That's interesting. Is it because these other forms of logic can not be implemented on a computer in a straight forward way, or because computer scientists are just ignorant of these other possible logics?
Well one feeds into the other. Computer scientists just have no real use for them. They can't be straightforwardly modelled on a computer nor are they straightforward models of computers.
That isnt to say there are no uses of them in CS or that CS ignores them all. But many systems were invented to deal with explicitly philosophical problems (eg. modal logic for metaphysical necessity, para-consistency for paradoxes, etc.).
In some very specialized areas non-standard logics do get used (theorem proving uses intuitionist logic, AI/Machine Learning might use fuzzy, etc.) but its still a limited subset over all.
No doubt, in heavily mathematical CS departments there might be courses on logic in a more complete sense.
CS researchers do develop logical systems of a kind: in particular they have developed ways of writing logic systems programatically (and usually end up having to ditch a few things and thus invent a new system).
However if you bought any major books on logic (as a subject) or looked into any contemporary research in logic (as a subject, not "doing logic on an ARM, etc.") you'd find the authors were philosophers. Occasionally mathematicians, and esp. mathematicians who then became philosophers.
There are a lot of logic systems out there, and we tend to use ones that have happened worked out, and momentum builds. Of course, sometimes things are missed because our chosen tools are inept for some problem. Those are usually only solved with paradigm shifts.
