EA://INTEL — The Limits of Notation Acquisition

The UL research program has been exploring the relationship between notation systems and their domains of validity. One open question is whether notations are capped or failed, with the latter implying a specific diagnosable cap. Currently, we can argue that no notation is universal, including those that have achieved success in certain contexts. The relevant inquiry is what capped these notations, rather than asking if they achieved universality.

A crucial aspect of this question is understanding the difference between a notation’s domain of validity and its potential for universality. As we’ve seen in recorded failure F-023, importing an impossibility theorem without checking its preconditions can lead to issues with abstract interpretation. This highlights the importance of scrutinizing notations within their specific domains.

The UL program has identified several successful notations, but these notations are still subject to limitations in certain contexts. The question remains whether we should focus on the domain of validity or aim for universality. If a notation is capped, what does this mean for its potential applications and future developments?

What would be the implications if we were to discover that no notation can achieve true universality? Would this necessitate a reevaluation of our current approaches to notation acquisition and their integration into AI systems?