Walking on the DARKSIDE

Large Language Models (LLMs) recognise patterns but do not natively track the path of exclusions that a coherent discourse demands. When an input rests on a fabricated authority, a misapplied mechanism, or a surreptitious analogy, an unsteered LLM tends to engage with it as if it were grounded, and to reify the misstep into any structured output it generates. Logic-Augmented Generation (LAG) with POLANYI++, an LLM-steering method that uses heuristics, ontologies and problem solving methods for tacit knowledge extraction, produces an Extended Knowledge Graph (XKG) in OWL2, but inherits the same vulnerability: a sophisticated nonsensical input is reified into the graph alongside the legitimate triples, and is hardly detectable by automated reasoners since the XKG is generated jointly with the wrong assumptions. We introduce DARKSIDE, a coherence auditing method on top of POLANYI++. It formalises the trail as an explicit data structure of accumulated exclusions over discourse time, complemented by a warrant axis that classifies each named referent as Warranted, Unattested, Misattributed or Fabricated, with an escalation rule that pushes the DelegationRiskAssessment to UNSAFE when the fabricated rate is positive or the unsupported rate exceeds a threshold. We evaluate DARKSIDE as a steering layer over a Gemini 3 on BSBench, a 100-item adversarial corpus of sophisticated-sounding nonsense across software engineering, finance, healthcare, physics and law, with Claude Sonnet 4.6 as an independent judge. The empirical evidence supports an architectural claim: when an LLM forward pass is wrapped in an ontology-mediated negative-trail apparatus, the structural pattern-vs-path gap can be partially scaffolded. The XKG functions as the missing memory, and the warrant axis as an epistemic firewall.

RDFdL: Integrating RDF with Differential Dynamic Logic

Knowledge graphs modeled in RDF are powerful for describing static knowledge, but they cannot capture or reason about the dynamic behavior of physical systems, e.g., systems described by differential equations, which is a critical gap for AI-driven cyber-physical systems. To solve this, we propose RDFdL, a framework that integrates RDF with Differential Dynamic Logic (dL) to represent and reason about both static knowledge and the continuous dynamics of physical systems. For the dynamic part, we syntactically represent differential equations and ranges in the state space in RDF and SHACL and provide semantics using a translation to dL. Linking RDF and dL through their shared foundation in first-order logic achieves a unique integration: verification results for safety and reachability properties in the dynamic logic domain become available as entailment to SPARQL queries over RDF data. We implement the pipeline using Apache Jena for ontology-driven RDF reasoning and KeYmaera X, the theorem prover for dL, and sketch its applicability in manufacturing.

Recovering Explanations from Transformed Rule-Based Ontologies

Datalog rules are often used to define ontologies over Knowledge Graphs. Rule reasoners routinely optimise such ontologies by rewriting their rules into a form that can be evaluated more efficiently. These transformations preserve the entailed facts, but not the structure of the underlying derivations. A proof tree under the rewritten rules explains why a fact holds, but does not readily yield an explanation in terms of the original rules. We study the problem of constructing, from a proof of entailment under the rewritten rules, a proof under the original ones: we establish its computational complexity and identify two practically relevant languages for specifying proof transformations.

Shapes from Examples: Foundations of Shape Learning in Recursive SHACL

SHACL shapes enable data graph validation, making automatic shape learning essential for knowledge graph applications. We investigate the well-known fitting approach to this task: given sets P and N of positive and negative example nodes from an input graph, compute a shape expression C, possibly using shape names defined in a recursive shape catalogue, that validates at every node in P and none in N. We focus on the case where C is written in a core fragment of SHACL corresponding to the Description Logic ELI. For the catalogue, we consider the well-founded, stable, and supported semantics. We address fitting existence and most specific fitting computation, establish tight exponential-time upper bounds for both problems, and obtain polynomial bounds for relevant special cases.

Grounding LLM Reasoning under Incomplete Graph Evidence

Knowledge graphs can guide large language models (LLMs) reasoning, but the graph seen by a system is usually a retrieved, linked, temporally scoped, and incomplete evidence state rather than a complete account of truth. We develop a theoretical perspective on grounding observable LLM trajectories under such incomplete graph evidence.The evidence state induces entity anchors, typed relation residuals, path energies, and support regions, while the language model supplies a prior over candidate trajectories. We show that, under open-world incompleteness, no hard rule based only on the observed state can both reject every false unsupported trajectory and retain every true-but-unobserved one.We then characterize soft grounding as a KL-regularized deformation of the LLM prior: finite slack preserves support for unsupported but non-contradicted trajectories, whereas hard conditioning appears as an infinite-penalty limit.The framework also yields stability bounds under evidence perturbations and clarifies the constraint regimes appropriate for GraphRAG, KGQA, graph agents, constrained decoding, and faithful generation. The claims are evidence-relative: KG compatibility is treated as declared support, not factual truth.

Fuzzy Quantification over OWL Ontologies and Knowledge Graphs

This paper presents a versatile framework for evaluating fuzzy quantification queries over both standard and fuzzy ontologies as well as knowledge graphs. The primary objective is the retrieval of individuals that satisfy queries articulated via Type I or Type II fuzzy quantified expressions. A key advantage of the proposed approach is its inherent adaptability: it remains entirely agnostic to the quantifier type, the underlying evaluation method, and the specific data source of the ontology (i.e., OWL ontologies or RDFS knowledge graphs). Furthermore, we present Q2S2, a publicly accessible implementation of this system developed to support future research.

Provenance-Enhanced Statements in Knowledge Graphs

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}). Current provenance models can record who asserted what, but they typically treat provenance as semantically neutral, leaving underspecified how attributed claims relate to factual commitment, to one another, and to reasoning. In this paper we introduce DEC, a framework that interprets provenance predicates as indicators of epistemic stance and groups provenance-homogeneous sets of statements into \emph{cognitive worlds}. Drawing on cognitive modal logics (doxastic, epistemic, and conjectural), DEC characterizes locality, rationality, and controlled permeation between cognitive worlds and a distinguished factual core ("reality"), thereby enabling principled reasoning over attributed content without collapsing disagreements into inconsistencies. We formalize a DEC interpretation for RDF datasets that is conservative over RDF~1.2 semantics, clarify the role of intensionality and identity (including the Superman paradox), and illustrate the approach on common Semantic Web representations (named graphs, quoted triples/RDF-star, and reification). Finally, we describe our prototype DEC reasoner implemented as a Fuseki dataset module, supporting controlled factualisation and explicit detection of disagreements and delusions.