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\section{Discussion}\label{sec:discussion}

\noindent Conceptually, the relativity of causal knowledge can drive a paradigm shift in how causality is typically understood in AI/ML. 
By stripping causality of its oracular and absolute meaning, the relativity of causal knowledge situates it within a different ontological setting, where truth is not monolithic but emerges inevitably and relatively from a set of relationships. 
This is mathematically formalized by the path-dependent RCK in \Cref{eq:rel_caus_know}.
Our framework paves the way to multiple intriguing areas of reasearch, pivotal to fully characterize RCK and make it applicable. \\
\noindent\textbf{Learning Theory.} 
We developed our theoretical framework with an underlying intuition: RCK could be a better framework to empower AI/ML with the ladder of causation \cite{pearl2018book}. 
A learning theory is needed for this. 
It is surely of interest to develop a statistical theory for models that can ingest network sheaves and cosheaves of causal knowledge to solve downstream learning tasks. 
In many cases, the restriction and expansion maps -- the formal instance of \enquote{perspective} -- are given, e.g., privacy requirements of the subjects in an agentic network or communication constraints in a sensor network. 
However, when they are not available, the problem of \emph{(co)sheaf inference}, i.e., learning them in a data-driven fashion given the network connectivity, is fundamental. 
An even harder problem is \emph{(co)sheaf discovery}, i.e., jointly learning the restriction, extension maps, and network connectivity. 
Interestingly, both for inference and discovery, the learning losses and models are useful to induce a particular notion of perspective, that could be fairness-, safety-, information-, or trustworthiness-driven, just to name a few.\\
\noindent\textbf{Cohomology Theory.} 
\CSprob is not an Abelian category, as it is not additive, i.e.,  there is no natural way to \enquote{add} two affine maps to get another affine map such that all group axioms are globally satisfied. 
Consequently, defining a cochain complex -- and thus a cohomology theory -- on network sheaves of causal knowledge is nontrivial.
Developing such a theory would yield rich algebraic invariants that offer global insights into the network structure. 
These invariants would be instrumental in revealing when and why multiple sheaves of CK share a common structure.
Practically, a cohomology theory could help us understand how and why different networks of subjects, each developing causal knowledge about different phenomena, exhibit similarities.\\
\noindent\textbf{Hodge Theory.} 
The Hodge theorem \cite{griffiths2014principles} shows that the kernel of the Laplacian on a Riemannian manifold recovers its de Rham cohomology.  
Combinatorial versions of the Hodge theory have been developed for cellular sheaves of inner-product spaces (e.g., vector spaces and Hilbert spaces), building on suitable properties of the adjoint maps \cite{hansen2019toward}. 
Unfortunately, porting these arguments to the $\CSprob$ category is nontrivial.
In this context, a Hodge(-like) theory could be instrumental in defining diffusion-type operators and developing spectral theories \cite{hansen2019toward} for RCK. 
Practically, having a Hodge theory might help us understand which are the dynamics that lead to global sections in \Cref{def:global_section} and why, providing insights on when and why RCK aligns.