基于蕴涵算子族Lλ0λG的模糊推理三I约束算法

提出了基于蕴涵算子族Lλ0λG的模糊推理的思想,这将有助于提高推理结果的可靠性。针对蕴涵算子族Lλ0λG给出了模糊推理的FMP模型及FMT模型的三I约束算法。     

基于蕴涵算子族Lλ0λG的反向三I支持算法

提出了基于蕴涵算子族Lλ0λG的模糊推理的思想,这将有助于提高推理结果的可靠性。针对蕴涵算子族Lλ0λG给出了模糊推理的FMP模型及FMT模型的反向三I支持算法。     

基于蕴涵算子族Lλ0λG的反向α-三I支持算法

提出了基于蕴涵算子族Lλ0λG的模糊推理的思想,这将有助于提高推理结果的可靠性。针对蕴涵算子族Lλ0λG给出了模糊推理的FMP模型及FMT模型的反向α-三I支持算法。     

基于蕴涵算子族L-λ-G的反向三I约束算法

提出了基于蕴涵算子族L-λ-G的模糊推理的思想,这将有助于提高推理结果的可靠性。针对蕴涵算子族L-λ-G给出了模糊推理的FMP模型及FMT模型的反向三I约束算法、α-反向三I约束算法。     

系统L在非均匀概率空间下命题的真度理论

将经典二值命题逻辑L中公式的真度概念推广到势为2的非均匀概率空间上;当p∈(0,1)时,证明了全体公式的真度值之集在[0,1]中没有孤立点;利用真度定义公式间的p-相似度和伪距离,进而定义了p-逻辑度量空间,证明了该空间没有孤立点,并在此空间中提出了三种不同类型的近似推理模式。     

基于含参数蕴涵算子族L-λ -R0的三I支持算法 ——仅就FMP模型进行讨论

提出了基于蕴涵算子族L-λ-R₀的模糊推理的思想,这将有助于提高推理结果的可靠性。针对蕴涵算子族L-λ-R₀给出了模糊推理的FMP模型的三I支持算法、α-三I支持算法。     

n值乘积逻辑系统中的随机化研究

利用赋值集的随机化方法,在n值乘积逻辑中提出了公式的随机真度,证明了所有公式的随机真度之集在[0,1]中没有孤立点;给出了两公式间的D_πn-相似度与伪距离的概念,并建立了D_πn逻辑度量空间,证明了此空间没有孤立点。     

基于蕴涵算子L-λ-0-λ-G的模糊推理的三I算法

研究了基于蕴涵算子L-λ-0-λ-G模糊推理的FMP三I支持算法,给出了FMP模型和FMT模型的三I算法的计算公式。     

一种增强的隐私保护K-匿名模型——（α，L）多样化K-匿名

K-匿名化是数据发布环境下保护个人隐私的一种有效的方法。指出目前已有的一些K-匿名模型存在隐私泄露问题,给出了一种新的有效的K-匿名模型——（α,L）多样化K-匿名模型解决存在的问题。通过一个局部化泛化算法对新模型的有效性进行实验验证。     

最优无向双环网络G（N；±1，±s）的构造

创造性地将直角坐标系引入无向双环网络的研究,通过直角坐标系,系统研究无向双环网络G（N;±1,±s）的仿真图形,提出最优无向双环网络BestG（N;±1,±s）（直径、平均直径均达到下界）的构造方法并研究步长s和其直径之间的关系。与传统L型瓦方法在无向双环网络研究中相比,该方法克服其不足,大大提升了无向双环网络的研究水平,相关研究在国内外文献中尚未见到。     

Determination of α-resolution in lattice-valued first-order logic LF(X)

Key issues for resolution-based automated reasoning in lattice-valued first-order logic LF(X) are investigated with truth-values in a lattice-valued logical algebraic structure-lattice implication algebra (LIA). The determination of resolution at a certain truth-value level (called α-resolution) in LF(X) is proved to be equivalently transformed into the determination of α-resolution in lattice-valued propositional logic LP(X) based on LIA. The determination of α-resolution of any quasi-regular generalized literals and constants under various cases in LP(X) is further analyzed, specified, and subsequently verified. Hence the determination of α-resolution in LF(X) can be accordingly solved to a very broad extent, which not only lays a foundation for the practical implementation of automated reasoning algorithms in LF(X), but also provides a key support for α-resolution-based automated reasoning approaches and algorithms in LIA based linguistic truth-valued logics.     

Filter-based resolution principle for lattice-valued propositional logic LP(X)

As one of most powerful approaches in automated reasoning, resolution principle has been introduced to non-classical logics, such as many-valued logic. However, most of the existing works are limited to the chain-type truth-value fields. Lattice-valued logic is a kind of important non-classical logic, which can be applied to describe and handle incomparability by the incomparable elements in its truth-value field. In this paper, a filter-based resolution principle for the lattice-valued propositional logic LP(X) based on lattice implication algebra is presented, where filter of the truth-value field being a lattice implication algebra is taken as the criterion for measuring the satisfiability of a lattice-valued logical formula. The notions and properties of lattice implication algebra, filter of lattice implication algebra, and the lattice-valued propositional logic LP(X) are given firstly. The definitions and structures of two kinds of lattice-valued logical formulae, i.e., the simple generalized clauses and complex generalized clauses, are presented then. Finally, the filter-based resolution principle is given and after that the soundness theorem and weak completeness theorems for the presented approach are proved.     

-Resolution principle based on lattice-valued propositional logic LP(X)

In the present paper, resolution-based automated reasoning theory in an L-type fuzzy logic is focused. Concretely, the -resolution principle, which is based on lattice-valued propositional logic LP(X) with truth-value in a logical algebra – lattice implication algebra, is investigated. Finally, an -resolution principle that can be used to judge if a lattice-valued logical formula in LP(X) is always false at a truth-valued level (i.e., -false), is established, and the theorems of both soundness and completeness of this -resolution principle are also proved. This will become the theoretical foundation for automated reasoning based on lattice-valued logical LP(X).     

格值命题逻辑系统L9P（X）中的自动推理算法

给出了格值命题逻辑系统L₉P（X）上的放缩原理和放缩归结原理,基于放缩归结原理,给出了一种判断L₉P（X）上子句集S为M－可满足的自动推理算法（这里M为L₉上的中界元）,并证明了其可靠性和完备性。     

ON SEMANTICS OF L-VALUED FIRST-ORDER LOGIC Lvft

Abstract

Many-valued logic system always plays a crucial role in artificial intelligence. Many researchers have paid considerable attention to lattice-valued logic with truth values in a lattice. In this paper, based on lattice implication algebras introduced by Xu (Journal of Southwest Jiaolong University (in Chinese), Sum. No. 89(1), 20-27, 1993, and L-valued propositional logic _vft, established by Xu et al. (Information Sciences, 114, 20S-235, 1999a), the semantics of a L-type lattice-valued first-order logic L_vft, with truth values in lattice implication algebras were investigated. Some basic concepts about semantics of L_vftsuch as the language and the interpretation etc. were given and some semantic properties also were discussed. Finally, a concept of g-Skolem standard form was introduced, and it was shown that the unsatisfiability of a given lattice-valued formula was equivalent to that of its g-Skolem standard form. It will become a foundation to investigate the resolution principle based on first-order logic L_vft     

四值非链格值命题逻辑系统L4P(X)的语义归结方法*

为了提高归结方法处理带有不可比较性信息的能力,给出了四值格值命题逻辑系统上的语义归结原理,并证明了其可靠性和完备性,其上归结原理的研究为归结算法的实现提供了理论基础,从而为处理含有不可比真值的格值逻辑系统在智能推理系统中的实际应用提供了有力的支持。     

Fuzzy operator logic and fuzzy resolution

There have been only few attempts to extend fuzzy logic to automated theorem proving. In particular, the applicability of the resolution principle to fuzzy logic has been little examined. The approaches that have been suggested in the literature, however, have made some semantic assumptions which resulted in limitations and inflexibilities of the inference mechanism. In this paper we present a new approach to fuzzy logic and reasoning under uncertainty using the resolution principle based on a new operator, the fuzzy operator. We present the fuzzy resolution principle for this logic and show its completeness as an inference rule.     

A Framework for Automated Reasoning in Multiple-Valued Logics

The language of signed formulas offers a first-order classical logic framework for automated reasoning in multiple-valued logics. It is sufficiently general to include both annotated logics and fuzzy operator logics. Signed resolution unifies the two inference rules of annotated logics, thus enabling the development of an SLD-style proof procedure for annotated logic programs. Signed resolution also captures fuzzy resolution. The logic of signed formulas offers a means of adapting most classical inference techniques to multiple-valued logics.