Ontology Summit talk by Majumdar and Sowa

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John F Sowa

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Aug 11, 2026, 5:20:57 PM (2 days ago) Aug 11
to ontolo...@googlegroups.com, CG, Arun Majumdar
James Lee Stakelum wrote a favorable, detailed, and quite accurate review of the talk by Arun and me in the Ontology Summit.   He has no association with Permion, and neither of us was aware that he was writing a review.  Copy below.

In his review, the author also shows why the triple store representation used by OWL and related software is obsolete.  Legacy software will have to be supported indefinitely, but OWL and triple stores should never be used for new systems.  (But newer more general systems can easily accept triples from legacy software.)

By the way, the author notes that Arun was giving a demo on a laptop, which showed rapid response to complex questions on large amounts of data.  Permion customers run much larger amounts of data on much larger systems. But they do not require the immense numbers of Nvidia chips with the acres of space and rivers of water to cool them.

The author includes comments and comparisons with his own SGF system.  Since Arun and I are not familiar with it, we won't comment on it.  For more information, see his links below.

John
_________

The Architecture That Makes AI Trustworthy Wasn’t Invented. It Was Discovered

by James Lee Stakelum

John Sowa and Arun Majumdar demonstrated a breakthrough inference engine at the 2026 Ontology Summit — twelve agents on a laptop, no GPU, refusing to guess. But the architecture beneath it inherits an open-predicate model that has failed at scale every time it has been tried. This article reveals the convergence between Permion’s engineering and an open architecture called the Symbol Grounding Framework, and explains why the bridge between them will define the next decade of trustworthy AI.

1. The Scene

The Ontology Summit. June 3, 2026. John Sowa takes the virtual podium. He is 86 years old. Co-author of the ISO 24707 Common Logic standard. Creator of conceptual graphs. Six decades of work in knowledge representation.

He begins, as he often does, with a warning.

“Anything generated by LLMs is basically a hypothesis,” he says. “It’s a best guess. If it’s inconsistent with the ontology or a verified database, it might be rejected as false.”

This is vintage Sowa. He has been saying this since before LLMs existed. The message is not new. What is new is the context. He is speaking as a Fellow of Permion, a company that just won the G7 GovAI Grand Challenge against over a hundred submissions from across the G7 and EU.

Then Arun Majumdar, Permion’s CEO, takes over. He opens a terminal on a standard MacBook Pro — an Apple M1 Max from 2021, 64 GB of RAM, no GPU. He runs a command. The machine starts processing 100 HTML documents. It uses a graph-based ranking algorithm derived from TextRank, co-authored by the late Paul Tarau, a Permion researcher. It selects the relevant documents. It runs twelve LLM agents simultaneously. Each contributes to a structured threat assessment report. The system processes 9,000 tokens per second. The logic engine — built on Definite Clause Grammars and Common Logic — governs the entire process. If an agent cannot answer, it does not guess. The final report is structured, cited, and formatted precisely.

Twelve agents. On a laptop. No cloud. No GPU.

This is not a vaporware demo. This is running on hardware anyone can buy.

2. What Permion Actually Achieved

The demo deserves attention on its own terms.

Running twelve LLMs simultaneously on a consumer laptop represents a fundamental shift in how AI systems can be deployed. Most multi-agent architectures require cloud infrastructure — GPU clusters, high-bandwidth interconnects, centralized orchestration. Permion’s approach runs locally. Every document stays on the machine. Every inference happens on the device. No data leaves the air gap.

Their disk streaming technology is a genuine engineering achievement. Instead of loading entire models into RAM, it indexes the model, predicts which tensors will be needed for a given query, and streams only those tensors from SSD to memory. A system that cannot fit in RAM can still run in real time.

Their Definite Clause Grammar provides semantic constraints that regular expressions cannot express. Variables carry type restrictions. The grammar knows what kind of thing can go where. Their graph-based ranking algorithm, derived from TextRank, finds relevant documents without the blind spots of chunk-based RAG. Their logic engine controls generation, validates outputs, and enforces policy.

This matters beyond the technology itself. Local-first, sovereign AI — running on hardware you own, processing data that never leaves your control — is the only architecture that can meet the security and privacy requirements of government, defense, and regulated industries. Permion has demonstrated that this is not a theoretical possibility but a working reality.

They also won the G7 GovAI Grand Challenge. The problem set was cross-risk geopolitical analysis — a genuinely complex, open-ended problem. Their DSME application won for its explainability, auditability, and compliance. It is deployed on AWS GovCloud and the AWS classified cloud.

Sowa provided the philosophical foundation that makes the architecture coherent. He described Charles Peirce’s cycle of pragmatism: abduction proposes hypotheses, deduction evaluates them against an ontology, action tests them, induction incorporates what was learned into knowledge. This cycle — observe, orient, decide, act — is the fundamental pattern of intelligence. Any system that skips the deduction step cannot be trusted.

For a moment, it seemed complete. Here was a company with both the deep understanding and the engineering to build trustworthy AI.

3. The Structural Inheritance

But the engineering and the architecture are two different layers.

Permion uses Common Logic — ISO 24707 — as its representational foundation. Common Logic is a standard for exchanging first-order logic expressions. It is flexible. Any domain expert can define any relation their field requires. In medicine, you can define has_contraindication. In law, statutory_precedence. In aerospace, is_aerodynamically_coupled_with. The predicate vocabulary is open.

This flexibility is a real strength for a single organization. It allows domain experts to express knowledge in whatever terms are natural to their field.

The architecture also uses conceptual graphs, where relations are edges between concept nodes. Subject-predicate-object. The predicate is the connecting edge. This is the standard approach. It is well-understood and widely deployed.

But Common Logic is an open-predicate system. So is RDF. So is OWL. The Semantic Web was built on this same open-predicate foundation, and it failed at scale. Not because the technology was wrong. Because the cost of integration grows quadratically with the number of participants.

Consider two organizations. Organization A defines owes. Organization B defines has_contraindication. Integration requires one mapping. Three organizations require three mappings. Four require six. Ten require forty-five. One hundred require four thousand nine hundred and fifty.

This is the Babel Tax. It is not a theoretical risk. It is a demonstrated failure mode that the Semantic Web community documented over 25 years. The open-predicate model is structurally incapable of escaping it. Every new participant adds new predicates. Every new predicate requires new mappings. The cost compounds.

Permion’s architecture inherits this property because Common Logic, like RDF and OWL, allows any relation to be defined by any party. The demo runs on one machine. The architecture would face the same federation barrier that every open-predicate system has faced.

There is a second inherited weakness. In the edge-based model, an event like “Beethoven composed the Ninth Symphony in Vienna in 1824” becomes three separate fragments:

  • Beethoven composed Ninth Symphony.
  • Ninth Symphony was created in 1824.
  • Beethoven was in Vienna in 1824.

Each fragment is correct. None preserves the unity of the event. A query that asks “what was Beethoven doing in Vienna in 1824?” must reassemble the pieces. The event is not a first-class object. It is a reconstruction.

And there is a third. A verified fact and a provisional guess share the same structural form. Both are Common Logic statements. They are distinguished only by external policy, not by the structure of the claim itself. The demo showed the right behavior — the system refused to guess. But the architecture did not enforce it. The behavior was governed by policy, not by structure.

These are not flaws in Permion’s implementation. They are properties of the underlying standard. Permion’s engineers inherited them.

4. The Discovery

I found the Symbol Grounding Framework through a different path — not through the ontology community, but through the knowledge graph and reasoning community. It was not a product. It was a public-domain architecture, published at symbolgrounding.io, with reference code under Apache 2.0.

SGF starts from a different question than Permion does. Permion asks: how do we make inference fast on a single machine? SGF asks: how do we make meaning portable so that two systems that have never met can trust each other on first contact?

The answer was discovered through a process the author calls the qualification gauntlet. It works like this: propose a candidate structure. Subject it to adversarial tests designed to destroy it. If it can be eliminated, eliminate it. Keep only what survives.

The architect began with a hundred candidate semantic roles. Each was tested: could it be expressed as a combination of the others? If yes, it was eliminated. HAS_PURPOSE was eliminated — it is HAS_REASON with a specific frame. HAS_RESULT was eliminated — it is a changed HAS_PATIENT or a separate SynapseLink. HAS_VALUE was eliminated — it is a TypedLiteral or HAS_ATTRIBUTE.

The first pass killed forty. The second killed thirty more. When the dust settled, fifteen roles survived. They were not chosen. They could not be eliminated.

The same process was applied to binary relations. Five survived. To link types. Eight survived. To the verb vocabulary. One generic verb survived — RELATES_TO — with domain-specific relations expressed as concepts rather than primitives.

The result is a grammar of 33 primitives that is closed by construction. Vocabulary is infinite. The grammar is fixed. Integration cost becomes linear. The Babel Tax is not managed or reduced. It is structurally prevented.


But the architecture goes deeper.


Every claim carries an epistemic status from 7 tiers: CORE_DEFINITION, CONSTITUTIVE, SOURCED, CLAIMED, INFERRED, PROVISIONAL, GHOST. A verified fact from WordNet and a provisional guess from an LLM are structurally distinct. The reasoning engine treats them differently by construction, not by policy.

When a term cannot be grounded, SGF cannot guess. There is no mechanism for it. The grammar requires all Spokes to target grounded Canonical IDs or explicitly marked Ghosts. A Ghost node carries a provisional identifier and a GapReport. The system says “I don’t know” because it literally cannot produce a claim without a grounded target.

Below everything sits the Prime Registry. Approximately 65 semantic primes — SOMEONE, SOMETHING, DO, HAPPEN, MOVE, GOOD, BAD, THINK, KNOW, BEFORE, AFTER, HERE, NOW — serve as the bedrock. Every grounded concept must have a finite path down to one or more of these primes. This enables the Stranger Rule: two systems that have never met can understand each other on first contact because every term in an HFF packet can be traced back to shared primes.

Above it all sits Omega, a governance language that compiles policy into deterministic checks. UNKNOWN maps to HALT. The system halts rather than guessing.

Each mechanism exists because a simpler one failed. The open-predicate model failed at scale, so the grammar was closed. The edge-based model fragmented events, so the verb became the hub. The absence of epistemic tracking made facts indistinguishable from guesses, so the status hierarchy was built. The inability to say “I don’t know” allowed hallucinations to propagate, so the Ghost Protocol was created. The lack of a stopping rule for definitions allowed infinite regress, so the Prime Registry was established.

The architecture was not designed on a whiteboard. It was discovered by systematically eliminating everything that broke.

5. The Convergence

I went back to the 2024 video. Sowa said: “Without ontology, LLMs are clueless.”

I went back to the 2026 demo. Majumdar said: “LLMs are abduction machines. They create hypotheses.”

Then I looked at the SGF architecture.

Sowa said every output must be tested by deduction. SGF has an epistemic status hierarchy that structurally classifies every claim.

Sowa said reasoning is a cycle of abduction, deduction, induction, action. SGF has a Semantic CPU that walks a grounded graph in exactly this cycle.

Sowa said the system must refuse to guess when uncertain. SGF has a Ghost Protocol and a GapReport that make “I don’t know” a first-class output.

Majumdar showed twelve agents running under a logic engine that controls generation and refuses hallucination. SGF provides the wire protocol and governance language that let those same agents interoperate across organizational boundaries without the quadratic cost of the Babel Tax.

Two independent efforts. Different starting premises. Same structural conclusion.

What Sowa and Majumdar described What SGF provides LLMs are hypothesis generators that must be tested The Probabilistic Sandwich — LLMs propose, gates dispose Outputs must be verified against an ontology Epistemic status hierarchy, SOAM alignment, ProofTrace Reasoning is a cycle of abduction, deduction, induction, action Semantic CPU — deterministic kernel walking grounded graph Multiple agents must be orchestrated under logic HFF/AFP wire protocol for multi-agent coordination The system must refuse to answer when uncertain Ghost Protocol and GapReport An ontology must provide the criteria for truth Closed grammar, Prime Registry, Omega governance

The convergence is not a coincidence. The architecture is not one design among many. It is the shape that emerges when you eliminate everything that does not work.

6. The Complementarity

The two efforts are not in competition. They operate at different layers.

Permion’s inference engine is a breakthrough in local-first, multi-agent AI. Twelve agents on a laptop with no GPU. Disk streaming that makes models larger than RAM runnable in real time. A logic engine that refuses to guess. These are genuine achievements.

SGF’s closed grammar prevents the Babel Tax that has crippled every open-predicate system at scale. Its epistemic hierarchy makes the trustworthiness of every claim structurally explicit. Its Ghost Protocol ensures the system cannot guess. Its Stranger Rule enables federation on first contact. Its governance language compiles policy into deterministic checks.

One builds the engine. The other builds the chassis, the steering, and the brakes.

Permion could implement SGF on their XVM. The closed grammar would eliminate the quadratic integration cost. The epistemic hierarchy would make claim trustworthiness structural. The Ghost Protocol would make “I don’t know” an architectural invariant. The Stranger Rule would enable their multi-agent systems to federate across organizational boundaries on first contact.

SGF is public domain. Anyone can implement it. Including Permion.

7. What This Means

For AI architects building the next generation of multi-agent systems. The question is no longer whether a closed grammar, an epistemic hierarchy, a gap protocol, and a prime registry are architecturally necessary. The convergence proves they are. The open standard exists at symbolgrounding.io. You can implement it today.

For knowledge graph engineers who have lived through the Babel Tax. The open-predicate model has been the bottleneck for thirty years. SGF’s closed grammar eliminates the quadratic integration cost. Vocabulary is infinite. Grammar is fixed. Integration cost is linear. The architecture exists today.

For venture capitalists looking for the next infrastructure wave. The market for trustworthy AI coordination is larger than the market for AI inference. The convergence proves the architecture is necessary. The specification is open. The opportunity is in the implementation layer.

For ontologists and knowledge representation researchers. Sowa’s pragmatic cycle has been validated by independent discovery. The fifteen semantic roles are the universal joints of machine meaning. The convergence is evidence that the field is converging on a structural consensus.

For Permion. Your inference engine is a breakthrough. The engineering is real. The architectural layer that makes it scale across organizational boundaries is available now, in the public domain, ready to implement.

8. The Invitation

The architecture for trustworthy AI was not designed in a boardroom. It was discovered by elimination. Two independent teams, starting from different premises, arrived at the same structural conclusion. That convergence is evidence that the architecture is necessary, not optional.

Permion built the fastest local-first inference engine in production. Twelve agents. No GPU. Nine thousand tokens per second. The G7 winner.

SGF provides the semantic substrate that makes that engine scalable across organizational boundaries without the Babel Tax.

One builds the machine. The other preserves the meaning.

The code is in the public domain. The specifications are published. The bridge between them has not been built yet.

The blueprints are on the table. The engine is running. The question is no longer whether this architecture works. The question is who will build the integration layer first.

That answer will define the next decade of trustworthy machine intelligence.

Learn more about SGF

You can learn more about SGF on its GitHub repository: https://github.com/SymbolGroundingFramework/SGF-manifest

RFC specifications: https://github.com/SymbolGroundingFramework/SGF-manifest/tree/main/specs

The six‑volume SGF book series: https://www.amazon.com/dp/B0H3FGSPK6





Simon Polovina

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Aug 12, 2026, 6:26:19 AM (2 days ago) Aug 12
to ontolo...@googlegroups.com, Arun Majumdar, CG

Hi all.

What I’ve written below (with the help of Gemini) may be of interest. My motivation is that I’m always asked, ‘Why use CGs? ’. I also refer to a real-world use case: SAP Business Data Cloud, as I have an SAP background. I’ve updated it for Stakelum’s review, as that article and John’s comment are pertinent.

Thanks for reading it and for helping me move the discussion forward.

Simon

 

Enterprise Knowledge Representation: Conceptual Graphs, ISO Common Logic, and SAP Graph Foundations

Simon Polovina

2026-08-12

Abstract

This document presents a comprehensive discussion of the theoretical and practical role of Conceptual Graphs (CGs) in enterprise architectures, their comparative expressivity relative to First-Order Logic (FOL), Description Logics (OWL), and RDF, and their alignment with the ISO/IEC 24707 Common Logic. Additionally, it highlights recent perspectives on trustworthy AI, open vs. closed predicate grammars, and evaluates the comparative landscape of SAP Graph, SAP HANA Knowledge Graph, and SAP Business Data Cloud (BDC) Knowledge Graph across CGIF and CLIF representations.

 

1 Introduction & Conceptual Graphs Overview

Conceptual Graphs (CGs), developed by John F. Sowa (Sowa 1984), bridge human-readable visual semantics with formal mathematical logic. As introduced in previous foundational work (Polovina 2007), CGs provide a versatile environment for knowledge representation and automated reasoning that directly aligns with enterprise object models.

Key structural advantages of CGs over alternative formalisms include:

  • Visual Syntax with FOL Rigour: CGs use an intuitive visual bipartite graph syntax (concepts and conceptual relations) while maintaining an exact mapping via the -operator to First-Order Logic.
  • Native -ary Relations: Unlike RDF triples (), CGs support -ary relations without artificial reification.
  • Nested Contexts: CGs support nested propositional contexts, allowing clean modal, temporal, and belief representations.
  • Graph-Based Reasoning: Operations such as graph projection, join, and restriction enable sound structural reasoning without requiring resolution theorem provers.

This paper evaluates these theoretical properties within modern enterprise architectures. Specifically, we analyse the trade-offs of RDF-based knowledge foundations in SAP Business Data Cloud (BDC) and demonstrate how ISO/IEC 24707 Common Logic representations (CGIF and CLIF) provide a more robust substrate for neuro-symbolic AI.

 

2 Trustworthy AI, Common Logic, and Closed Grammars

Recent discussions surrounding multi-agent systems and local-first AI architectures highlight the crucial distinction between open-predicate systems and closed relational grammars (Stakelum 2026). Unconstrained open predicates (found in RDF, OWL, and raw Common Logic) incur an integration bottleneck (the “Babel Tax”) when federating across independent domains.

By leveraging standardised specifications under ISO/IEC 24707 Common Logic (ISO/IEC 2018), architectures can combine bounded relational primitives with rich, open concept lattices (e.g., via Formal Concept Analysis), enabling sound neuro-symbolic reasoning without hallucination.

 

3 Comparing SAP Graph Architectures

Enterprise data foundations often combine multiple distinct graph paradigms. Table 1 outlines three core SAP graph technologies.

Comparison of SAP Graph Technologies

Feature/Aspect

SAP Graph

SAP HANA Knowledge Graph

SAP BDC Knowledge Graph

Primary Purpose

Unified API graph for cross-SAP integration

In-memory graph engine for HANA Cloud analytics

Business-context-aware semantic graph for AI

Scope

Cross-SAP application data

Technical graph database

Business processes, roles, and policies

Data Sources

S/4HANA, SuccessFactors, etc.

Relational, spatial, and vector data in HANA

SAP and non-SAP data with embedded context

Deployment

SAP BTP

SAP HANA Cloud

SAP BTP (BDC Architecture)

Query Languages

SPARQL, SQL

SPARQL, Cypher, SQL

SPARQL, SQL

AI Enablement

High

Medium

Very High

Among these paradigms, the SAP BDC Knowledge Graph represents the most context-aware layer for enterprise AI. However, as evaluated in the following section, its technical implementation on an RDF triple-store foundation introduces structural friction that could be mitigated by a Conceptual Graph architecture.

 

4 Replacing RDF with Conceptual Graphs in Enterprise Data Foundations

Replacing Resource Description Framework (RDF) with Conceptual Graphs (CGs) in enterprise data foundations—such as the SAP Knowledge Graph capability and its technical implementation in SAP Business Data Cloud (BDC)—would fundamentally transform how enterprise AI, multi-agent systems, and business process models interact with underlying ERP data.

While SAP chose RDF for the SAP Knowledge Graph engine in SAP BDC primarily to leverage established SPARQL standards and existing triple-store tech, opting for a Conceptual Graph foundation would have solved several structural challenges inherent to large-scale ERP semantic layers.

4.1         Architectural Impact: RDF vs. Conceptual Graphs in Enterprise Systems

4.1.1     Eliminating -ary Reification in Complex Business Transactions

The RDF Reality: Standard ERP business entities rarely fit neat binary triples (). An SAP purchase order line item involves a vendor, material, quantity, plant, currency, pricing condition, and tax code. In RDF, representing this -ary transaction requires extensive reification or artificial intermediate nodes, bloating the number of triples into the billions and degrading SPARQL join performance.

The CG Advantage: CGs natively support -ary relation nodes linked directly to concept nodes. A multi-party sales order or supply chain movement remains a single, unfragmented hypergraph node. This drastically reduces graph size, avoids join overhead, and makes the schema mirror actual SAP business objects (BAPIs/IDocs) directly.

4.1.2     Built-in Modal Logic for SAP Business Contexts

The RDF Reality: Enterprise data is deeply contextual. A price isn’t just “100 EUR”; it is valid from date to , under condition type , within company code , and subject to a pending workflow approval. RDF lacks a native concept of contexts, forcing developers to resort to Named Graphs or annotations—which break standard triple semantics and fragment reasoning engines.

The CG Advantage: Conceptual Graphs feature nested contexts as a core primitive. A belief state, a temporal validity window, a hypothetical “what-if” planning scenario, or an unapproved workflow step can be cleanly enclosed within a context box. Reasoning rules apply precisely inside specified contexts without leaking state into the broader knowledge base.

4.1.3     Direct Neuro-Symbolic Grounding for AI Agents (Joule & LLM Orchestration)

The RDF Reality: Modern enterprise architectures (like SAP’s Business AI Hub and SAP Knowledge Graph) use Knowledge Graphs to ground LLM agents and prevent hallucinations. However, converting LLM outputs into SPARQL triple patterns is notoriously fragile due to predicate drift, URI matching issues, and rigid triple structures.

The CG Advantage: CGs support graph projection—a sound and complete mechanism for pattern matching. An LLM acting as an abductive engine can propose a tentative solution in Conceptual Graph Linear Form (CGLF/CGIF). The engine uses projection to test if the proposed structure is a valid specialisation of an existing business rule or schema. If the projection fails, the logic engine rejects the hypothesis or pinpoints the exact ungrounded concept.

4.1.4     Convergence with ISO Standards

While RDF is a W3C web recommendation optimised for web-scale linking, CGs align directly with ISO/IEC 24707 Common Logic (ISO/IEC 2018). In enterprise ERP systems where auditability, compliance, and deterministic business rules are non-negotiable, having an underlying representation that translates losslessly into First-Order Logic provides a stronger governance guarantee than triple-store heuristics.

Structural Dimension

SAP Knowledge Graph on RDF (in BDC)

Conceptual Graph Alternative

Transaction Modelling

Fragmented into binary triples via reification

Native -ary structures preserving event unity

Business Contexts & Rules

Named Graphs / Annotations (Ad-hoc)

First-class Nested Contexts

Reasoning Mechanism

Tableau-based subsumption / RDFS rules

Graph Projection, Join, and Restriction

Agent AI Grounding

SPARQL translation (prone to join complexity)

Structural graph projection & unification

Schema Complexity

Quadratic expansion of edge types (Babel Tax risk)

Compact type hierarchies mapped to business objects

4.2 Why Didn’t SAP Do It?

The barrier has never been theoretical superiority—it has been ecosystem momentum. The RDF/SPARQL stack offered off-the-shelf open-source parsers, mature triple-store database engines, and an established developer base familiar with Semantic Web tooling. Implementing CGs natively would have required SAP to build and maintain a commercial-grade ISO Common Logic graph engine from scratch.

However, as enterprise systems pivot toward neuro-symbolic AI and local multi-agent orchestration, the architectural overhead of triple stores is becoming a bottleneck. Systems designed around -ary events, nested contexts, and graph projection are proving far better suited for grounding autonomous agents than legacy triple stores.

 

5 Formal Logic Representations: CGIF and CLIF

5.1 Conceptual Graph Interchange Format (CGIF)

Below is the linear CG serialisation of the comparison among the three SAP technologies, adhering, through CGIF,  to ISO/IEC 24707 standards (ISO/IEC 2018).

[Comparison: Study_SAP_Graphs] -
   (compares)-> [Technology: SAP_Graph],
   (compares)-> [Technology: SAP_HANA_Knowledge_Graph],
   (compares)-> [Technology: SAP_BDC_Knowledge_Graph].

[Technology: SAP_Graph] -
   (primaryPurpose)-> [Purpose: "Unified graph service for cross-SAP application integration"],
   (scope)-> [Scope: "Cross-SAP application data integration"],
   (deployment)-> [Platform: "SAP BTP"],
   (aiEnablement)-> [Rating: "High"].

[Technology: SAP_HANA_Knowledge_Graph] -
   (primaryPurpose)-> [Purpose: "Graph engine for storing/querying connected data in SAP HANA Cloud"],
   (scope)-> [Scope: "Technical graph database in HANA Cloud"],
   (deployment)-> [Platform: "SAP HANA Cloud"],
   (aiEnablement)-> [Rating: "Medium"].

[Technology: SAP_BDC_Knowledge_Graph] -
   (primaryPurpose)-> [Purpose: "Business-context-aware graph for AI-driven process automation"],
   (scope)-> [Scope: "Business semantics, processes, and context"],
   (deployment)-> [Platform: "SAP BTP"],
   (aiEnablement)-> [Rating: "Very High"].

5.2         Common Logic Interchange Format (CLIF)

The corresponding ISO 24707 CLIF representation provides a direct Lisp-style S-expression syntax suitable for first-order logic provers.

(cl-text SAP_Graph_Comparison_Ontology

  (cl-comment "Root Comparison Structure")
  (Comparison Study_SAP_Graphs)
  (compares Study_SAP_Graphs SAP_Graph)
  (compares Study_SAP_Graphs SAP_HANA_Knowledge_Graph)
  (compares Study_SAP_Graphs SAP_BDC_Knowledge_Graph)

  (cl-comment "SAP Graph Assertions")
  (Technology SAP_Graph)
  (primaryPurpose SAP_Graph "Unified graph service for cross-SAP application integration")
  (deploymentEnvironment SAP_Graph SAP_BTP)
  (aiEnablementLevel SAP_Graph High)

  (cl-comment "SAP HANA Knowledge Graph Assertions")
  (Technology SAP_HANA_Knowledge_Graph)
  (primaryPurpose SAP_HANA_Knowledge_Graph "Graph engine for storing/querying connected data in SAP HANA Cloud")
  (deploymentEnvironment SAP_HANA_Knowledge_Graph SAP_HANA_Cloud)
  (aiEnablementLevel SAP_HANA_Knowledge_Graph Medium)

  (cl-comment "SAP BDC Knowledge Graph Assertions")
  (Technology SAP_BDC_Knowledge_Graph)
  (primaryPurpose SAP_BDC_Knowledge_Graph "Business-context-aware graph for AI-driven process automation")
  (deploymentEnvironment SAP_BDC_Knowledge_Graph SAP_BTP)
  (aiEnablementLevel SAP_BDC_Knowledge_Graph VeryHigh)

  (cl-comment "General Inference Rule")
  (forall (x)
    (if (and (Technology x)
             (deploymentEnvironment x SAP_BTP)
             (aiEnablementLevel x VeryHigh))
        (BusinessContextAware x)))
)

 

6 Conclusion

While modern enterprise platforms such as SAP Business Data Cloud have successfully adopted RDF triple stores to build context-aware Knowledge Graphs, standard binary triple models introduce significant overhead when representing complex -ary business transactions and nested modal contexts. As demonstrated in this analysis, adopting Conceptual Graphs (CGs) directly resolves these structural bottlenecks through native -ary relations, first-class nested contexts, and graph-projection reasoning.

Furthermore, grounding enterprise architectures in ISO/IEC 24707 Common Logic provides the deterministic First-Order Logic rigour required for trustworthy neuro-symbolic AI and autonomous agent orchestration. By formalising enterprise semantic layers in standardised serialisations like CGIF and CLIF, enterprise architectures can bypass the combinatorial integration challenges of unconstrained open predicates while guaranteeing verifiable, hallucination-free decision support across complex business domains.

 

References

ISO/IEC. 2018. ISO/IEC 24707:2018 Information technology — Common Logic (CL): A framework for a family of logic-based languages. International Organization for Standardization.

Polovina, Simon. 2007. “An Introduction to Conceptual Graphs.” In Conceptual Structures: Knowledge Architectures for Smart Applications. Proceedings of the 15th International Conference on Conceptual Structures (ICCS 2007), edited by Uta Priss, Simon Polovina, and Richard Hill, vol. 4604. Lecture Notes in Artificial Intelligence. Springer-Verlag. https://doi.org/10.1007/978-3-540-73681-3_1.

Sowa, John F. 1984. Conceptual Structures: Information Processing in Mind and Machine. Addison-Wesley.

Stakelum, James Lee. 2026. The Architecture That Makes AI Trustworthy Wasn’t Invented. It Was Discovered. Review of the Ontology Summit 2026 Presentation by Arun Majumdar and John F. Sowa.

 

From: ontolo...@googlegroups.com <ontolo...@googlegroups.com> On Behalf Of John F Sowa
Sent: 11 August 2026 22:20
To: ontolo...@googlegroups.com; CG <c...@lists.iccs-conference.org>
Cc: Arun Majumdar <ar...@permion.ai>
Subject: [ontolog-forum] Ontology Summit talk by Majumdar and Sowa

 

Enterprise Knowledge Representation: Conceptual Graphs, ISO Common Logic, and SAP Graph Foundations

Simon Polovina

2026-08-12

Abstract

This document presents a comprehensive discussion of the theoretical and practical role of Conceptual Graphs (CGs) in enterprise architectures, their comparative expressivity relative to First-Order Logic (FOL), Description Logics (OWL), and RDF, and their alignment with the ISO/IEC 24707 Common Logic. Additionally, it highlights recent perspectives on trustworthy AI, open vs. closed predicate grammars, and evaluates the comparative landscape of SAP Graph, SAP HANA Knowledge Graph, and SAP Business Data Cloud (BDC) Knowledge Graph across CGIF and CLIF representations.

1        Introduction & Conceptual Graphs Overview

Conceptual Graphs (CGs), developed by John F. Sowa (Sowa 1984), bridge human-readable visual semantics with formal mathematical logic. As introduced in previous foundational work (Polovina 2007), CGs provide a versatile environment for knowledge representation and automated reasoning that directly aligns with enterprise object models.

Key structural advantages of CGs over alternative formalisms include:

  • Visual Syntax with FOL Rigour: CGs use an intuitive visual bipartite graph syntax (concepts and conceptual relations) while maintaining an exact mapping via the -operator to First-Order Logic.
  • Native -ary Relations: Unlike RDF triples (), CGs support -ary relations without artificial reification.
  • Nested Contexts: CGs support nested propositional contexts, allowing clean modal, temporal, and belief representations.
  • Graph-Based Reasoning: Operations such as graph projection, join, and restriction enable sound structural reasoning without requiring resolution theorem provers.

This paper evaluates these theoretical properties within modern enterprise architectures. Specifically, we analyse the trade-offs of RDF-based knowledge foundations in SAP Business Data Cloud (BDC) and demonstrate how ISO/IEC 24707 Common Logic representations (CGIF and CLIF) provide a more robust substrate for neuro-symbolic AI.

2        Trustworthy AI, Common Logic, and Closed Grammars

Recent discussions surrounding multi-agent systems and local-first AI architectures highlight the crucial distinction between open-predicate systems and closed relational grammars (Stakelum 2026). Unconstrained open predicates (found in RDF, OWL, and raw Common Logic) incur an integration bottleneck (the “Babel Tax”) when federating across independent domains.

By leveraging standardised specifications under ISO/IEC 24707 Common Logic (ISO/IEC 2018), architectures can combine bounded relational primitives with rich, open concept lattices (e.g., via Formal Concept Analysis), enabling sound neuro-symbolic reasoning without hallucination.

3        Comparing SAP Graph Architectures

Enterprise data foundations often combine multiple distinct graph paradigms. Table 1 outlines three core SAP graph technologies.

Comparison of SAP Graph Technologies

Feature/Aspect

SAP Graph

SAP HANA Knowledge Graph

SAP BDC Knowledge Graph

Primary Purpose

Unified API graph for cross-SAP integration

In-memory graph engine for HANA Cloud analytics

Business-context-aware semantic graph for AI

Scope

Cross-SAP application data

Technical graph database

Business processes, roles, and policies

Data Sources

S/4HANA, SuccessFactors, etc.

Relational, spatial, and vector data in HANA

SAP and non-SAP data with embedded context

Deployment

SAP BTP

SAP HANA Cloud

SAP BTP (BDC Architecture)

Query Languages

SPARQL, SQL

SPARQL, Cypher, SQL

SPARQL, SQL

AI Enablement

High

Medium

Very High

Among these paradigms, the SAP BDC Knowledge Graph represents the most context-aware layer for enterprise AI. However, as evaluated in the following section, its technical implementation on an RDF triple-store foundation introduces structural friction that could be mitigated by a Conceptual Graph architecture.

4        Replacing RDF with Conceptual Graphs in Enterprise Data Foundations

Replacing Resource Description Framework (RDF) with Conceptual Graphs (CGs) in enterprise data foundations—such as the SAP Knowledge Graph capability and its technical implementation in SAP Business Data Cloud (BDC)—would fundamentally transform how enterprise AI, multi-agent systems, and business process models interact with underlying ERP data.

While SAP chose RDF for the SAP Knowledge Graph engine in SAP BDC primarily to leverage established SPARQL standards and existing triple-store tech, opting for a Conceptual Graph foundation would have solved several structural challenges inherent to large-scale ERP semantic layers.

4.1     Architectural Impact: RDF vs. Conceptual Graphs in Enterprise Systems

4.1.1  1. Eliminating -ary Reification in Complex Business Transactions

The RDF Reality: Standard ERP business entities rarely fit neat binary triples (). An SAP purchase order line item involves a vendor, material, quantity, plant, currency, pricing condition, and tax code. In RDF, representing this -ary transaction requires extensive reification or artificial intermediate nodes, bloating the number of triples into the billions and degrading SPARQL join performance.

The CG Advantage: CGs natively support -ary relation nodes linked directly to concept nodes. A multi-party sales order or supply chain movement remains a single, unfragmented hypergraph node. This drastically reduces graph size, avoids join overhead, and makes the schema mirror actual SAP business objects (BAPIs/IDocs) directly.

4.1.2  2. Built-in Modal Logic for SAP Business Contexts

The RDF Reality: Enterprise data is deeply contextual. A price isn’t just “100 EUR”; it is valid from date to , under condition type , within company code , and subject to a pending workflow approval. RDF lacks a native concept of contexts, forcing developers to resort to Named Graphs or annotations—which break standard triple semantics and fragment reasoning engines.

The CG Advantage: Conceptual Graphs feature nested contexts as a core primitive. A belief state, a temporal validity window, a hypothetical “what-if” planning scenario, or an unapproved workflow step can be cleanly enclosed within a context box. Reasoning rules apply precisely inside specified contexts without leaking state into the broader knowledge base.

4.1.3  3. Direct Neuro-Symbolic Grounding for AI Agents (Joule & LLM Orchestration)

The RDF Reality: Modern enterprise architectures (like SAP’s Business AI Hub and SAP Knowledge Graph) use Knowledge Graphs to ground LLM agents and prevent hallucinations. However, converting LLM outputs into SPARQL triple patterns is notoriously fragile due to predicate drift, URI matching issues, and rigid triple structures.

The CG Advantage: CGs support graph projection—a sound and complete mechanism for pattern matching. An LLM acting as an abductive engine can propose a tentative solution in Conceptual Graph Linear Form (CGLF/CGIF). The engine uses projection to test if the proposed structure is a valid specialisation of an existing business rule or schema. If the projection fails, the logic engine rejects the hypothesis or pinpoints the exact ungrounded concept.

4.1.4  4. Convergence with ISO Standards

While RDF is a W3C web recommendation optimised for web-scale linking, CGs align directly with ISO/IEC 24707 Common Logic (ISO/IEC 2018). In enterprise ERP systems where auditability, compliance, and deterministic business rules are non-negotiable, having an underlying representation that translates losslessly into First-Order Logic provides a stronger governance guarantee than triple-store heuristics.

Structural Dimension

SAP Knowledge Graph on RDF (in BDC)

Conceptual Graph Alternative

Transaction Modelling

Fragmented into binary triples via reification

Native -ary structures preserving event unity

Business Contexts & Rules

Named Graphs / Annotations (Ad-hoc)

First-class Nested Contexts

Reasoning Mechanism

Tableau-based subsumption / RDFS rules

Graph Projection, Join, and Restriction

Agent AI Grounding

SPARQL translation (prone to join complexity)

Structural graph projection & unification

Schema Complexity

Quadratic expansion of edge types (Babel Tax risk)

Compact type hierarchies mapped to business objects

4.2     Why Didn’t SAP Do It?

The barrier has never been theoretical superiority—it has been ecosystem momentum. The RDF/SPARQL stack offered off-the-shelf open-source parsers, mature triple-store database engines, and an established developer base familiar with Semantic Web tooling. Implementing CGs natively would have required SAP to build and maintain a commercial-grade ISO Common Logic graph engine from scratch.

However, as enterprise systems pivot toward neuro-symbolic AI and local multi-agent orchestration, the architectural overhead of triple stores is becoming a bottleneck. Systems designed around -ary events, nested contexts, and graph projection are proving far better suited for grounding autonomous agents than legacy triple stores.

5        Formal Logic Representations: CGIF and CLIF

5.1     Conceptual Graph Interchange Format (CGIF)

Below is the CGIF serialisation of the comparison among the three SAP technologies, adhering to ISO/IEC 24707 standards (ISO/IEC 2018).

[Comparison: Study_SAP_Graphs] -
   (compares)-> [Technology: SAP_Graph],
   (compares)-> [Technology: SAP_HANA_Knowledge_Graph],
   (compares)-> [Technology: SAP_BDC_Knowledge_Graph].

[Technology: SAP_Graph] -
   (primaryPurpose)-> [Purpose: "Unified graph service for cross-SAP application integration"],
   (scope)-> [Scope: "Cross-SAP application data integration"],
   (deployment)-> [Platform: "SAP BTP"],
   (aiEnablement)-> [Rating: "High"].

[Technology: SAP_HANA_Knowledge_Graph] -
   (primaryPurpose)-> [Purpose: "Graph engine for storing/querying connected data in SAP HANA Cloud"],
   (scope)-> [Scope: "Technical graph database in HANA Cloud"],
   (deployment)-> [Platform: "SAP HANA Cloud"],
   (aiEnablement)-> [Rating: "Medium"].

[Technology: SAP_BDC_Knowledge_Graph] -
   (primaryPurpose)-> [Purpose: "Business-context-aware graph for AI-driven process automation"],
   (scope)-> [Scope: "Business semantics, processes, and context"],
   (deployment)-> [Platform: "SAP BTP"],
   (aiEnablement)-> [Rating: "Very High"].

5.2     Common Logic Interchange Format (CLIF)

The corresponding ISO 24707 CLIF representation provides a direct Lisp-style S-expression syntax suitable for first-order logic provers.

(cl-text SAP_Graph_Comparison_Ontology

  (cl-comment "Root Comparison Structure")
  (Comparison Study_SAP_Graphs)
  (compares Study_SAP_Graphs SAP_Graph)
  (compares Study_SAP_Graphs SAP_HANA_Knowledge_Graph)
  (compares Study_SAP_Graphs SAP_BDC_Knowledge_Graph)

  (cl-comment "SAP Graph Assertions")
  (Technology SAP_Graph)
  (primaryPurpose SAP_Graph "Unified graph service for cross-SAP application integration")
  (deploymentEnvironment SAP_Graph SAP_BTP)
  (aiEnablementLevel SAP_Graph High)

  (cl-comment "SAP HANA Knowledge Graph Assertions")
  (Technology SAP_HANA_Knowledge_Graph)
  (primaryPurpose SAP_HANA_Knowledge_Graph "Graph engine for storing/querying connected data in SAP HANA Cloud")
  (deploymentEnvironment SAP_HANA_Knowledge_Graph SAP_HANA_Cloud)
  (aiEnablementLevel SAP_HANA_Knowledge_Graph Medium)

  (cl-comment "SAP BDC Knowledge Graph Assertions")
  (Technology SAP_BDC_Knowledge_Graph)
  (primaryPurpose SAP_BDC_Knowledge_Graph "Business-context-aware graph for AI-driven process automation")
  (deploymentEnvironment SAP_BDC_Knowledge_Graph SAP_BTP)
  (aiEnablementLevel SAP_BDC_Knowledge_Graph VeryHigh)

  (cl-comment "General Inference Rule")
  (forall (x)
    (if (and (Technology x)
             (deploymentEnvironment x SAP_BTP)
             (aiEnablementLevel x VeryHigh))
        (BusinessContextAware x)))
)

6        Conclusion

While modern enterprise platforms such as SAP Business Data Cloud have successfully adopted RDF triple stores to build context-aware Knowledge Graphs, standard binary triple models introduce significant overhead when representing complex -ary business transactions and nested modal contexts. As demonstrated in this analysis, adopting Conceptual Graphs (CGs) directly resolves these structural bottlenecks through native -ary relations, first-class nested contexts, and graph-projection reasoning.

Furthermore, grounding enterprise architectures in ISO/IEC 24707 Common Logic provides the deterministic First-Order Logic rigour required for trustworthy neuro-symbolic AI and autonomous agent orchestration. By formalising enterprise semantic layers in standardised serialisations like CGIF and CLIF, enterprise architectures can bypass the combinatorial integration challenges of unconstrained open predicates while guaranteeing verifiable, hallucination-free decision support across complex business domains.

ISO/IEC. 2018. ISO/IEC 24707:2018 Information technology — Common Logic (CL): A framework for a family of logic-based languages. International Organization for Standardization.

Polovina, Simon. 2007. “An Introduction to Conceptual Graphs.” In Conceptual Structures: Knowledge Architectures for Smart Applications. Proceedings of the 15th International Conference on Conceptual Structures (ICCS 2007), edited by Uta Priss, Simon Polovina, and Richard Hill, vol. 4604. Lecture Notes in Artificial Intelligence. Springer-Verlag. https://doi.org/10.1007/978-3-540-73681-3_1.

Sowa, John F. 1984. Conceptual Structures: Information Processing in Mind and Machine. Addison-Wesley.

Stakelum, James Lee. 2026. The Architecture That Makes AI Trustworthy Wasn’t Invented. It Was Discovered. Review of the Ontology Summit 2026 Presentation by Arun Majumdar and John F. Sowa.

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Simon Polovina

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Aug 12, 2026, 6:49:22 AM (2 days ago) Aug 12
to ontolo...@googlegroups.com, Arun Majumdar, CG

Hi again all.

I’ve attached a cleaner version as a PDF. Please remember I used Gemini, so there may be residual howlers. Usually, I keep these as my internal draft ‘working’ documents, but in this case I thought it might be better to share it, given the recent discussion.

Thanks again,

Simon

Why_CGs.pdf

Kingsley Idehen

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Aug 12, 2026, 7:28:38 PM (2 days ago) Aug 12
to ontolo...@googlegroups.com, Arun Majumdar, John Sowa
Hi John,

On 8/11/26 5:20 PM, John F Sowa wrote:
In his review, the author also shows why the triple store representation used by OWL and related software is obsolete.  Legacy software will have to be supported indefinitely, but OWL and triple stores should never be used for new systems.  (But newer more general systems can easily accept triples from legacy software.)

I find the statement above a little confusing. 

What do you mean by OWL and triples stores? 

BTW -- I have a collection of live demonstrations created by AI agents constrained by an RDF-based harness that's been working fine for me. It can work on any OS, including my personal notebook that has pretty much the same config as Arun's :) 

Links:

[1] https://linkeddata.uriburner.com/weblog/ -- weblog comprising lots of live demos, since each post is an HTML doc fronting an RDF-based Knowledge Graph that accessible via SPARQL, SQL, GQL etc.. 

[2] https://github.com/OpenLinkSoftware/ai-agent-skills/blob/main/agent-rdf-memory/ -- RDF-based AI Agent harness

-- 
Regards,

Kingsley Idehen	      
Founder & CEO 
OpenLink Software   
Home Page: http://www.openlinksw.com
Community Support: https://community.openlinksw.com

Social Media:
LinkedIn: http://www.linkedin.com/in/kidehen
Twitter : https://twitter.com/kidehen


Simon Polovina

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Aug 13, 2026, 7:16:00 AM (20 hours ago) Aug 13
to Arun Majumdar, ontolo...@googlegroups.com, John F Sowa

Thanks, Arun, that’d be great!

I hope we can support each other.

Simon

 

From: Arun Majumdar <ar...@permion.ai>
Sent: 12 August 2026 18:20
To: Simon Polovina <si...@similelogics.ltd>; ontolo...@googlegroups.com
Cc: John F Sowa <so...@bestweb.net>
Subject: Re: Why CGs [referring to the Ontology Summit talk by Majumdar and Sowa]

 

Hi Simon,

 

Thank you for sharing this.  I will read it carefully and get back to you.

 

Appreciated,

 

Arun

Kingsley Idehen

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Aug 13, 2026, 10:38:01 AM (16 hours ago) Aug 13
to ontolo...@googlegroups.com, Simon Polovina, Arun Majumdar, John F Sowa
Hi Simon, 

I've had one of my AI agents generate a rebuttal to the claims you make in the post below. I'm replying at the top due to the length of your post.

You can read the rebuttal at:

[1] https://linkeddata.uriburner.com/weblog/ — where it's the latest entry.

[2] https://linkeddata.uriburner.com/weblog/?post=cgif-clif-rdf-rebuttal-claude_sonnet_5-1.html — direct weblog entry.

Note:

The system I'm using is 100% based on the very RDF stack you're criticizing. The AI Agent is constrained by a harness that's also RDF-based :)

Ideally, you should be able to make your counterargument using a similar system that showcases the claimed superiority.


Kingsley 

Kingsley Idehen

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Aug 13, 2026, 12:38:28 PM (14 hours ago) Aug 13
to Arun Majumdar, ontolo...@googlegroups.com, Simon Polovina, John F Sowa
Hi Arun,

On 8/13/26 11:30 AM, Arun Majumdar wrote:
"RDF (Resource Description Framework) has several problems in handling science, physics, mathematics and theorem proving.   RDF, by design, cannot represent full first-order logic (FOL) or constrain logic solvers unless the use of RDF is itself encapsulated in a substantial new programmer created framework.    For example, an individual RDF triple can be translated into a simple atomic binary predicate in simplified restricted predicate logic such as likes(john, Mary) that uses a single relation and two arguments to state facts which can be interpreted as a triple. 
The main limits are an inability to handle complex internal structures, relying on much more difficult programmer effort, methods to be added for changing information over time, and uncertain facts.  This requires a much more sophisticated external representation handler.  Base RDF lacks core FOL features like explicit negation ("not"), disjunction ("or"), universal quantification ("for all"), and existential quantification ("there exists") embedded natively in its data structure.   In the same way, ISO24707 does not represent the operational semantics of reasoning or thinking or modal logics which are critical for real-world enterprise applications.  Therefore, Conceptual Graphs also require programmer built external representations like Actors to add to the representation because they are not included in the base standard.”

Generated by AI multi-models at Permion.


I disagree because RDF capability is being misaligned with issues solved by the RDF stack which comprises other complementary layers. 



My own two cents is this:   who cares whether code is written in raw-binary, 1’s and 0’s or whether it used RDF or whether it used CGIF?    People only care about solutions and results - not how the tool itself was manufactured.   When I use a hammer, I don’t think about the work of mining and ore, the iron  extraction and then the process to make steel!     So I think as you long as you have a solution that works for you, continue to use that and prosper 😊


Yes, that's a better perspective. In the age of AI, so much easier to utilize :) 



For a much better view of the approach that Permion actually works on please see:


I'll take a look, and have my AI agent digest it too.


Kingsley 


Cheers,

-Arun

Kingsley Idehen

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Aug 13, 2026, 2:09:45 PM (13 hours ago) Aug 13
to ontolo...@googlegroups.com, Arun Majumdar, Simon Polovina, John F Sowa
On 8/13/26 12:38 PM, 'Kingsley Idehen' via ontolog-forum wrote:
Hi Arun,

On 8/13/26 11:30 AM, Arun Majumdar wrote:
"RDF (Resource Description Framework) has several problems in handling science, physics, mathematics and theorem proving.   RDF, by design, cannot represent full first-order logic (FOL) or constrain logic solvers unless the use of RDF is itself encapsulated in a substantial new programmer created framework.    For example, an individual RDF triple can be translated into a simple atomic binary predicate in simplified restricted predicate logic such as likes(john, Mary) that uses a single relation and two arguments to state facts which can be interpreted as a triple. 
The main limits are an inability to handle complex internal structures, relying on much more difficult programmer effort, methods to be added for changing information over time, and uncertain facts.  This requires a much more sophisticated external representation handler.  Base RDF lacks core FOL features like explicit negation ("not"), disjunction ("or"), universal quantification ("for all"), and existential quantification ("there exists") embedded natively in its data structure.   In the same way, ISO24707 does not represent the operational semantics of reasoning or thinking or modal logics which are critical for real-world enterprise applications.  Therefore, Conceptual Graphs also require programmer built external representations like Actors to add to the representation because they are not included in the base standard.”

Generated by AI multi-models at Permion.


I disagree because RDF capability is being misaligned with issues solved by the RDF stack which comprises other complementary layers. 



My own two cents is this:   who cares whether code is written in raw-binary, 1’s and 0’s or whether it used RDF or whether it used CGIF?    People only care about solutions and results - not how the tool itself was manufactured.   When I use a hammer, I don’t think about the work of mining and ore, the iron  extraction and then the process to make steel!     So I think as you long as you have a solution that works for you, continue to use that and prosper 😊


Yes, that's a better perspective. In the age of AI, so much easier to utilize :) 



For a much better view of the approach that Permion actually works on please see:


I'll take a look, and have my AI agent digest it too.


Kingsley 

Hi Arun and others, 

Digested.

See report produced by my Agent at: https://linkeddata.uriburner.com/weblog/?post=tensor-logic-domingos-odsc-2026.html.

Note: The HTML document is loosely coupled to an underlying RDF-based knowledge graph constructed using Linked Data principles, thereby making it easy to query and highly navigable by both humans and AI agents.

John F Sowa

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Aug 13, 2026, 3:55:06 PM (11 hours ago) Aug 13
to Arun Majumdar, ontolo...@googlegroups.com, CG
Arun,

Thanks for your  detailed reply to Kingsley.  I was planning to reply on the issues about RDF and OWL, but your note covers those very well,    But there are serious issues with the following citation:


That note contains good information about what LLMs can do.  But it makes the opposite mistake:  It claims that logic based on LLMs is superior to and replaces the 60 years of symbolic AI research, which includes  conceptual graphs and other versions of logic.

The purely symbolic methods of VivoMind technology from 2000 to 2010 were vastly superior to any kind of logic that is based ONLY on LLMs.  Fundamental llimitation:  LLMs are a probabilistic technology that  can never guarantee 100% precision.  For mathematical computations that must be precise, LLM computations must be tested and verified by symbolic methods.

Of course, you know that.  But when you cite a purely LLM-based method, it's essential to post that warning right up front..  That is the Permion advantage that enabled us to be the only US company to win the G7 challenge.

And by the way, your starting  quotation is a good example of how Permion enhances the kinds of technical responses generated by LLM methods.  That critique of RDF shows why it's impossible to add improvements to OWL that can overcome the limitations of a triple store.

For the raw data, it's essential to go beyond triples to N-tuples, as in a relational DB -- or in a spreadsheet.  Imagine the difficulty of using a spreadsheet that was limited to 3 columns.  If people require more than 3 columns to express what they mean, why would anybody imagine that triples would be adequate for an AI language?

And for reasoning, you need a complete system of logic.  That leads to the full Common Logic standard.  And to link the logic to the computation, you need the actor nodes on CGs.   That enabled Permion to  beat all the big guys in being the only US company to win the G7 challenge.

John
 


From: "Arun Majumdar" <ar...@permion.ai>
Sent: 8/13/26 11:30 A

"RDF (Resource Description Framework) has several problems in handling science, physics, mathematics and theorem proving.   RDF, by design, cannot represent full first-order logic (FOL) or constrain logic solvers unless the use of RDF is itself encapsulated in a substantial new programmer created framework.    For example, an individual RDF triple can be translated into a simple atomic binary predicate in simplified restricted predicate logic  such as likes(john, Mary) that uses a single relation and two arguments to state facts which can be interpreted as a triple. The main limits are an inability to handle complex internal structures, relying on much more difficult programmer effort, methods to be added for changing information over time, and uncertain facts.  This requires a much more sophisticated external representation handler.  Base RDF lacks core FOL features like explicit negation ("not"), disjunction ("or"), universal quantification ("for all"), and existential quantification ("there exists") embedded natively in its data structure.   In the same way, ISO24707 does not represent the operational semantics of reasoning or thinking or modal logics which are critical for real-world enterprise applications.  Therefore, Conceptual Graphs also require programmer built external representations like Actors to add to the representation because they are not included in the base standard.”

Generated by AI multi-models at Permion.

My own two cents is this:   who cares whether code is written in raw-binary, 1’s and 0’s or whether it used RDF or whether it used CGIF?    People only care about solutions and results - not how the tool itself was manufactured.   When I use a hammer, I don’t think about the work of mining and ore, the iron  extraction and then the process to make steel!     So I think as you long as you have a solution that works for you, continue to use that and prosper 😊

For a much better view of the approach that Permion actually works on please see:

Cheers,

-Arun

From: Kingsley Idehen <kid...@openlinksw.com>

Kingsley Idehen

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Aug 13, 2026, 4:19:02 PM (11 hours ago) Aug 13
to Arun Majumdar, ontolo...@googlegroups.com, John F Sowa
Hi Arun,

On 8/13/26 3:41 PM, Arun Majumdar wrote:
Nice visual presentation!  
We are very much a “back end” infrastructure not application technology - so we do not have that (well, we had to build something for the AI Grand Challenge as that needs GUI … )

But nice work :)


Thanks!

Note, I am simply demonstrating an RDF-based AI harness that is loosely coupled with data spaces (databases, knowledge bases, file systems, and APIs). It just so happens that our Virtuoso platform is designed to handle multiple open standards, making it a single server with the combined capabilities of a multi-model DBMS (SQL-accessible tables and SPARQL-accessible graphs), an HTTP application server, a WebDAV file system, etc.

The RDF-based harness works with any SPARQL- or WebDAV-supporting backend. Naturally, it also works with a local file system without any of the aforementioned infrastructure in place; i.e., it simply reads and writes files. This is essentially a progressively enhanced knowledge management system that goes beyond the viral "LLM Wiki" meme by Andrej Karpathy [1].

Note, you too can have the UI functionality by simply installing the harness and its loosely coupled skills [2]. :)

Links:

[1] https://linkeddata.uriburner.com/weblog/?post=tony-seale-yaml-ld-vault-ld-claude_sonnet_5-1.html -- a post that covers the LLM Wiki concept

[2] https://github.com/OpenLinkSoftware/ai-agent-skills/ -- harness (agent-rdf-memory) and loosely coupled skills 

Kingsley 





From: Kingsley Idehen <kid...@openlinksw.com>
Sent: Thursday, 13 August 2026 14:09:35
To: ontolo...@googlegroups.com <ontolo...@googlegroups.com>; Arun Majumdar <ar...@permion.ai>; Simon Polovina <si...@similelogics.ltd>

Cc: John F Sowa <so...@bestweb.net>
Subject: Re: [ontolog-forum] RE: Why CGs [referring to the Ontology Summit talk by Majumdar and Sowa]

Polovina, Simon (BTE)

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Aug 13, 2026, 4:41:22 PM (10 hours ago) Aug 13
to so...@bestweb.net, Arun Majumdar, ontolo...@googlegroups.com, CG

Hi Kingsley, Arun, John, and all,

Kingsley, thank you for putting together the detailed rebuttal and demonstrating the SPARQL queries against your Virtuoso setup. It's helpful to see runnable code brought directly into this discussion.

You got me thinking! Let me get my head around the matter. The exchange highlights a fundamental engineering trade-off:

On one hand, Kingsley shows what can be done with the mature W3C stack. By combining RDF 1.1, Named Graphs, RDF-star, SHACL, and SPARQL CONSTRUCT rules, an RDF-based harness can certainly model complex contexts and govern agent behaviour in practice.

On the other hand, the arguments in my document concern structural simplicity at the base layer. Enterprise events—such as an SAP purchase order line item or supply chain movement—are inherently -ary. Modelling them using binary triples requires surrounding those triples with auxiliary nodes, quads, and validation rules. As John noted with the spreadsheet metaphor, handling -tuple transactions natively in Conceptual Graphs and ISO/IEC 24707 Common Logic avoids that structural friction at the foundation, providing -ary nodes and nested contexts natively rather than through an assembled toolchain.

Arun's point on pragmatism is well taken—working systems can clearly be built on either stack. However, as enterprise platforms like SAP integrate neuro-symbolic AI, starting with a representation that directly mirrors -ary business objects simplifies schema design and makes deterministic verification much cleaner.

Thanks again to Kingsley for taking the time to write such a thorough response and continuing the discussion on the forum. I love it!

Best regards,

Simon

John F Sowa

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Aug 13, 2026, 5:42:41 PM (9 hours ago) Aug 13
to Polovina, Simon (BTE), Arun Majumdar, ontolo...@googlegroups.com, CG
Simon,

I'm glad that you mentioned SAP:  "as enterprise platforms like SAP integrate neuro-symbolic AI, starting with a representation that directly mirrors N-ary business objects simplifies schema design and makes deterministic verification much cleaner." 

Klaus Tschira, a co-founder of SAP, was an employee of IBM Germany.  The founding software of the SAP company consisted of technology that IBM had decided not to continue.  But IBM allowed Tschira and his colleagues to continue developing it to supp;ort the IBM customers that had adopted it.

SAP coinued to build on that technology, and Tschira continued to subscribe to IBM publications for related ideas.  In 1976, I published the first article on conceptual graphs in the IBM Joural of R & D.  Tschira liked the ideas, which inspired the representations he designed for SAP.  In 1983, he invited me to a research conference he sponsored.

Although SAP does not use conceptual graphs, their technology can be mapped directly to the notations in the ISO standard for Common Logic (CL), which specifies conceptual graphs as one of three CL notations.  

Any logic that can be mapped to and from CL can be called a dialect of CL.  I don't know the details of the SAP system, but it's quite likely that their notation or some subset of it could be called a CL dialect.

John
 


From: "Polovina, Simon (BTE) via CG" <c...@lists.iccs-conference.org>

Kingsley Idehen

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Aug 13, 2026, 9:05:38 PM (6 hours ago) Aug 13
to ontolo...@googlegroups.com
Hi Simon,

On 8/13/26 4:41 PM, 'Polovina, Simon (BTE)' via ontolog-forum wrote:

Hi Kingsley, Arun, John, and all,

Kingsley, thank you for putting together the detailed rebuttal and demonstrating the SPARQL queries against your Virtuoso setup. It's helpful to see runnable code brought directly into this discussion.


You're welcome.

You got me thinking! Let me get my head around the matter. The exchange highlights a fundamental engineering trade-off:

On one hand, Kingsley shows what can be done with the mature W3C stack. By combining RDF 1.1, Named Graphs, RDF-star, SHACL, and SPARQL CONSTRUCT rules, an RDF-based harness can certainly model complex contexts and govern agent behaviour in practice.

On the other hand, the arguments in my document concern structural simplicity at the base layer. Enterprise events—such as an SAP purchase order line item or supply chain movement—are inherently -ary. Modelling them using binary triples requires surrounding those triples with auxiliary nodes, quads, and validation rules. As John noted with the spreadsheet metaphor, handling -tuple transactions natively in Conceptual Graphs and ISO/IEC 24707 Common Logic avoids that structural friction at the foundation, providing -ary nodes and nested contexts natively rather than through an assembled toolchain.


In the age of LLMs, where natural language processing has become part of computing's UI/UX stack, syntactic preferences are no longer hurdles. For instance, I would never have been able to produce the rebuttals by hand in the time it took, which demonstrates what LLMs (a/k/a Langulators) bring to the table when used within the constraints of a harness.

LLMs have been trained on a vast range of specifications, notations, and syntaxes, so they don't have strong preferences about how information is represented.


Arun's point on pragmatism is well taken—working systems can clearly be built on either stack. However, as enterprise platforms like SAP integrate neuro-symbolic AI, starting with a representation that directly mirrors -ary business objects simplifies schema design and makes deterministic verification much cleaner.


It doesn't matter anymore, as my rebuttal document demonstrates. Arun's pragmatism bent is the way forward :) 


Thanks again to Kingsley for taking the time to write such a thorough response and continuing the discussion on the forum. I love it!


Great to hear!

BTW -- I've updated the article adding a rebuttal section scoped to John's most recent RDF criticisms :) 

[1] https://linkeddata.uriburner.com/DAV/demos/daas/why-the-triple-is-the-wrong-grain-rebuttal-claude_code-1.html#sowa-objections

Kingsley

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