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I have created formal concept analysis, as a place to put material from the Café discussions, but also to develop some of the concepts a bit further.
the running convention is to have all entry titles to be in lower case if they are proper keywords, and uppercase only if thery are names, such as titles of texts.
I personally think that the name “formal concept analysis” should be descriptive name for a wider area of science and not only for one disappointing extremely simplistic model of describing one formal aspect of semantic relationships (and few new versions which are based on the same basic approach).
I think agree with Zoran that the name is too grandiose for what it actually manages to do, but that is the name that is used! Actually the applications of FCA in AI can be reasonably impressive just because the very simplicity of the algorithms allows quite substantial examples to be studied.
Computational linguistics was far further before the FCA was invented.
I think that FCA actually came out of Dowker’s theorem on the homology of relations which is 1953, but the date is not important. I see a problem in the interaction of maths with AI. We mathematicians and physicists have aims that include production of an elegant theory that does something neat. In AI if they manage to do something that clarifies the foggy world of AI and allows machine computations that mimic something we can do quite naturally, then they feel that progress has been made! They need ’concepts’ and FCA provides a simple basic method of saying what might be a stable concept of ’concept’ and which might give a starting point for something deeper, but it needs a lot of (mathematical) work done on it and the sort of links that Simon is exploring (and I looked at a few years ago) may help.
Q-C. Zhang looked at possible notions of morphism for formal concepts and found links with domain theory which gave new tools for applications …. , so perhaps mathematicians and theoretical computer scientists need to look at the existing theory, find where there is significant mathematics in it (if there is) and start developing it (for its own sake).
BTW are there two Zhangs as Lili Shen worked with her supervisor who is called Zhang, but the other name is different.
I added a link to Galois connection.
Could anyone expand on the sentence in the Idea section, here? Currently it is vague to the point of being meaningless. Similarly, the cross-link to “Galois connection” could do with a minimum of commentary in order not to look too odd.
Tim, okay, thanks. So now the Idea-section says the FCA looks at matrices of 0s and 1s.But there must be something non-trivial to be said about this seemingly trivial content to justify the terminology. What is the non-trivial operation on or insight about these matrices that drives the field?
I agree but this will need a bit more time than I could put in yesterday. My plan is to copy the example that in on the café discussion. (I thought I had something typed up but I worked with these 15 or more years ago and cannot find my typed notes!!!!) The example in Simon’s discussion on the café will help, but I hope someone has some of deeper stuff typed up so that it can be adapted and I do not have to type up a lot of stufff!!!
The basic idea is simple It uses the relation to build a closure operation on subsets of the objects and of the attributes. …. but probably no time today.
Some of the content of Simon’s post can be used as is, if the code is available. (I do not have access.)
The webpage of Zhang is unavailable. Perhaps he has moved university away from Case Western.
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