Boolean Operator Fuzzy Logic In The Mediation Act

With the development of artificial intelligence, especially the approach of knowledge-based system, people are more and more clear about the innate limitations of the first-order logic: it's difficult for it to describe and deal with the uncertainty, inconsistency and insufficient of knowledge. The aim we establish the logic frame BOFL (Boolean Operator Fuzzy Logic) is to solve the innate limitation of the first-order logic.Equality is a very important relation, and many theorems can be easily symbolized through its use. The equality relation has many special properties: it is reflexive, symmetric, and transitive. In addition, we can also substitute equals for equals. It will be more concise and intuitively to use equality predicate to describe a theorem. It is so important to use equality predicate that many researchers had studied the problem that the equality relation was deal with by resolution method, such as paramodula-tion, E - resolution and RUE-NRF resolution.First we briefly introduce BOFL, including some basic concepts and some important theorems. In view of the importance of equality, the thesis proposes the paramodulaton in BOFL. At beginning, we give the equality axiom set and the reflexive axiom set. After that we prove the soundness of the paramodulation in BOFL. And then we prove that paramodulation is generalized complete when used with resolution for 2E - unsatisfied clause set.X. H. Liu and Z. An prensented the generalized paramodulation in1985. Y. Y. Wang presented the generalized substitutive paramodulation in1986. So the paramodulation can be used in generalized clause set. Theadvantage of the generalized clause set is that it can avoid abound of redundancy and make describing problem more natural. This thesis proposes the generalized paramodulation in BOFL and proves the soundness of it. Together we prove that generalized paramodulation is generalized complete when used with generalized resolution for E - unsatisfied clause set.In the end the thesis compares its work to relative work. And draw a few advantages as follow:Firstly, the paramodulation in BOFL is more concise and nature. Its form is unified with the paramodulation in first-order logic.Secondly, because the operator is associativity, so it is possible to avoid the boring complicated letters Thirdly, because the association of resolution and paramodulation is generalized complete, we can use the infimum of the operator to gradually close the false level of cause set. so it is not necessary to choose threshold before resolution and paramodulation. The operator is got from every resolution and paramodulation.