Rough Logic And Its Quantitative Research

The studied of rough logic are attended since the rough set is proposed by Pawlak. Pre-rough logic system and RSL system are two important rough logic systems, which research methods are similar to the classical mathematical logic and multi-value mathematical logic, which studied the soundness and completeness of the logic system. In recent years, Professor Wang Guojun proposed the theory framework of quantitative logic that combines numerical calculation and logic reasoning, which provide a new direction to study the mathematical logic.According to the research method of quantitative logic, the concept of true degrees are proposed on Pre-rough logic system and RSL system respectively in this thesis, and the research on the theory of true degree and approximate reasoning are given. The main research contents and innovations as follows:Firstly, for the pre-rough logic system, the theory of truth degrees on3-valued propositional pre-rough logic are given, and the truth density of all the formula is proved on the set [0,1], moreover, the similarity degree and pseudo-distance between two formulas are defined and approximate reasoning on3-valued propositional pre-rough logic is considered.Secondly, for the3-valued propositional pre-rough logic system, the definitions of a-truth degree a-similarity degree and a-pseudo-metric between two formulas are given are given, and the properties of them are studied.Thirdly, the theory of truth degrees on4-valued propositional pre-rough logic is studied.Lastly, for RSL system, the theory of truth degrees is studied on3-valued RSL system, and some reasoning rules, such as, MP, HS, truth degrees intersection etc, are proved true in it. Moreover, the similarity degree and pseudo-distance between two formulas are introduced, and the properties of them are studied.The quantitative research on3-valued,4-valued pre-rough logic system and3-valued RSL logic system are studied in this thesis, and the related research achievements enrich the research content of rough logic, which provide the basis for the further research.