Logical operations run a small country (7)
I believe the answer is:
andorra
'small country' is the definition.
(Andorra is a small European country)
'logical operations run a' is the wordplay.
'logical operations' becomes 'and or' ('and' and 'or' in logic).
'run' becomes 'r' (cricket abbreviation).
'andor'+'r'+'a'='ANDORRA'
(Other definitions for andorra that I've seen before include "Autonomous principality in the Pyrenees" , "Self-governing principality in Pyrenees" , "Small republic between Spain and France" , "Tax haven" , "Principality in SW Europe" .)