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

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

	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)