We outline the progress we have made in connection with the Alvey Grant "Proving Properties of Logic Programs" (SERC GR/D/44270 and Alvey IKBS 137). This grant runs for three years from 1st November 1985. The grant holders are Professor Alan Bundy and Dr Don Sannella and it employs or has employed Dr Fausto Giunchiglia, Frank van Harmelen, Jane Hesketh, Dr Alan Smaill and Dr Lincoln Wallen as Research Associates. Pete Madden and Andrew Stevens are attached Ph.D. students.