I am referring to logic-based languages of any sort and not restricting myself to programming. So markup language would be included. Also, it might be that there are logical approaches for computers envisaged but not yet implemented.
Here is where I am coming from. I have identified and validated 7 distinct ways that people "use language" within my taxonomy (at http://thee-online.com). The 6th way is named "logical" where everything that is said is precise and each term has an unequivocal reference, where consistency and coherence are of paramount importance. You can see a one-page initial summary on the website at: TOP Studio > Frameworks Room > Using Language > Get Oriented > Grasping Foundations
(NB: you need to be logged in to see the TOP Studio menu in the navigation).
It is normal in my taxonomy for there to be a nested hierarchy within the 6th level which contains special systems. In this case it would be a "logical language system/paradigm", and there would be 7 of these, because each would have to draw its rationale or have some correspondence to the 7 "uses of language".
I am conjecturing that computing-oriented languages must be the special nested hierarchy here.