As a layperson, using my brain’s ‘algorithms’, trying to pattern-recognize the tree from the forest, I wish to share my ignorant “insight,” obtained during my ongoing life-long learning, being confident someone somewhere (perhaps a future me) will find an attribute or two to disagree on:
 
‘Symbolic Artificial Intelligence’ is synonymous to the more colloquial ‘Good Old-Fashioned AI’, which is in turn simplified to the abbreviation ‘GOFAI’. Symbolic AI uses symbols that could be read by humans. These symbols represent ‘real world’ concepts. These concepts could be formal logic concepts or other (e.g. ‘linguistic’). These symbols are used (or ‘manipulated’) to create ‘rules.’

‘Rules’ are also used to enable the use (or manipulation) of these symbols. This, in its entirety, I understand, for now, as an integrated whole that encapsulates human (‘expert’) knowledge, and these aforementioned rules, into a system which I understand as a ‘Rule-Based System’.

For instance then, ‘Reasoning through syllogisms’ is a rule-based method toward logic reasoning and implies a set of rules used by humans that are also computational and hence, I sense, could be used in the above-mentioned AI systems.

As an added bonus, I think to understand that if these rules and symbols are then used with, for instance, human (aka ‘natural’) language processing (‘NLP’), then one can see the ‘deterministic’ at work. And yet, here, I feel my learning is still very shaky.

That stated, my syntactic logic, of the latter, should not be turned around in thinking that I believe to have learned that NLP is inevitably and only GOFAI. I don’t think so; for now, I do not understand it as such.

This is where the last paragraph of my story here above is trying to imply the second major branch, along the first branch as described here above, in the field of AI: (un)supervised ML, ANNs and the likes; or so I am understanding it to the present day.

Some of these terms and words, in this second branch of the AI field, I explore elsewhere here on the blog, and that as output of my auto-didactic learning processes.
 

Keeping it as basic as possible, with the aim to explain it to anyone who might ask me (while I do think it more cautious not to ask this layperson), where could I improve or correct this “understanding” (which I assume to be lacking)?