Non-revision Approaches To Horn Clausal Inconsistent Beliefs

Belief revision method is one of the most important topics in common reasoning researches. It focuses on specific logic model and deals with the inconsistent or incomplete information, which is defined as belief. The set of beliefs is called assumption. There are several kinds of belief revision methods. These belief revision methods, by the means of imposing structure on belief sets or establishing the reasoning rules, attempt to set up a consistent theorem set for reasoning.Although it seemed perfect, the idea of belief revision has several disadvantages. First of all, in the revising process, some expected information would lose, for what reconstruction algorithm must be design to find them back, which would make the system complex and inefficient. Secondly, as the core idea of all the belief revision methods is that new information, which might be false, must be reserved in the belief set, that would deduce unwanted conclusions in reasoning process, which are hardly ruled out.To deal with these problems, belief non-revision method is presented. Instead of revising beliefs, it keeps the belief and constructs the belief set that deduce insistent information as conclusions set, which is defined as the extension of assumption.Then it turns out to be necessary for belief non-revision method to impose a structure on the reasoning process in order to guide the decisions about what to retain and what to retract for constructing the extension. The need for such a structure is especially evident if the belief set is considered to be a deductively closed theory. Several works has been done in this. In this paper, the belief sets, i.e. assumptions are defined as first logic Horn clause sets. Its extensions are constructed by Unite Resolution Principle. Proofs are given to present that the extensions of Horn clause-formed assumptions have several good mathematical properties, such as consistency, uniqueness and deductively closed. It also is proved that these extensions converge to a definite limit in the epistemic process.