Re: Foundations for a Large Graph Model

Milton,

Of course. And being FCA Contexts / Lattices a manner of knowledge
representation, I propose rendering knowledge graphs in this form of KR,
leveraging an arithmetic framework for embeddings and inference:

https://sebxama.blogspot.com/2026/03/foundations-for-large-graph-model.html

Regards,
Sebastián.


On Fri, Mar 20, 2026, 1:46 PM Milton Ponson <rwiciamsd@gmail.com> wrote:

> Dear Sebastian,
>
> Knowledge graphs are the number one priority for all manner of knowledge
> representation and mathematical frameworks for empirical analysis,  not
> just AI.
>
> Milton Ponson
> Rainbow Warriors Core Foundation
> CIAMSD Institute-ICT4D Program
> +2977459312
> PO Box 1154, Oranjestad
> Aruba, Dutch Caribbean
>
> On Fri, Mar 20, 2026, 12:40 Sebastian Samaruga <ssamarug@gmail.com> wrote:
>
>> Hi everybody. Let me reshape my original post. It was a mess. Let's start
>> sharing some context to the discussion:
>>
>> "Gartner just made Knowledge Graphs the number 1 infrastructure priority
>> for enterprise agentic systems"
>>
>> https://share.google/aimode/m7XZVTIYCnyWMLefG
>>
>>
>> https://www.linkedin.com/posts/amyhodler_graph-chat-neo4js-philip-rathle-on-neuro-symbolic-activity-7432506087985291265-rfB7
>>
>> And an FCA attempt to render Large Graph Models. Maybe adding some little
>> algebraic semantics into embeddings could be of any help.
>>
>> ---
>>
>> Foundations for a Large Graph Model:
>>
>> FCA (Formal Concept Analysis):
>> FCA Contexts: Objects x Attributes matrix.
>>
>> Context triples encoding:
>> ContextPoint : (context : ContextPoint, object : ContextPoint, attribute :
>> ContextPoint);
>>
>> ContextPoint class:
>> - uri : String
>> - primeID : long
>> - context : ContextPoint
>> - object : ContextPoint
>> - attribute : ContextPoint
>> - contextOccurrences : Set<ContextPoint>
>> - objectOccurrences : Set<ContextPoint>
>> - attributeOccurrences : Set<ContextPoint>
>> + getContext
>> + getObject
>> + getAttribute
>> + getContexts
>> + getObjects
>> + getAttributes
>> + getPrimeIDEmbedding
>>
>> Occurrence Monad: ContextPoint (Context, Object, Attribute Occurrences)
>> wrapper / filter / traversal streams reactive composition / activation.
>>
>> Render SPO Graphs into FCA Contexts from input triples:
>> Each S, P, O from input triples with Contexts of their own. Example:
>> Predicate Context, Subject Objects, Object Attributes (P, S, O). "Rotated"
>> SPO Contexts.
>>
>> (S, P, O) Context;
>> (P, S, O) Context;
>> (O, P, S) Context;
>>
>> Prime ID Embeddings:
>>
>> Each ContextPoint (singleton for a given URI) is assigned an unique
>> incremental Prime Number Identifier.
>>
>> For a given ContextPoint occurrences in a given Context its Prime ID
>> Embedding is calculated as the product of this occurrence Prime ID with
>> the
>> Prime ID Embeddings of the other two parts of the occurrences.
>>
>> For example: given an object in a given context its Prime ID Embedding is
>> the product of its Prime ID (Embedding) by the Prime ID (Embedding) of the
>> occurrence context by the Prime ID (Embeddings) of this object's
>> attributes
>>
>