线性时序关系下推理的概率计量化模型

项目名称： 线性时序关系下推理的概率计量化模型

项目编号： No.11426148

项目类型： 专项基金项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 时慧娴

作者单位： 陕西师范大学

项目金额： 3万元

中文摘要： 不确定性推理是人工智能的核心研究课题之一。从推理的研究方法看，概率逻辑与计量逻辑是处理知识的不确定性问题时常用的逻辑推理方法，但二者面对同时带有模糊性与随机性的复杂知识时均显出各自的局限性；从推理依据的逻辑框架看，现有的推理机制多采用命题逻辑或二值式的推理模式，其表达能力已不能满足复杂推理的需要。本项目拟将概率、计量方法结合引入到时序逻辑中，针对随机Kripke语义结构构建适当的概率测度，并利用动态模型序列的时序特点给出判断规约语句有效性的程度化方法，最终建立基于线性时序关系下推理的概率计量化模型，使推理机制随时间的推进呈现动态化的特点，从而在更为宽泛的框架下展开不确定性推理研究。具体包括以下专题研究：(i)针对线性时序逻辑构造范式表示并化简公式构成；(ii)基于线性时序关系建立判断规约语句有效性的程度化模型；(iii)讨论推理系统的安全性、公平性及活跃性。

中文关键词： 不确定性推理；线性时序逻辑；计量逻辑；随机Kripke语义；

英文摘要： Reasoning about Uncertainty is one of the core research topics for Artificial Intelligence. As two commonly used logical deduction approaches for reasoning, Probabilistic Logic and Quantitative Logic both have limitations when dealing with complex knowledge that represents randomness as well as fuzziness. Besides, most existing reasoning mechanisms adopt propositional logic or two-valued deduction mode as their logical frames, which cannot be sufficient for the need of complex reasoning. This project aims to simultaneously introduce probabilistic and quantitative approaches into reasoning under linear time sequence. Based on random Kripke structures and dynamic model sequences, suitable measures are adopted in order to construct a method of gradedly judging validness for specifications. It includes the following special subjects: (i) Normal form and formulae simplification for linear temporal logic. (ii) Graded models for judging validness of specifications under linear time sequence. (iii) Discussion about the safety, fairness and liveness properties for reasoning systems.

英文关键词： reasoning about uncertainty；Linear Temporal Logic；quantitative logic；random Kripke semantics；