基于动态描述逻辑的主体模型

在动态描述逻辑的基础上，提出了一种智能主体的心智状态模型．它充分利用了动态描述逻辑统一的形式化框架，同时从静态的知识表示与推理和动态的运行与变化两个方面来刻画主体的心智状态．探讨了主体信念、行为能力、目标和规划等心智要素的表示、推理与修改等基本问题．该主体模型将理论和实践有机地结合起来，表达能力强，能够充分体现智能主体的本质特征与运行机制，为智能主体的设计与编程奠定了很好的基础．     

基于动态描述逻辑的多主体协作模型

基于动态描述逻辑的主体模型和协作过程就是既考虑了智能主体的知识表示与推理问题，又紧密地结合主体的设计与编程问题，把表示与推理应用到主体的具体设计中．它充分利用了动态描述逻辑的统一的形式化框架，同时从静态的知识表示与推理和动态的运行与变化两个方面来刻画主体的心智状态和协作过程，探讨了主体信念、行为能力、目标和规划等心智要素的表示、推理与修改以及联合目标的形成、多目标的规划问题．多主体协作模型将理论和实践有机地结合起来，能够充分体现智能主体的本质特征与运行机制，为多主体系统的设计与编程奠定了很好的基础．     

智能主体的信念认知时态子结构逻辑模型*

智能主体获取信念的途径主要有两种：一种为他省,通过外界交互,从其他主体获取信息;另一种为自省,通过自己的历史数据库获取相关知识。对于主体信念的描述与刻画,两种途径缺一不可,但当前的BDI理论模型中较多地为他省系统,没有做到两者相结合。其次,在当前的许多理论模型中,通常使用的是二值逻辑、经典模态逻辑或其变形系统,使得相应的逻辑系统普遍存在逻辑全知和粗精度刻画等问题。针对上述问题进行了相关研究,采用了认知时态子结构逻辑建模的方法,表达了智能主体获得“双省”信念的方式,针对其建立了相应的逻辑系统BSoET。     

一种新的类BAN逻辑模态语义模型——兼论类BAN逻辑的语法缺陷

由于类BAN逻辑缺乏明确而清晰的语义，其语法规则和推理的正确性就受到了质疑。本文定义了安全协议的计算模型，在此基础上定义了符合模态逻辑的类BAN逻辑“可能世界”语义模型，并从语义的角度证明了在该模型下的类BAN逻辑语法存在的缺陷，同时，指出了建立或改进类BAN逻辑的方向。     

现代模态逻辑在计算机科学中的应用研究

现代模态逻辑是在经典数理逻辑基础上发展起来的,主要包括狭义模态逻辑、道义逻辑、认知逻辑、信念逻辑、时态逻辑与动态逻辑。克里普克语义模型的建立,使得模态逻辑成为现代逻辑的重要分支之一,并成功应用到数学、经济学、社会科学、计算机科学和量子力学等众多领域。介绍了现代模态逻辑研究的主要内容,重点综述了现代模态逻辑在计算机科学的程序设计语言、知识表示与多代理系统以及模型检测、定理机器证明和非单调逻辑5个方面的应用,阐述了现代模态逻辑在计算机科学领域的研究目标、研究进展和发展趋势,最后指出现代模态逻辑研究中存在的问题,并预测其未来可能的研究与发展方向。     

公式分层的谓词模态逻辑

由于必然模态词□的引入,谓词模态逻辑的公式在一个可能世界中的真假值可能依赖于其可达的可能世界.在谓词模态逻辑中存在个体跨可能世界相等问题.针对这一问题,Lewis提出了对应物理论,并且在对应物理论中用对应物关系来表示个体跨可能世界相等.但是,当一个对象具有一个以上的对应物时,谓词模态逻辑中的跨可能世界相等关系无法与对应物关系建立一一对应.通过限制谓词模态逻辑中全称量词∀的范围,给出了一种公式分层的谓词模态逻辑.它是谓词模态逻辑的一个子逻辑,并且其语言与谓词模态逻辑的语言是相同的.但其公式是分层定义的,使得∀可以出现在□的范围内,并且□不能出现在∀的范围内.由于任意形如∀x□φ（x）的表达式都不是该逻辑的公式,以量词开头的公式在一个可能世界w中的真假值只依赖于w,该逻辑避免了个体跨可能世界相等问题.给出了该逻辑的语言、语法和语义,并证明了该逻辑是可靠的和完备的.     

基于完备拟序的开放逻辑

开放逻辑是一个可以刻画知识的增长，更新以及假说的进化的逻辑理论，它开辟了常识推理研究一条新途径，并在机器学习，知识获取，故障诊断及知识库维护等领域有广泛的应用，基本的开放逻辑不能体现认知主体对所拥有的知识在相信程度上的区别，为此，文中给出了基于完备拟序的开放逻辑，该文采用假说上的完备拟序刻画信度区别，给出了新的重构概念，讨论了假说及完备拟序在知识进化过程中的更新，定义了新的认识进程并证明了所定义的认识进程具有收敛性。     

基于模态的模糊描述逻辑(M-FALC)的形式化公理体系

模糊描述逻辑的提出是针对现实生活中存在的模糊现象,而模态逻辑解决的是现实生活中具有的状态和状态转换现象等。将模态逻辑中的模态思想和模糊逻辑中的模糊理论相结合,同时结合描述逻辑,形成模态模糊描述逻辑(M-FALC)。考虑不同论域中的可能存在的模糊概念,关系,公式等,本文给出M-FALC的形式化公理体系及其推理,既能解决现实问题中的状态现象又解决模糊现象。     

描述逻辑FL0概念及术语公理集的表达能力刻画

表达能力和推理复杂性是一个逻辑的两个重要特征,也是一对相互制约的关系。解释之间的互模拟关系是从语义的角度刻画逻辑表达能力的一个有效途径,其代表性的结果是命题模态逻辑表达能力的刻画定理-van Benthem刻画定理。文中给出了描述逻辑FL0(含构造子:原子概念、顶概念、概念交、全称量词约束)的模拟关系,建立了FL0中概念和术语公理集的表达能力刻画定理,即一阶逻辑公式与FL0概念和术语公理集等价的充分必要条件。上述结果为寻求表达能力与推理复杂性之间的最佳平衡提供了有效的支持。     

描述逻辑εLU概念及术语公理集的表达能力刻画

表达能力和推理复杂性是一个逻辑的两个重要特征,也是一对相互制约的关系.解释之间的互模拟关系是从语义的角度刻画逻辑表达能力的一个有效途径,其代表性的结果是命题模态逻辑表达能力的刻画定理——vanBenthem 刻画定理.给出了描述逻辑εLU（含构造子：原子概念、顶概念、概念交、概念并、完全存在约束）的模拟关系,建立了εLU中概念和术语公理集的表达能力刻画定理,即一阶逻辑公式与ELU中概念和术语公理集等价的充分必要条件.上述结果为寻求表达能力与推理复杂性之间的最佳平衡提供了有效的支持.     

Fibring Non-Truth-Functional Logics: Completeness Preservation

Fibring has been shown to be useful for combining logics endowed withtruth-functional semantics. However, the techniques used so far are unableto cope with fibring of logics endowed with non-truth-functional semanticsas, for example, paraconsistent logics. The first main contribution of thepaper is the development of a suitable abstract notion of logic, that mayalso encompass systems with non-truth-functional connectives, and wherefibring can still be dealt with. Furthermore, it is shown that thisextended notion of fibring preserves completeness under certain reasonableconditions. This completeness transfer result, the second main contributionof the paper, generalizes the one established in Zanardo et al. (2001) butis obtained using new techniques that explore the properties of a suitablemeta-logic (conditional equational logic) where the (possibly)non-truth-functional valuations are specified. The modal paraconsistentlogic of da Costa and Carnielli (1988) is studied in the context of this novel notionof fibring and its completeness is so established.     

Fibred semantics for feature-based grammar logic

This paper gives a simple method for providing categorial brands of feature-based unification grammars with a model-theoretic semantics. The key idea is to apply the paradigm of fibred semantics (or layered logics, see Gabbay (1990)) in order to combine the two components of a feature-based grammar logic. We demonstrate the method for the augmentation of Lambek categorial grammar with Kasper/Rounds-style feature logic. These are combined by replacing (or annotating) atomic formulas of the first logic, i.e. the basic syntactic types, by formulas of the second. Modelling such a combined logic is less trivial than one might expect. The direct application of the fibred semantics method where a combined atomic formula like np (num: sg & pers: 3rd) denotes those strings which have the indicated property and the categorial operators denote the usual left- and right-residuals of these string sets, does not match the intuitive, unification-based proof theory. Unification implements a global bookkeeping with respect to a proof whereas the direct fibring method restricts its view to the atoms of the grammar logic. The solution is to interpret the (embedded) feature terms as global feature constraints while maintaining the same kind of fibred structures. For this adjusted semantics, the anticipated proof system is sound and complete.     

Multi-modal nonmonotonic logics of minimal knowledge

In this paper we introduce multi-modal logics of minimal knowledge. Such a family of logics constitutes the first proposal in the field of epistemic nonmonotonic logic in which the three following aspects are simultaneously addressed: (1) the possibility of formalizing multiple agents through multiple modal operators; (2) the possibility of using first-order quantification in the modal language; (3) the possibility of formalizing nonmonotonic reasoning abilities for the agents modeled, based on the principle of minimal knowledge. We illustrate the expressive capabilities of multi-modal logics of minimal knowledge to provide a formal semantics to peer-to-peer data integration systems, which constitute one of the most recent and complex architectures for distributed information systems.      

Preservation of Interpolation Features by Fibring

Fibring is a metalogical constructor that permits to combinedifferent logics by operating on their deductive systems undercertain natural restrictions, as for example that the two givenlogics are presented by deductive systems of the same type.Under such circumstances, fibring will produce a new deductivesystem by means of the free use of inference rules from bothdeductive systems, provided the rules are schematic, in thesense of using variables that are open for application to formulaswith new linguistic symbols (from the point of view of eachlogic component). Fibring is a generalization of fusion, a lessgeneral but wider developed mechanism which permits resultsof the following kind: if each logic component is decidable(or sound, or complete with respect to a certain semantics)then the resulting logic heirs such a property. The interestfor such preservation results for combining logics is evident,and they have been achieved in the more general setting of fibringin several cases. The Craig interpolation property and the Maeharainterpolation have a special significance when combining logics,being related to certain problems of complexity theory, someproperties of model theory and to the usual (global) metatheoremof deduction. When the peculiarities of the distinction betweenlocal and global deduction interfere, justifying what we callcareful reasoning, the question of preservation of interpolationbecomes more subtle and other forms of interpolation can bedistinguished. These questions are investigated and several(global and local) preservation results for interpolation areobtained for fibring logics that fulfill mild requirements.     

Deciding Regular Grammar Logics with Converse Through First-Order Logic

We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF², which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. The translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. It is practically relevant because it makes it possible to use a decision procedure for the guarded fragment in order to decide regular grammar logics with converse. The class of regular grammar logics includes numerous logics from various application domains. A consequence of the translation is that the general satisfiability problem for every regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Other logics that can be translated into GF² include nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF² without extra machinery such as fixed-point operators.     

Kripke Semantics for Modal Substructural Logics

We introduce Kripke semantics for modal substructural logics, and provethe completeness theorems with respect to the semantics. Thecompleteness theorems are proved using an extended Ishihara's method ofcanonical model construction (Ishihara, 2000). The framework presentedcan deal with a broad range of modal substructural logics, including afragment of modal intuitionistic linear logic, and modal versions ofCorsi's logics, Visser's logic, Méndez's logics and relevant logics.     

Reasoning about Minimal Knowledge in Nonmonotonic Modal Logics

We study the problem of embedding Halpern and Moses's modal logic of minimal knowledge states into two families of modal formalism for nonmonotonic reasoning, McDermott and Doyle's nonmonotonic modal logics and ground nonmonotonic modal logics. First, we prove that Halpern and Moses's logic can be embedded into all ground logics; moreover, the translation employed allows for establishing a lower bound (3p) for the problem of skeptical reasoning in all ground logics. Then, we show a translation of Halpern and Moses's logic into a significant subset of McDermott and Doyle's formalisms. Such a translation both indicates the ability of Halpern and Moses's logic of expressing minimal knowledge states in a more compact way than McDermott and Doyle's logics, and allows for a comparison of the epistemological properties of such nonmonotonic modal formalisms.     

带函数的描述逻辑

描述逻辑是包含了概念、角色以及概念和角色构造子的一阶逻辑的子逻辑,具有表达能力强且推理可判定的特征。但现有描述逻辑无法表示概念和角色上的函数,因此在图书馆的概念模型中,有一些问题便不能表示,如图书的本数、借书的条目数等。在现有描述逻辑基础上引入函数来解决这个问题。首先分析现有描述逻辑在图书馆的概念模型中不能表示的一些问题并提出解决方法,然后给出带函数的描述逻辑的语法和形式语义,最后用带函数的描述逻辑形式化表示图书馆概念模型中的一些实际问题。