Abstract Intelligence (aI - alpha I) is the general mathematical form of intelligence as a complex natural mechanism that transfers information into behaviors and knowledge at the embodied neurological, physiological, cognitive, and logical levels from bottom-up aggregations and top-down reductions (ICIC, http://www.ucalgary.ca/icic/).
It's recognized that sophisticated artificial intelligence systems may not rigorously be studied before the theoretical foundations of intelligence science and brain science, in term of aI, are well explored. Within the aI framework, any paradigm of intelligence will be treated as an instance of aI.
Modelling (mathematically) a system property (intelligence) requires you need measurements (samples) to fit to some model. If on the other hand you model with text (non mathematically) you need to find commonality with the meaning in other people's minds so here goes:
intelligence what do you mean ?
abstract intellgence is that different?
information -> becomes knowledge and or responses (agreed)
but what is the information prior to the transform
Looking at a paper from your quoted site (your paper I believe) you appear to see cognitive computing principally in terms of lingustic and logical processes.
I believe that intelligence is linked to viability in a consistent environment thus the humble shellfish adapting its feeding position in changing currents has a minor component of the property intelligence without having an logical or linguistic components from this small beginning we can establish a evolutionary approach to the development of full blown cognitive ability. At some point in the development, language and its restriction (logic) arrive.
So to develop your original question : 1) Look for evolving viable life to see the fundamental property intelligence. 2) Look further for the invention of a symbolically driven modelling mechanism (language) to see conventional intelligence.
To make a mathematical model you need define models in terms of viability eg goal directed decompositional systems. Real-time control systems (with loop closure being supported by modelling (uses the mind). This probably using operating mechanisms defined in a state-space rather than a data space (because of neural systems underlying it) This is a departure from normal thinking and represent a genuine attempt on my part to change the philosophy (see some of my other answers on researchgate on related topics) that underlies current AI beliefs and as such I expect it not to find much favour. But I believe it will lead to a much clearer understanding of cognition
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I truly hope that my answer will be of use to you.
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