Research On Lossless Simplifying And Solving Methods Of Function Tree For Innovative Reasoning

As the key factor for manufacturing to get victory in market competition, products' innovative reasoning lies on the conceptual design phase in product design, and function models are the main operating objects of conceptual design, so innovative reasoning of function models becomes the key problem of conceptual design. Nowadays, function tree with and/or decomposition (function tree for short) is a typical, popular function model in conceptual design, and moreover simplifying and solving problems of function tree are kernel problems in innovative reasoning of function tree. However, the essence of innovative reasoning is to solve problems by eliminating conflicts, which are equivalent to the situation of "not", therefore function tree with and/or/not decomposition (and/or/not function tree for short) need to be investigated. Meanwhile, function tree is able to be regarded as an application of Boolean algebra theory, but it was found that simplification based on that theory leads to loss of innovative ability. Aiming at that problem, the idea of losslessness has been aready proposed for and/or function tree, which is still not mature, self-contained with many shortages. As a result, problems of lossless simplifying and solving for and/or/not function tree are carried through research in this dissertation. The main content includes:1) The lossless simplifying theory for two-valued propositional logic is prososed. From the close relation between Boolean algebra and classical two-valued propositional logic, innovative reasoning can be studied from two-valued propositional logic. Loss of innovative ability originated from two-valued logic is analysed based on the concept of initial solving space of which strict definition is given in advance before provement of lossless simplifying theorem.2) The theory of lossless simplifying of and/or/not function tree is brought forward. To begin with, following given definitions related to function tree, lossless simplifying and AND/OR tree, function tree is converted to AND/OR tree for convenience. Next, some theorems of lossless simplifying for AND/OR tree are put forward. At last, the algorithm of lossless simplifying for and/or/not function tree is proposed.3) The theory of lossless solving of and/or/not function tree is put forward. The concepts of many-valued matrix and extending many-valued matrix are put forward before defining and/or/not operation and proving the property of many-valued matrix algebra systems. What's more, according to lossless simplifying theory, the lossless simplifying rules of many-valued matrix are proposed with provement of expanding theorem of many-valued matrix. Finally, the algorithm of lossless solving based on extending many-valued matrix is proposed.Conceptual Design; Innovative Reasoning; Artificial Intelligence; Function Tree; Lossless Simplifying; Logic Reasoning...