensus in both domains. By representing a swarm as a factor graph our method ensures scalability and robustness in dynamic environments, relying on purely peer-to-peer message passing. We demonstrate the effectiveness of our general framework through two applications where agents in a swarm must achieve consensus on global behaviour whilst relying on local communication. In the first, robots must perform path planning and collision avoidance to create shape formations. In the second, we show how the same framework can be used by a group of robots to form a consensus over a set of discrete decisions. Experimental results highlight our method's scalability and efficiency compared to recent approaches to these problems making it a promising solution for multi-robot systems requiring distributed consensus. We encourage the reader to see the supplementary video demo.

Belief propagation is a fundamental message-passing algorithm for probabilistic reasoning and inference in graphical models. While it is known to be exact on trees, in most applications belief propagation is run on graphs with cycles. Understanding the behavior of "loopy" belief propagation has been a major challenge for researchers in machine learning and other fields, and positive convergence results for BP are known under strong assumptions which imply the underlying graphical model exhibits decay of correlations. We show, building on previous work of Dembo and Montanari, that under a natural initialization BP converges quickly to the global optimum of the Bethe free energy for Ising models on arbitrary graphs, as long as the Ising model is ferromagnetic (i.e.

However, in real-world applications, the network structure is typically dynamic, with nodes that join over time. In this setting, we would like a detection algorithm to perform only a limited number of updates at each node arrival. While standard voting approaches satisfy this constraint, it is unclear whether they exploit the network information optimally. We introduce a simple model for networks growing over time which we refer to as streaming stochastic block model (StSBM). Within this model, we prove that voting algorithms have fundamental limitations.

We characterize a notion of confidence that arises in learning or updating beliefs: the amount of trust one has in incoming information and its impact on the belief state. This learner's confidence can be used alongside (and is easily mistaken for) probability or likelihood, but it is fundamentally a different concept -- one that captures many familiar concepts in the literature, including learning rates and number of training epochs, Shafer's weight of evidence, and Kalman gain. We formally axiomatize what it means to learn with confidence, give two canonical ways of measuring confidence on a continuum, and prove that confidence can always be represented in this way. Under additional assumptions, we derive more compact representations of confidence-based learning in terms of vector fields and loss functions. These representations induce an extended language of compound "parallel" observations. We characterize Bayes Rule as the special case of an optimizing learner whose loss representation is a linear expectation.

Utilizing Vision-Language Models as Action Models for Intent Recognition and Assistance (Extended Abstract) Cesar Alan Contreras 1, Manolis Chiou 2, Alireza Rastegarpanah 3, Michal Szulik 4, Rustam Stolkin 1 1 School of Metallurgy & Materials, University of Birmingham, Birmingham B15 2SE, United Kingdom 2 School of Electronic Engineering and Computer Science, Queen Mary University of London, London E14 4NS, United Kingdom 3 School of Computer Science and Digital Technologies, Aston University, Birmingham B4 7ET, United Kingdom 4 United Kingdom National Nuclear Laboratory Ltd., Warrington W A3 6AE, United Kingdom Abstract --Human-robot collaboration requires robots to quickly infer user intent, provide transparent reasoning, and assist users in achieving their goals. Our recent work introduced GUIDER, our framework for inferring navigation and manipulation intents. We propose augmenting GUIDER with a vision-language model (VLM) and a text-only language model (LLM) to form a semantic prior that filters objects and locations based on the mission prompt. A vision pipeline (YOLO for object detection and the Segment Anything Model for instance segmentation) feeds candidate object crops into the VLM, which scores their relevance given an operator prompt; in addition, the list of detected object labels is ranked by a text-only LLM. Once the combined belief exceeds a threshold, autonomy changes occur, enabling the robot to navigate to the desired area and retrieve the desired object, while adapting to any changes in the operator's intent.

What nodes and edges should be included in the augmented region graph?

In multi-agent environments, effective interaction hinges on understanding the beliefs and intentions of other agents. While prior work on goal recognition has largely treated the observer as a passive reasoner, Active Goal Recognition (AGR) focuses on strategically gathering information to reduce uncertainty. We adopt a probabilistic framework for Active Goal Recognition and propose an integrated solution that combines a joint belief update mechanism with a Monte Carlo Tree Search (MCTS) algorithm, allowing the observer to plan efficiently and infer the actor's hidden goal without requiring domain-specific knowledge. Through comprehensive empirical evaluation in a grid-based domain, we show that our joint belief update significantly outperforms passive goal recognition, and that our domain-independent MCTS performs comparably to our strong domain-specific greedy baseline. These results establish our solution as a practical and robust framework for goal inference, advancing the field toward more interactive and adaptive multi-agent systems.

With the remarkable advancement of AI agents, the number of their equipped tools is increasing rapidly. However, integrating all tool information into the limited model context becomes impractical, highlighting the need for efficient tool retrieval methods. In this regard, dominant methods primarily rely on semantic similarities between tool descriptions and user queries to retrieve relevant tools. However, they often consider each tool independently, overlooking dependencies between tools, which may lead to the omission of prerequisite tools for successful task execution. To deal with this defect, in this paper, we propose Tool Graph Retriever (TGR), which exploits the dependencies among tools to learn better tool representations for retrieval. First, we construct a dataset termed TDI300K to train a discriminator for identifying tool dependencies. Then, we represent all candidate tools as a tool dependency graph and use graph convolution to integrate the dependencies into their representations. Finally, these updated tool representations are employed for online retrieval. Experimental results on several commonly used datasets show that our TGR can bring a performance improvement to existing dominant methods, achieving SOTA performance. Moreover, in-depth analyses also verify the importance of tool dependencies and the effectiveness of our TGR.