How can I check if a particular application is installed in the system

Applescript FAQ OS X Finder
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#1

You should ask to the Finder about the specific creator type of such application. For example, we will ask for “GraphicConverter”:

try
	tell application "Finder" to application file id "GKON"
	--> do whatever
on error --> app does not exist!!!
	--> do whatever
end try

And… How do you know the creator type of a particular application? Just select its icon in the Finder and run this code:

tell application "Finder" to creator type of (selection as alias)