The paper introduces Positive Topology, a framework built on a basic relation between points (or models) and observable properties. It identifies two complementary structures: universal refinement and cover, and positivity and witnessed existence, showing that each can reconstruct the underlying relation. The authors present both information‑theoretic and game‑theoretic interpretations, and discuss how resource constraints can be integrated, illustrating applications in medical diagnosis, legal reasoning, and AI.
By Mirco A. Mannucci, Giovanni Sambin
arXiv:2608.29311v1 Announce Type: new
Abstract: Classic Formal Concept Analysis (FCA) primarily focuses on the positive relationships between objects and attributes and does not have mechanisms for h...
By Zhenghua Pan
Recent work in defeasible reasoning has seen notions of preferential semantics and entailment in the style of Kraus et al. applied to modal logics.
arXiv:2606. 03655v1 Announce Type: new Abstract: Recent work in defeasible reasoning has seen notions of preferential semantics and entailment in the style of Kraus et al.
By Nicholas Leisegang, Thomas Meyer, Ivan Varzniczak
arXiv:2602.02940v2 Announce Type: replace-cross
Abstract: Formal semantics and distributional semantics are distinct approaches to linguistic meaning: the former models meaning as reference via model...
By Daniel Quigley
The paper introduces Knowledge Cards, a new structured artefact designed to capture validated knowledge about specific concepts that AI systems use to make decisions. Unlike existing model, data, and system cards, Knowledge Cards focus on the layer between inputs and outputs, documenting entities, relationships, reasoning patterns, conditions for validity, and provenance, all grounded in a formal domain ontology and signed off by a domain expert. Prototype cards have been created in the energy and pharmaceutical domains, and the schema is released as a public draft for community engagement.
By Liliana Ferreira
arXiv:2607. 20500v1 Announce Type: new Abstract: Large Language Models (LLMs) perform strongly on well-specified reasoning tasks with a feasible answer.
By Sizhe Tang, Guangyu Jiang, Yu Li, Rongqian Chen, Ioannis G. Kevrekidis, Tian Lan
arXiv:2606. 15246v1 Announce Type: cross Abstract: Provenance-enhanced statements of the form "according to $X$, $\varphi$" are pervasive in contemporary knowledge graphs, especially in domains where graph content primarily represents claims, interpretations, and hypotheses (\emph{capta}) rather than observer-independent facts (\emph{data}).
By Fabio Vitali, Valentina Pasqual
arXiv:2607. 10248v1 Announce Type: cross Abstract: Language builds discourse contexts other than the actual: a painting, a belief, a memory, a hypothetical.
By Oliver Steele, Jiangtao Wen, Yuxing Han
arXiv:2606. 17851v1 Announce Type: new Abstract: A wide range of neurosymbolic (NeSy) systems compute one functional: a belief-weighted sum of a logical quantity over a space of $\sigma$-structures, of which weighted model counting, fuzzy logic, and probabilistic logic are special cases.
By Fernando Zhapa-Camacho, Robert Hoehndorf
arXiv:2606. 08503v1 Announce Type: new Abstract: In this paper, we integrate the defeasible logic of Kraus, Lehmann and Magidor (KLM) with the standpoint logic framework of G\'omez \'Alvarez and Rudolph.
By Nicholas Leisegang, Thomas Meyer, Sebastian Rudolph
The paper proposes a four‑dimensional formal framework—Semantic Expressivity, Agentic Discoverability, Task‑Relative Grounding, and Epistemic Trust Scope—to extend current KG metadata standards (VoID and DCAT). It introduces the Agentic Affordance Profile (AAP), a semantic layer that enables agents to select, compose, and diagnose failures in knowledge graphs at planning time. A scholarly‑search example illustrates the framework and outlines a five‑point research agenda for scaling AAP‑based affordance matching.
By Terry R. Payne, Valentina Tamma, Enrico Daga