P-Prolog is put forward as an alternative proposal to the difficulties faced in the main research areas of parallel logic programmings, which have been studied. P-Prolog provides the advantages of guarded Horn clauses while retaining don't know non-determinism where required. This monograph presents also an or-tree model and an implementation scheme for it, to combine and- and or- parallelism with reasonable efficiency. The model and implementation scheme discussed can be applied to P-Prolog and other parallel logic languages.