Godan verb with 'ru' ending, Transitive verb
to infer; to figure out; to get an idea of; to tell; to imagine; to guess; to grasp; to fathom; to understand; to know
彼がどうなっているか私にはうかがいしる事ができない。I cannot guess at all what is going on with him.
Also written 窺い知る【うかがいしる】、伺い知る【うかがいしる】