Knowledge Graph Question Answering (KGQA) aims to improve factual accuracy by leveraging structured knowledge. However, real-world Knowledge Graphs (KGs) are often incomplete, leading to the problem of Incomplete KGQA (IKGQA). A common solution is to incorporate external data to fill knowledge gaps, but existing methods lack the capacity to adaptively and contextually fuse multiple sources, failing to fully exploit their complementary strengths. To this end, we propose Debate over Mixed-knowledge (DoM), a novel framework that enables dynamic integration of structured and unstructured knowledge for IKGQA. Built upon the Multi-Agent Debate paradigm, DoM assigns specialized agents to perform inference over knowledge graphs and external texts separately, and coordinates their outputs through iterative interaction. It decomposes the input question into sub-questions, retrieves evidence via dual agents (KG and Retrieval-Augmented Generation, RAG), and employs a judge agent to evaluate and aggregate intermediate answers. This collaboration exploits knowledge complementarity and enhances robustness to KG incompleteness. In addition, existing IKGQA datasets simulate incompleteness by randomly removing triples, failing to capture the irregular and unpredictable nature of real-world knowledge incompleteness. To address this, we introduce a new dataset, Incomplete Knowledge Graph WebQuestions, constructed by leveraging real-world knowledge updates. These updates reflect knowledge beyond the static scope of KGs, yielding a more realistic and challenging benchmark. Through extensive experiments, we show that DoM consistently outperforms state-of-the-art baselines.

Distributed knowledge is a key concept in the standard epistemic logic of knowledge-that. In this paper, we propose a corresponding notion of distributed knowledge-how and study its logic. Our framework generalizes two existing traditions in the logic of know-how: the individual-based multi-step framework and the coalition-based single-step framework. In particular, we assume a group can accomplish more than what its individuals can jointly do. The distributed knowledge-how is based on the distributed knowledge-that of a group whose multi-step strategies derive from distributed actions that subgroups can collectively perform. As the main result, we obtain a sound and strongly complete proof system for our logic of distributed knowledge-how, which closely resembles the logic of distributed knowledge-that in both the axioms and the proof method of completeness.

Modern data processing workflows frequently encounter ragged data: collections with variable-length elements that arise naturally in domains like natural language processing, scientific measurements, and autonomous AI agents. Existing workflow engines lack native support for tracking the shapes and dependencies inherent to ragged data, forcing users to manage complex indexing and dependency bookkeeping manually. We present Operon, a Rust-based workflow engine that addresses these challenges through a novel formalism of named dimensions with explicit dependency relations. Operon provides a domain-specific language where users declare pipelines with dimension annotations that are statically verified for correctness, while the runtime system dynamically schedules tasks as data shapes are incrementally discovered during execution. We formalize the mathematical foundation for reasoning about partial shapes and prove that Operon's incremental construction algorithm guarantees deterministic and confluent execution in parallel settings. The system's explicit modeling of partially-known states enables robust persistence and recovery mechanisms, while its per-task multi-queue architecture achieves efficient parallelism across heterogeneous task types. Empirical evaluation demonstrates that Operon outperforms an existing workflow engine with 14.94x baseline overhead reduction while maintaining near-linear end-to-end output rates as workloads scale, making it particularly suitable for large-scale data generation pipelines in machine learning applications.

Whence we get the simpler assumption (A" In other cases, one needs more specific theorems such as Dunford-Pettis' theorem for L The other conditions are difficult to verify for given functionals. We conclude by using Lemma 13. In this space, the shortest distance paths between measures are given by their square-norm distance. While both frameworks yield optimisation algorithms on measure spaces, the geometries and algorithms are very different. F is decreasing at each iteration.

This avoids the use of second-order information or the need to estimate local smoothness parameters of previous work.

This avoids the use of second-order information or the need to estimate local smoothness parameters of previous work.