Resolution based on six lattice-valued proposition logic LP6(X)

Resolution-based automated reasoning theory is an important and active research field in artificial intelligence. It is used to judge the satisfiability of any logic formula. With the development of classical and non-classical logic, the resolution theory and method based on different logic system has been discussed widely and deeply. In the present paper, a new resolution principle by using ultrafilter in LP₆(X) is put forward. Different from existed method of resolution, this resolution in this paper is based on ultrafilter of lattice implication algebra. In this paper, resolution principle based on any formula is discussed and soundness theorem is proved. Subsequently, algorithm of this resolution based on ultrafilter is given. Because of LP₆(X) is a non-chain, non-boolean and non-well-ordered algebra structure, resolution based on LP₆(X) will be the theoretical foundation of resolution on lattice-valued truth-field. Accordingly, the research in this paper will be helpful support for the application of intelligent reasoning system based on lattice-valued logic.