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
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. 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
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
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
The paper presents three Isabelle/HOL embeddings of monadic second‑order logic (MSO): a deep embedding, a maximal‑shallow embedding, and a minimal‑shallow embedding that collapses formulas to bool. It introduces a two‑sorted substitution system that ensures capture‑avoiding substitution and proves the faithfulness of all embeddings. A fully mechanised two‑sorted downward Löwenheim‑Skolem theorem is established, showing that the minimal embedding recovers deep validity relative to countable assignments and aligns with both the general (Henkin‑style) and standard readings of MSO, while also demonstrating differences in classical MSO properties across the embeddings.
By Christoph Benzmueller, Daniel Kirchner