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Provenance-Enhanced Statements in Knowledge Graphs

This paper introduces DEC, a framework that interprets provenance in knowledge graphs as indicators of epistemic stance to organize attributed claims into "cognitive worlds," thereby enabling principled reasoning over disagreements and hypotheses without collapsing them into inconsistencies.

Original authors: Fabio Vitali, Valentina Pasqual

Published 2026-06-16

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Fabio Vitali, Valentina Pasqual

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Core Problem: Facts vs. Opinions in Digital Libraries

Imagine a giant digital library (a Knowledge Graph) where every book, fact, and claim is stored. In most current systems, if you write down "The Earth is flat," the computer treats that statement almost the same way it treats "The Earth is round." It just stores the sentence. It doesn’t really care who said it or how sure they were.

The authors argue that this is a problem because much of what we store isn’t hard, cold "data" (like the weight of a rock), but rather "capta"—information that has been interpreted, guessed, or believed by people.

Data is like a photograph of a tree. It’s just there.
Capta is like a critic’s review of the tree. It’s subjective. It depends on who is looking.

Currently, when a Knowledge Graph stores a claim like "Leonardo da Vinci painted Salvator Mundi," it often ignores the fact that this is a hotly debated opinion among art historians, not a settled fact. The paper wants to fix this by giving the computer a way to understand the source and the confidence behind every statement.

The Solution: The "DEC" Framework

The authors propose a new system called DEC (standing for Doxastic, Epistemic, and Conjectural). Think of DEC as a set of colored tags or "lenses" that the computer uses to look at information. Instead of treating all statements as equal, DEC sorts them into different "Cognitive Worlds" based on how certain the source is.

Here are the three main types of worlds DEC creates:

The Epistemic World (The "Fact" Zone):
- Analogy: This is like a verified news report or a scientific law.
- Meaning: If a statement is here, the system treats it as true reality. If Alice knows something is true, and she is in the Epistemic World, the computer accepts it as a fact for everyone else to use.
The Doxastic World (The "Belief" Zone):
- Analogy: This is like a personal diary or a rumor.
- Meaning: If Bob believes something, it stays in his private bubble. The computer records that Bob believes it, but it doesn’t assume it’s true for the rest of the library. Bob can believe whales are fish; the computer notes this belief but doesn’t change the biological facts in the main database.
The Conjectural World (The "Hypothesis" Zone):
- Analogy: This is like a "What If?" scenario in a sci-fi movie.
- Meaning: This is for testing ideas. If Carl supposes that dragons are reptiles, the computer creates a temporary world where that is true. It allows Carl to explore the consequences of that idea (e.g., "If dragons are reptiles, then Toothless is a reptile") without messing up the real-world facts.

How It Works: The "Permeation" Rule

The magic of DEC is how these worlds interact. The authors use the word "Permeation" to describe how information flows between these bubbles.

Epistemic → Reality: Information flows out. If you know something, it becomes a fact.
Doxastic → Isolated: Information stays in. Your beliefs don’t leak out to change the facts.
Conjectural ← Reality: Information flows in. You start with the known facts and add your hypothesis on top.

This prevents the system from getting confused. It allows the library to hold contradictory views (e.g., "Art Historian A says it’s Leonardo; Art Historian B says it’s a student") without the computer crashing or declaring the whole library "broken."

Solving the "Superman Paradox"

One famous problem in computer logic is the Superman Paradox.

The Problem: Lois Lane knows that Superman can fly. Superman is Clark Kent. Therefore, logic suggests Lois Lane must know that Clark Kent can fly. But in the story, she doesn’t! Standard computer logic fails here because it swaps "Superman" and "Clark Kent" automatically.
The DEC Fix: DEC uses "Intensionality." This means the computer respects the context of the belief. It understands that Lois’s belief is locked inside her specific "Cognitive World." Just because Superman = Clark Kent in the real world doesn’t mean that identity swaps over inside Lois’s head. DEC keeps the identity swap contained within the specific world where it applies, solving the paradox.

Detecting "Delusions" and "Disagreements"

Because DEC tracks where information comes from, it can spot interesting patterns:

Disagreement: If two experts have different beliefs, DEC marks them as "disagreeing" but keeps both records. It doesn’t delete one; it just notes they are incompatible.
Delusion: If someone’s belief directly contradicts a verified fact (e.g., believing the Earth was created in 4004 BC when science says otherwise), DEC flags this as a "delusion." It doesn’t mean the person is crazy; it means their specific claim is incompatible with the established reality graph.
Settlement: Over time, if a hypothesis (Conjectural) is proven true, DEC can "settle" it, moving it from the "What If?" zone into the "Fact" zone.

The Prototype: A Smart Librarian

The authors built a prototype tool (a "reasoner") that sits on top of existing web technologies. Think of it as a Smart Librarian who stands at the entrance of the digital library.

When a new book (statement) arrives, the Librarian checks the tag.
If it’s tagged "Fact," the Librarian puts it on the main shelf.
If it’s tagged "Opinion," the Librarian puts it in a special "Views" section, ensuring it doesn’t get mixed up with the facts.
If two books contradict each other, the Librarian doesn’t throw one away; they just put a sticky note on them saying, "These two disagree."

Summary

In short, this paper argues that we need to stop treating all information in Knowledge Graphs as equal facts. By using the DEC framework, we can teach computers to distinguish between facts, beliefs, and hypotheses. This allows digital libraries to store complex, debated, and evolving human knowledge without getting confused by contradictions, making them much smarter and more useful for research and history.

Technical Summary: Provenance-Enhanced Statements in Knowledge Graphs

Problem Statement
The paper addresses the semantic limitations of current Knowledge Graph (KG) technologies in handling "provenance-enhanced statements" (PES), which take the form "according to X, $\phi$ ." In domains where KG content represents capta (claims, interpretations, and hypotheses) rather than observer-independent data (objective facts), provenance is not merely contextual metadata but a decisive factor in the epistemic status of a statement. Current models, such as PROV-O or Wikidata’s ranking systems, treat provenance as semantically neutral. This neutrality fails to capture the epistemic commitment of assertions, obscuring the distinction between factual knowledge, belief, conjecture, and delusion. Consequently, existing approaches struggle to manage disagreement without collapsing into inconsistency and lack a principled mechanism for reasoning over attributed content, often avoiding epistemic reasoning due to issues like the "Superman paradox" (the failure of substitutivity of identicals in intensional contexts).

Methodology
The authors introduce DEC, a framework grounded in cognitive modal logics—specifically Doxastic, Epistemic, and Conjectural logics. The methodology involves:

Cognitive Worlds: Statements are grouped into "cognitive worlds" based on provenance homogeneity. These worlds are interpreted as subjective informational states (beliefs, knowledge, or hypotheses) relative to a distinguished "reality" graph.
Modal Logic Axioms: The framework utilizes specific axioms to define the relationship between cognitive worlds and reality:
- Locality (Axiom K): Reasoning is confined within a cognitive world; inferences do not automatically cross world boundaries.
- Rationality (Axiom D): Cognitive worlds are internally consistent.
- Permeation:
  - Inside-out (Axiom T): Characterizes Epistemic worlds (knowledge). Statements here permeate into the reality graph, contributing to factual commitment.
  - Outside-in (Axiom C): Characterizes Conjectural worlds (hypotheses). Facts from reality permeate into these worlds, allowing hypothetical reasoning based on established facts.
  - No Permeation: Characterizes Doxastic worlds (beliefs). These are isolated from reality; beliefs do not affect factual truth, nor do facts automatically enter the belief set.
DEC Interpretation for RDF: The authors formalize a DEC interpretation for RDF datasets that is conservative over RDF 1.2 semantics. It defines a "reality graph" as the union of all epistemic content. Satisfaction in DEC is determined solely by the RDF satisfaction of this reality graph. Non-epistemic worlds (doxastic, conjectural, verbatim) do not contribute to factual truth conditions, allowing for the coexistence of incompatible claims without trivializing inference.
Intensionality: The framework adopts an intensional view of identity and substitution. Identity assertions (e.g., owl:sameAs) are treated as ontological predicates within the base logic, not as global metalinguistic rewriting rules. This resolves the Superman paradox by confining identity effects to the cognitive world in which they are asserted, unless explicit permeation rules apply.

Key Contributions

Theoretical Framework: The introduction of the DEC framework, which maps provenance predicates to specific cognitive modal logics (KD45 for doxastic, S5 for epistemic, KDC for conjectural).
Inclusion Theorem: A formal theorem establishing a strict correspondence between cognitive modal axioms and the set-theoretic relationship of cognitive worlds to reality (e.g., epistemic worlds are subsets of reality; conjectural worlds are supersets).
Dynamic Operator: The definition of a settle operator that transforms conjectural commitments into factual establishment, modeling the evolution of epistemic states (e.g., scientific consensus) without deleting competing capta.
Phenomena Characterization: Formal definitions for epistemically relevant phenomena:
- Disagreement: Incompatibility between two cognitive worlds.
- Delusion: Incompatibility between a cognitive world and the reality graph.
- Personal Opinion: Cognitive worlds detached from reality (neither supported nor refuted by facts).
Prototype Implementation: A DEC reasoner implemented as a Fuseki dataset module. It supports named graphs, RDF-star (quoted triples), and reification. The reasoner applies permeation policies, delegates standard RDF/OWL inference to the underlying engine, and optionally detects disagreements and delusions.

Results
The paper demonstrates that the DEC framework can be operationalized over standard Semantic Web technologies. The prototype reasoner successfully:

Identifies cognitive worlds and assigns DEC types based on governing predicates or explicit typing.
Materializes permeated triples (e.g., injecting facts into conjectural worlds or epistemic statements into reality).
Performs standard RDF/RDFS/OWL inference on the permeated graphs.
Detects inconsistencies. Using dec:checkInconsistencies, it identifies logical conflicts via the underlying reasoner. Using dec:closedFor, it detects epistemic disagreements based on explicit closure constraints (e.g., mutually exclusive authorship claims) even when standard OWL reasoning would not flag an inconsistency.
Preserves delusional or disagreeing statements as queryable metadata rather than deleting them, maintaining the historical and scholarly record of capta.

Significance
The paper claims that DEC provides a principled semantic characterization of provenance-enhanced statements, bridging the gap between the representation of capta and factual commitment. By treating provenance as an indicator of epistemic stance, DEC enables KGs to represent divergence, disagreement, and uncertainty explicitly without collapsing into inconsistency. It resolves historical barriers to epistemic reasoning in the Semantic Web, such as the Superman paradox, through intensional semantics. The framework allows for the coexistence of multiple perspectives (theories, beliefs, hypotheses) and supports the analysis of their relationships to reality and to each other, thereby preserving the informational richness of scholarly and scientific debates within knowledge graphs.