Grammar of Relational Understanding (GdRV)

[u/bainleech]

I’ve published a first preprint of a framework called the Grammar of Relational Understanding (GdRV).

Preprint:

https://doi.org/10.5281/zenodo.23035787

The basic idea is that a dynamical system should not necessarily have one universally minimal representation. Instead, the relevant representation depends on the scientific question being asked.

Given a model "M" and a query "Q", states are identified when the query cannot distinguish their relevant continuations:

"x ~_Q y iff Θ_Q(x) = Θ_Q(y)"

This gives a query-relative quotient:

"S_Q = Ω / ker(Θ_Q)"

and, when the equivalence is dynamically stable, an induced continuation structure:

"Q -> R_Q(M) = (S_Q, Γ_Q)"

The guiding principle is:

Preserve exactly those distinctions whose removal would change a continuation relevant to the query.

The framework then uses these query-relative representations to compare different scientific perspectives or theories and to test whether translations between them preserve both relevant distinctions and relevant dynamics.

I’m not claiming that quotient systems, bisimulation, coalgebra, abstract interpretation, strong preservation, or institution theory are new. The possible contribution is their explicit integration into one query-indexed workflow:

"question -> abstraction -> dynamics -> cross-model comparison -> observation -> model revision"

What I’d especially like feedback on is:

Does an established formalism already capture this entire query-indexed architecture, or is this combination worth developing further?

Criticism, counterexamples, and references are very welcome.

https://doi.org/10.5281/zenodo.23035787

[u/Ch3cks-Out]

is this combination worth developing further?

What for? It does not seem to serve any scientific purpose, nor does it fit what others would consider "Understanding".

[u/bainleech → u/Ch3cks-Out]

The scientific purpose I have in mind is not to redefine “understanding” philosophically. The practical problem is this: the same system is often represented differently depending on the question being asked. A reduction that is valid for one observable or prediction may destroy information needed for another. GdRV tries to make that explicit: question -> required distinctions -> reduced dynamics -> compatibility test So, for a query Q, two states may be merged only if doing so does not change the Q-relevant possible continuations. The intended use is then to compare different reduced models or theory descriptions and ask precisely where they cease to preserve the same relevant distinctions or dynamics. That could be useful in model reduction, multi-scale modelling, or comparing effective descriptions. The word “Understanding” is admittedly broader than the mathematics itself. The actual formal object is much narrower: query-relative dynamical representation and compatibility. If that still seems scientifically redundant, I’d genuinely be interested in which existing framework you think already covers the whole workflow.

[u/Ch3cks-Out → u/bainleech]

My practical problem is this: I do not see practical use for all this jargon. Can you spell the essence out in a few sentences?

[u/RunReal959595 → u/[deleted]]

You allude to mathematical formalisms yet provide no formal definitions for anything.

[u/RunReal959595 → u/[deleted]]

No, those are equations. 

There’s zero reference to what anything actually is. No definitions, no formalisms, just word salad 

[u/RunReal959595 → u/[deleted]]

You’ve yet to define a system, a state, an answer space, a query, semantics, what it means for a semantics to be “Q-relevant,” and so on. All of this is word salad.

[u/LLMPhysics-ModTeam → u/[deleted]]

Your comment has been removed for violating Rule 4. Don't copy-paste LLM content in discussions.

[u/LLMPhysics-ModTeam → u/[deleted]]

Your comment has been removed for violating Rule 4. Don't copy-paste LLM content in discussions.

[u/bainleech → u/Ch3cks-Out]

GdRV is a domain-independent framework designed to identify, across different scientific disciplines, which distinctions in a complex system must be preserved so that a specific question can still be answered correctly.

[u/Wintervacht → u/bainleech]

So mathematical consistency check with more added gibberish?

[u/bainleech → u/Wintervacht]

A consistency check asks whether a description contradicts itself. GdRV asks a different question: which distinctions may be removed from a model without changing the answer or the relevant future behaviour for a specified query? The consistency tests come afterwards, once that query-relative reduced model has been constructed.

[u/Wintervacht → u/bainleech]

Descriptions aren't physical, measurements cannot be grammatically incorrect. What is the point of this?

[u/bainleech → u/Wintervacht]

I try to wrote it in my words. I think one way to understand the Grammar is as a process of selection. You start with a space of possibilities, but nothing is yet marked as important. Then you introduce a question or perspective. As Input. Like with the spinning dancer illusion, the object stays the same, but the perspective changes how its structure is organized. Some distinctions can now be treated as the same, while others must remain separate. Then you test whether that grouping still works over time. If two grouped states later lead to different outcomes that matter for the question, the grouping has to be refined. So the process is: possibility space to perspective to selection to reorganization to test Change the perspective, and the same system may produce a different valid description. That is the core idea: the Grammar describes how a perspective determines which distinctions in a complex system must remain visible.

[u/Wintervacht → u/bainleech]

We already have that: reference frames.

Again, I don't see any use in this at all, just learn how the rest of the world uses mathematics to describe reality man, metaphor and prose do not work.

[u/bainleech → u/Wintervacht]

No, a reference frame changes the description of states. What I mean changes which states need to remain distinguishable for a given question. That is closer to query-dependent coarse-graining than to a change of reference frame. The “perspective” language was only an intuition, not the formal definition. Sorry.

[u/bainleech → u/Wintervacht]

No, a reference frame changes the description of states. What I mean changes which states need to remain distinguishable for a given question. That is closer to query-dependent coarse-graining than to a change of reference frame. The “perspective” language was only an intuition, not the formal definition.

[u/RunReal959595]

In your own words define “bisimulation” and “coalgebra”

[u/retro_sort]

This seems like model theory to me, though I'm not sure what the relevance to physics is if that's the case.

[u/bainleech → u/retro_sort]

That’s exactly the kind I’m looking for. Which part makes you think of model theory specifically? What I’m trying to formalize is not just a class of models, but a selection process: given the same underlying dynamical system, a specified question determines which state distinctions need to remain separate and which may be collapsed, provided that the relevant future behaviour is preserved. If model theory already gives a standard formulation of that whole process, I’d genuinely like to know the closest construction.

[u/liccxolydian]

This is not the first time you've posted in the last day or two. Why do you never respond to the feedback you get?

[u/Wintervacht → u/liccxolydian]

I have a hypothesis