Re: Foundations for a Large Graph Model

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.

---

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..

Layers. Stream Pipelines:
Aggregation, Alignment, Activation steps. Leverage Prime ID Embeddings for
reactive functional composition.

Aggregation
Type Inference. Same attributes: same type. Attributes subset / superset:
super / sub types. Aggregated rotated contexts for S / P / O Contexts type
inference:
(aPerson(worksAt, anEmployeer))
(worksAt(aPerson, anEmployeer))
(anEmployeer(worksAt, aPerson))

Alignment
Attribute / Link prediction:
Given type aggregated hierarchies and taking contexts into account as a
given axis, predict objects attributes for an axis value shift:
(Yesterday(Price, Low))
(Today(Price, Mid))
(Tomorrow(Price, High))

Activation
Transforms: available actors in roles in interaction context states
transition change activations predictions:
(CurrentStateContext(PreviousStateContext x NextStateContext))
(Semisenior(Junior x Senior))

Implementation (Runtime):
Reactive streams.
FCA Contexts.
SPO / FCA I/O.
Prime Embeddings.
ML. Embeddings Tensors:
.. Train (source context encodings)
.. Predict (materialize contexts) reactive on contexts updates
.. Aggregation (classification)
.. Alignment (clustering).
.. Activation (regression)
Models. Apache Spark.

References (outdated):
https://sebxama.blogspot.com/2025/10/application-integration-and-multi.html
[FCA1] https://en.wikipedia.org/wiki/Formal_concept_analysis
[FCA2] https://jfsowa.com/logic/math.htm#Lattice

Best Regards,
Sebastián.


On Tue, Mar 10, 2026, 6:34 PM Sebastian Samaruga <ssamarug@gmail.com> wrote:

> Sorry, Context hierarchy is:
>
> Context
> Context::getObjects / getAttributes
>
> Object extends Context
> Object::getContexts / getAttributes
>
> Attribute extends Context
>
> Note:
>
> This, my posts into this lists and the documents and "specifications"
> published in the blog are not yet implemented thoughts posted in the hope
> of someone could benefit realizing or implementing them and become a
> stakeholder which will allow me to guide my theoretical and implementation
> efforts.
>
> Regards,
> Sebastián.
>
>
> On Mon, Mar 9, 2026, 9:28 PM Sebastian Samaruga <ssamarug@gmail.com>
> wrote:
>
>> Daniel,
>>
>> Thanks a lot for your time and comments.
>>
>> Let me add some comments inline with your reply.
>>
>> On Mon, Mar 9, 2026, 11:58 AM Daniel Ramos <capitain_jack@yahoo.com>
>> wrote:
>>
>>> Hi Sebastián,
>>>
>>> Thank you for sharing your FCA-based integration framework proposal on
>>> the AIKR list. The idea of using Formal Concept Analysis contexts with SPO
>>> triples for aggregation/alignment is an interesting formalization approach.
>>>
>>> A few observations that may help you refine the proposal:
>>>
>>> The encoding layer (prime embeddings + tensors + Apache Spark) would
>>> benefit from concrete benchmarks showing how it compares to existing
>>> knowledge graph embedding methods (TransE, RotatE, etc.)
>>>
>>> The reactive context-update model (Aggregation → Alignment → Activation)
>>> is reminiscent of stream reasoning architectures — connecting to that
>>> literature could strengthen the framing
>>>
>>
>> Regarding streams, the proposal observes a functional reactive oriented
>> approach based in the Occurrence Monad:
>>
>> (Context, Object, Attribute) : FCA Triples encoding.
>>
>> Occurrence Monad (Context hierarchy Contexts, Objects and Attributes
>> wrapper): FCA Objects / Attributes in FCA Context w./ FCS Objects /
>> Attributes.
>>
>> Context hierarchy bound functions:
>>
>> Context::getObjects / getAttributes
>>
>> Object::getContexts / getAttributes : Context
>>
>> Attribute::getContexts / getObjects : Context
>>
>> Consider publishing a small reproducible example demonstrating one
>>> end-to-end pipeline (e.g., SPO ingestion → FCA lattice → prediction) to
>>> make the proposal more concrete
>>>
>>> Best regards,
>>> Daniel
>>> On 3/9/26 11:49 AM, Sebastian Samaruga wrote:
>>>
>>> Foundations for a Large Graph Model:
>>>
>>> FCA (Formal Concept Analysis):
>>> Contexts: Objects x Attributes matrix.
>>>
>>> SPO Input Triples Contexts:
>>> SPOContextAxis. S / P / O Objects / Attributes.
>>> Example Contexts:
>>> P SPOContextAxis Predicates, S Objects, O Attributes.
>>> S SPOContextAxis Subjects, P Objects, O Attributes.
>>> O SPOContextAxis Objects, P Objects, S Attributes.
>>>
>>> (SPOContextAxis(O x A)) : O / A (Recursive labeled occurrences).
>>>
>>> Aggregation:
>>> (StateContext(O : AggregatedTypeCtxAxis, A : SPOContextAxis))
>>> (Working(Employee, worksAt))
>>>
>>> Alignment:
>>> Attribute / Link prediction.
>>> Type (upper / hiers / order) alignment.
>>> (encoding)
>>>
>>> Activation:
>>> Transforms: available actors in role in interaction context state
>>> changes predictions.
>>> (CurrentStateContext(PreviousStateContext x NextStateContext))
>>> (Semisenior(Junior x Senior))
>>> (encoding)
>>>
>>> Encoding:
>>> FCA Contexts.
>>> SPO / Kinds Occurrences.
>>> Prime embeddings.
>>> Tensors. Train (source context encodings) / Predict (materialize
>>> contexts) reactive on contexts updates. Aggregation (classification),
>>> Alignment (regression), Activation (clustering) Models. Apache Spark.
>>>
>>> References: https://sebxama.blogspot.com
>>>
>>> Best regards,
>>> Sebastián.
>>>
>>>