各种类型的复杂推理是人工智能和计算机科学等领域所共同关心的问题，其主要特点是逻辑公式的真值域、推理模式的时序性、所容纳客体的多样性已远远超出经典逻辑的推理模式范畴。然而，承载不同复杂推理模式的逻辑系统所使用的基本逻辑概念仍然是非此即彼式的，从这层意义上讲，它们仍属于二值逻辑的范畴。本项目在分析各种复杂推理模式的基础上，旨在通过“聚合真值”的计量化方法，探求既能够承载多种复杂推理，又能在一定程度上兼顾序结构与代数结构和谐性的非经典逻辑推理系统。为此我们拟进行如下研究: (i) 计量逻辑理论体系的进一步完善；(ii) 语义计量化方法的随机化；(iii) 模态逻辑、谓词逻辑以及模型检测中的计量化理论；(iv) 逻辑计量化方法的公理化及代数化；(v) 模糊序与计量化方法的融合与统一。通过如上五个专题的研究，最终能为复杂推理建立起容错功能强、推理能力高的计量化模型。

Different kinds of complicated reasoning methods are problems of common concern in the communities of artificial intelligence and computer science. The main features of complicated reasoning are described by the valuation domains, temporal properties of the reasoning models and the diversity of agents, which are quite distinct from those in two-valued logic. However, the basic logical notions employed in different logical systems are “either black or white”. From this point of view, non-classical logical systems still belong to the category of two-valued logics. On the basis of analysis on different patterns of complicated reasoning, the present project aims to establish several kinds of non-classical logic systems, not only suitable for different types of complicated reasoning but also compatible with order and algebraic structures, by means of a quantitative approach to aggregate truth values. Under the above framework, we aim to study the following topics: (i) further improvement of quantitative logic theory; (ii) randomization of semantic quantification; (iii) quantitative theory in modal logic, predicate logic and model checking; (iv) axiomatization and algebraization of quantitative logic; (v) unification and compatibility of fuzzy order and semantic quantitative method. By studying the five topics mentioned above, a quantitative model with stronger compatibility and capacity for complicated reasoning can be finally established.