Neurosymbolic AI To Check and Correct LLMs

Mike's Notes

This is part of a series of thoughtful opinions about using Ontology in software information systems.

Pipi has an existing BORO Engine (bor) (inspired by Chris Partridge's book "Business Objects: Re-engineering for Re-use"), but it runs in reverse: it imports triples to extract entities and relationships, then uses them to build reference relational databases for back-end industry workspaces.

Part three: A presentation by John F. Sowa and Arun K. Majumdar about their Permion software at a recent Ontolog Summit.

Permion is amazingly efficient. The demo ran on a 64 GB MacBook.

Resources

• https://www.youtube.com/watch?v=oy-uzJuSr70
• https://ontologforum.com/index.php/ConferenceCall_2026_06_03
• https://www.permion.ai/

References

• Business Objects: Re-engineering for Re-use, Chris Partridge. 2005.

Repository

• Home > Ajabbi Research > Library >
• Home > Handbook > 

Last Updated

16/08/2026

Neurosymbolic AI To Check and Correct LLMs

By: John F. Sowa and Arun K. Majumdar

Ontolog Summit: 03/06/2026

John F. Sowa and Arun K. Majumdar.

John F. Sowa and Arun K. Majumdar presented "Neurosymbolic AI To Check and Correct LLMs" at the Ontology Summit on 3 June 2026.

Abstract: For over 60 years, the best AI reasoning was based on the four step cognitive cycle:  abduction, deduction, evaluation, induction, and repeat.  Abduction generates hypotheses or educated guesses.  Deduction derives implications.  Evaluation chooses the best option.  Induction combines the result with previous knowledge.

Many versions of the cognitive cycle have been invented and named. For guiding fighter pilots, John Boyd called it the OODA loop: Observe, Orient, Decide, Act.  He originally said that each step would be traversed in milliseconds, but he later applied the loop to design and analysis steps that may take minutes, hours, or days.  Whatever the time scale, the four steps are fundamental to reasoning in science, business, and life.

The pattern matching methods of Large Language Models (LLMs) are superb for translating languages, natural or artificial. They are also good for finding and relating patterns in large volumes of data of any kind. That enables them to answer questions by finding information or by applying previous methods to new data.  For many problems, pattern matching can discover abductions or educated guesses.  But deduction and evaluation cannot be done unless a similar cognitive cycle can be found somewhere on the WWW.

With the VivoMind system from 2000 to 2010, the authors used conceptual graphs for  symbolic reasoning about a wide range of problems. For the new Permion system, they added LLM pattern matching to map conceptual graphs to and from natural language.  But pattern matching, by itself, cannot do any reasoning unless it can find and adapt an appropriate cycle on the WWW.  It often requires a huge amount of searching even for relatively simple examples.

In summary, LLMs cannot do reasoning unless and until the system finds a suitable cognitive cycle on the WWW.  But the Permion reasoning methods automatically do the four-step cycle. If necessary, they can also do LLM searching, but none is required.

YouTube 1:17:07