Re: Foundations for a Large Graph Model

Sorry for the last reply omission of the word intelligence.  In the
paragraph below

Artificial is itself a field of mathematics that is by default empirical,
and this makes the its knowledge graphs modeling only applicable in
mentioned fields where empirical adequacy is required and or desired, but
not in mathematics itself.

After artificial the predictive texting mode of Gmail ate the word
intelligence.

Milton Ponson
Rainbow Warriors Core Foundation
CIAMSD Institute-ICT4D Program
+2977459312
PO Box 1154, Oranjestad
Aruba, Dutch Caribbean

On Fri, Mar 20, 2026, 13:05 Sebastian Samaruga <ssamarug@gmail.com> wrote:

> 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
>>>
>>