[FRIAM] A/R theory

[uǝlƃ ↙↙↙]

Re: transitivity -- What if "d(mp′,m′p)" were defined in an interesting (or pathological) way such that we don't use ≤ but something else ... maybe a partial order or something even weirder. Then instead of thinking of ε as some sort of "error", we think of it as a complicated similarity map ... a model in and of itself? Then maybe there would be some form of transitivity.

Re: the whole thing -- I'm a little worried about the practicalities in all the symmetric opposites {R_re,Ȓ_c}, {Ȓ_re,R_c}, {Ȓ_c,R_c}, {R_re,Ȓ_re}, {C_c,H_c}, {C_re,H_cr}, {C_re,C_c}, {H_re,H_c}, etc. The reason I'm worried about them is because they represent the many types of validation and verification beyond the "data validation" represented by ε-equivalence. Such "behavioral analogies" (comparing arrows) can be and are scored similarly to the "structural analogies" considered when comparing the boxes.

I may have missed it in the paper. Where do they talk about the degree to which the physical form of the abstract objects is arbitrary? I see where they say there's no need for universality, just sufficiently powerful, accurate, instantiable, etc. Don't we need such concepts in order to reason out *whether* there exist a commuting structure for any given abstraction or physical thing? I.e. just because we can find a commutation with a structural analogy doesn't imply a behavioral analogy ... and vice versa. And *if* that's the case, then what does this say about object-behavior (box-arrow) duality? ... if anything?

On 11/7/20 9:34 AM, jon zingale wrote:
> 𝜀-equivalence itself is interesting because it comes with a *competence
> constraint* that prevents it from being a transitive relation, that in
> general a =𝜀 b ^ b =𝜀 c ⊬ a =𝜀 c is crucial to the theory.

-- 
↙↙↙ uǝlƃ