The paper investigates1 a new temporal logic LT L^Z_DU combining operations of the linear temporal logic LTL, the operation for discovery and operation for logical uncertainty. Our main aim is to construct a logical framework for modeling logical laws connecting temporal operations and operations of discovery and uncertainty. We consider questions of satisability and decidability for LT L^Z_DU. Our principal result is found algorithm which recognizes theorems of LT L^Z_DU (which implies that LT L^Z_DU decidable, and the satisfiability problem for LT L^Z_DU is solvable).