arXiv:2604. 26977v2 Announce Type: replace-cross Abstract: In response to a concern raised by Horty, this paper develops a two-tiered, preference-based semantic framework for modeling defeasible conditional obligations.
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.
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:2609.07483v1 Announce Type: new Abstract: Modus Tollens (MT) is a classical logical inference rule, while counterfactuals are hypothetical statements that are contrary to facts, and counterfact...
arXiv:2601. 14271v2 Announce Type: replace Abstract: Shared accountability records are often used by parties who may never agree about causation, responsibility, or normative interpretation.
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. 21201v1 Announce Type: new Abstract: While the integration of linear constraints has significantly expanded the reach of Answer Set Programming (ASP), existing hybrid solvers often rely on disparate semantic underpinnings that lack a unified logical foundation.
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: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.
The paper presents a doxastic deontic logic designed for autonomous decision‑making under conflicting norms and uncertain information. It extends Chellas' Minimal Deontic Logic with explicit conditional norms and integrates it with multi‑agent KD45 to allow norms to depend on agents’ beliefs about facts and other norms. The authors formulate a Doxastic Norm Compliance Optimization Problem, distinguishing subjective from objective optimization, and identify conditions where the two coincide and where optimal decisions can be computed via weighted partial MaxSAT in polynomial time.
arXiv:2606. 05009v1 Announce Type: cross Abstract: Deontic reasoning is the task of answering questions by applying explicit rules and policies to case-specific facts, for example computing tax liability under a statute or determining the outcome of an immigration appeal.