Abstract: The multi-premise problem is an important research field of decision making and its optimal decision reflects the state of the art research of decision theory. Many methods can achieve it in multi-premise decision making, and each method has its own difficulties. This paper first introduced a new concept premise set, proposed an algorithm to decom- pose premise set into the simplest form, and proved that the algorithm outputs minimal, non-complete premise sets for any given goal. Next the credibility of each premise was defined for measuring the difficulty of premise set, and the opti- mal premise set was recommended for the goal. Then this paper gave a formal description of the logical framework()for evaluation of multiple-premise,and proved its computability and reasoning faculty. Finally,a prototype of framework O was implemented in Prolog and its soundness was proved via experiments and application in software engineering.

Key words: Multi-premise, Optimal premise set, Credibility, Difficulty of premise set, Evaluation