Studies On The Flexible Interval-logic And Its Reasoning

This dissertation comes from the National Nature Science Foundation of China "Research on Theories of Experience Knowledge Reasoning" (No. 60273087) and Beijing Nature Science Foundation of China "Research on Theories of imprecise reasoning" (No.4032009), and it is part of the research field of the Artificial Intelligence.The well-developed classical mathematical logic is rather rigid and it can only solve certainty problems. Studies of various non-classical logic and modern logic, which contain contradiction and uncertainties, have been the mainstream topics for further development of AI. In the study of general laws of logics, Professor Huacan He proposed a new flexible logic which was called Universal Logics. Various flexible-reasoning processes and evolution processes were comprehensively investigated, containing contradiction and uncertainties.In this dissertation, the idea of Universal Logics is introduced into the Interval Logic. The flexibility of the valued field and operations models of the Interval Logic has been realized. And Flexible Interval-reasoning process is deeply studied. The innovation and main results are summarized as follows:1. Based on Universal Logics principles, the generalized correlativity is introduced into the Interval Logic. The operation model clusters of the Interval Logic are defined, including the Flexible Interval Complement, the Flexible Interval Intersection, the Flexible Interval Union, the Flexible Interval Implication, the Flexible Interval Equivalence, the Flexible Interval Average and the Flexible Interval Combination; Moreover, properties of the Flexible Interval Intersection, the Flexible Interval Union, the Flexible Interval Implication and the Flexible Interval Average are investigated.2. Four operation model clusters of the Flexible Interval Implication are proposed. The boundary condition and monotonicity of the first operation model clusters of the Flexible Interval Implication are investigated; The Flexible Interval-intersection and the Flexible Interval-implication are proved to be an adjoint pair; Furthermore, the Flexible Interval-intersection, the Flexible Interval Union and the Flexible Interval-implication are proved to constitute complete residuated lattice, and have the well-known algebraic properties.3. The models of the Flexible Interval-reasoning are proposed, and found to...