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:2607. 10880v1 Announce Type: new Abstract: We extend, in Isabelle/HOL, the deep-and-shallow embedding methodology of our prior work from propositional to first-order modal logic (FML) with constant-domain Kripke semantics.
arXiv:2609.36279v1 Announce Type: cross Abstract: The shallow embedding of higher-order modal logic in classical higher-order logic, used in Benzm\"uller and Scott's Notes on G\"odel's and Scott's va...
arXiv:2606. 24279v1 Announce Type: new Abstract: In Description Logics (DLs), reasoning under Rational Closure (RC) is a well-known and widely accepted non-monotonic formalism to handle defeasible knowledge.
In Description Logics (DLs), reasoning under Rational Closure (RC) is a well-known and widely accepted non-monotonic formalism to handle defeasible knowledge. In this paper, we study the application of RC to the core and horn variants of the DL-Lite family of lightweight description logics.
arXiv:2607. 21203v1 Announce Type: new Abstract: Description logic programs are a powerful formalism for combining rules with ontologies.
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. 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: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...
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.
Description logic programs are a powerful formalism for combining rules with ontologies. The well-supported semantics for description logic programs ensures that no answer sets rely on cyclic dependencies.