The paper introduces the Evidential-Based Higher-Order Set Argumentation Framework (EHSAF), a unified formalism that extends Dung’s abstract argumentation by incorporating evidential support, higher-order relations, and collective interactions. Two complete semantics are defined: an adjacent complete labelling semantics allowing multiple truth values for arguments in support cycles, and an extension-based complete semantics that accepts only well‑founded support chains. The authors provide a propositional encoding in three‑valued Łukasiewicz logic and extend it to continuous fuzzy logics, proving key properties and showing equivalence under support‑acyclicity.
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.
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.
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...
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}).
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.
arXiv:2607. 21203v1 Announce Type: new Abstract: Description logic programs are a powerful formalism for combining rules with ontologies.
The paper introduces GUARD, a neuro‑symbolic system that autoformalizes argumentative material by completing missing premises (guards) before formal verification. It uses large language models to generate candidate guards, Isabelle/HOL to verify them, and a contrastive test to ensure the proof depends on the original premises and does not over‑generalize. Experiments on Debatepedia and ARCT show that GUARD improves verified‑faithful scores by over 30 points and reduces leakage by about 20 points compared to prior LLM‑driven theorem proving methods.
arXiv:2003. 05746v5 Announce Type: replace-cross Abstract: In this paper, we explore the issue of inconsistency handling over prioritized knowledge bases (KBs), which consist of an ontology, a set of facts, and a priority relation between conflicting facts.
arXiv:2607. 16715v1 Announce Type: new Abstract: We study Controlled Query Evaluation (CQE), a declarative approach to confidentiality-preserving data access, in the context of Description Logic (DL) ontologies, and for confidentiality policies expressed through Epistemic Dependencies (EDs).
arXiv:2606. 31861v1 Announce Type: cross Abstract: Dynamic epistemic logic represents belief change via model transformations induced by epistemic events.
arXiv:2609.08271v1 Announce Type: new Abstract: In various data models, the classical triple is a typical semantic data model. However, due to the design of the triple as a simple structure for repre...