基于动态时序语义的逻辑推理及其量化模型

Uncertainty for knowledge and information is a fundamental and unavoidable feature in our real life. To adequately and precisely express the uncertainty for knowledge and information, various kinds of quantitative approaches were adopted on logical reasoning. In recent decades, most of the quantitative research in the field of Uncertainty Reasoning only focused on single means of quantitative strategy. Generally speaking, single means of quantitative strategy expresses knowledge and information with one-sidedness, only representing one form of uncertainty at one time, such as fuzziness, randomness or roughness. Besides, most of the existing reasoning mechanisms were based on propositional logics or two-valued deduction modes. Although propositional logics usually have simple semantics and syntax, their reasoning ability are relatively weak and could not adapt to complex reasoning anymore. This project aims to construct a new reasoning model both quantitatively and dynamically by simultaneously adopting several kinds of quantitative approaches on logical reasoning. First we locally consider the Kripke structure of temporal logic and provide different quantitative operators to respectively interpret sets of states, agents and local relations. Then we assemble all kinds of Kripke structure by introducing one proper measure on the product space of states and agents, in order to establish quantitative semantics for temporal logic from the global angle. Finally we provide a kind of quantitative model for logical reasoning under dynamic sequential-timing semantics. The research of this project includes the following special subjects: (i) Normal form and formulae simplification for temporal logic; (ii) Quantitative Kripke semantics of temporal logic for gradedly judging the truth of formulae or events; (iii) Quantitative reasoning model under dynamic sequential-timing semantics; (iv) Discussion about several properties for reasoning system, such as consistency and safety.

知识与信息的不确定性是现实生活中普遍存在的规律与特征，将量化思想引入逻辑推理可以更准确地表达这种不确定性。量化逻辑推理的现有研究大多采用单一的量化手段，不能全面地反映事件的动态不确定性；且现有推理机制大多依据命题逻辑或二值式的推理模式，其表达与推理能力逐渐不能满足复杂推理的需要。本项目拟将多种量化手段交叉结合，通过采用“先局部后整体”的思路，逐步实现时序逻辑Kripke语义的量化，并在动态时序语义的背景下建立逻辑推理的量化模型。具体研究内容包括：(1)针对时序逻辑建立统一的范式表示并化简其公式构成；(2)“先局部后整体”地建立量化时序语义的基本框架；(3)在量化的时序语义框架下建立推理系统的动态化模型；(4)讨论量化时序推理模型的相容性、安全性等性质。拟建立的推理模型能够描述当事人对事件的量化判断，且这种判断可以随着时间的推进不断更新，从而为不确定性推理提供更合理、推理能力更强的逻辑依据。

本项目将模糊集合论、广义测度论等多种量化手段交叉结合，在时序语义的背景下展开逻辑推理研究，并基于时序语义的结构特点建立了动态化的量化推理模型，旨在为复杂推理模式提供更合理、推理能力更强的逻辑依据。本项目的相关研究成果已发表于《International Journal of Approximate Reasoning》、《Information Sciences》、《Iranian Journal of Fuzzy Systems》、《Journal of Intelligent & Fuzzy Systems》等国内外多个学术期刊，目前已正式发表的研究论文共10篇，其中SCI收录5篇、EI收录2篇、中文核心收录3篇。具体研究进展与成果包括以下内容：. (i) 建立了时序逻辑的范式表示与结构化简。项目组从时序逻辑的Kripke语义特点出发，为时序公式建立了“特征”与“满足集”概念；以特征为指标将公式进行分类，给出了不同类型公式之间特征与满足集的递归计算方法；基于此为全体时序公式建立了统一的范式表示，从而化简了时序逻辑的公式构成，为降低推理模型的复杂度作准备。. (ii) 建立了量化时序语义的基本框架。项目组将时序逻辑的Kripke语义进行了量化，针对时序逻辑的Kripke结构引入了某种迁移概率映射；为Kripke结构中各个状态及状态间的迁移关系建立了某种适当的概率分布，并针对所构建的随机Kripke结构引入了适当的概率测度；基于此将各类公式的满足集进行了量化，最终建立了判断规约语句有效性的程度化方法。. (iii) 建立了时序逻辑度量空间。项目组针对上述量化时序语义的基本框架，在时序公式满足度的基础上引入了公式间的相似度与伪距离；进一步建立了基于时序语义的逻辑度量空间，并在该度量空间中探讨了拓扑性质、内蕴结构及完备化等方面的问题。. (iv) 建立了量化推理的多粒度粗糙模型。项目组将现有的单粒度粗糙模型扩充为多粒度情形，通过论域上不同的等价关系来描述不同当事人对同一对象集所具有的信息，并展开不同当事人之间的知识推理与信息传递；在此基础上研究了多粒度粗糙模型与三值逻辑之间的密切联系，建立了三值逻辑中的各类合取算子所对应的多粒度粗糙模型，并为多粒度粗糙模型建立了量化推理的三值逻辑语义。