IDSRadar: a real-time visualization framework for IDS alerts

Intrusion Detection Systems(IDS) is an automated cyber security monitoring system to sense malicious activities.Unfortunately,IDS often generates both a considerable number of alerts and false positives in IDS logs.Information visualization allows users to discover and analyze large amounts of information through visual exploration and interaction efficiently.Even with the aid of visualization,identifying the attack patterns and recognizing the false positives from a great number of alerts are still challenges.In this paper,a novel visualization framework,IDSRadar,is proposed for IDS alerts,which can monitor the network and perceive the overall view of the security situation by using radial graph in real-time.IDSRadar utilizes five categories of entropy functions to quantitatively analyze the irregular behavioral patterns,and synthesizes interactions,filtering and drill-down to detect the potential intrusions.In conclusion,IDSRadar is used to analyze the mini-challenges of the VAST challenge 2011 and 2012.     

赋范格H蕴涵代数和模糊格H蕴涵代数

在范数的条件下扩充了格H蕴涵代数的概念,即赋范格H蕴涵代数,并讨论一些性质。然后将模糊集合论运用于赋范格H蕴涵代数,给出了模糊赋范格H蕴涵代数的定义,得到了一些基本性质。通过使用两个赋范格H蕴涵代数之间的映射定义了赋范格H蕴涵代数同态,且得到了一些性质。最后得到了在赋范格H蕴涵代数中的数列对于蕴涵距离是有界的结论。     

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.     

Lattice-valued soft algebras

Motivated by the rapidly developing theory of lattice-valued (or, more generally, variety-based) topological systems, which takes its origin in the crisp concept of S. Vickers (introduced as a common framework for both topological spaces and their underlying algebraic structures—frames or locales), the paper initiates a deeper study of one of its incorporated mathematical machineries, i.e., the realm of soft sets of D. Molodtsov. More precisely, we start the theory of lattice-valued soft universal algebra, which is based in soft sets and lattice-valued algebras of A. Di Nola and G. Gerla. In particular, we provide a procedure for obtaining soft versions of algebraic structures and their homomorphisms, as well as basic tools for their investigation. The proposed machinery underlies many concepts of (lattice-valued) soft algebra, which are currently available in the literature, thereby enabling the respective researchers to avoid its reinvention in future.     

Lattice implication ordered semigroups

From the viewpoint of semantics, lattice implication algebras provide a basis to establish lattice-valued logic with truth value in a relatively general lattice. In this paper, we first introduce two notions of lattice implication n-ordered semigroup and lattice implication p-ordered semigroup, which induced by lattice implication algebras. Secondly, we study some of their basic properties and prove that a lattice implication n-ordered semigroup is a residuated semigroup, and a lattice implication p-ordered semigroup is an arithmetic lattice ordered semigroup. We also define the homomorphism mapping between lattice implication n-ordered semigroups. Finally, we discuss some properties of filters and sl ideals in lattice implication n-ordered semigroups and lattice implication p-ordered semigroups.     

粗糙集代数与蕴涵格

在粗糙集的代数刻画方面,一个重要方法是在偶序对〈R（X）,R（X）〉构成的集合中通过定义基本运算寻找刻画偶序对所成集合的代数结构。其中,最有影响的代数结构是正则双Stone代数和Nelson代数。本文从偶序对〈T（X）,R（X）〉构成的集合入手,通过定义蕴涵运算证明了偶序对〈R（X）,R（X）〉所成集合构成蕴涵格,讨论了粗蕴涵格与
正则双Stone代数的关系。本文的讨论可为粗糙逻辑和粗糙推理奠定基础。     

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     

Production-logic relations on complete lattices

An algebraic system containing production-logic binary relations on a complete lattice is introduced. Some properties of such relations are studied without the use of recursions. The existence of a logical closure of a noetherian binary relation is proved. This allows for defining the notion of an equivalent relation.     

可换双剩余格上的广义模糊粗糙集及其公理化

双剩余格是t-模、t-余模、模糊剩余蕴涵及其对偶算子的代数抽象,基于格的L-模糊关系是普通模糊关系的推广。作为Pawlak经典粗糙集及多种模糊粗糙集模型的共同推广,提出了一种基于可换双剩余格及L-模糊关系的广义模糊粗糙集模型,引入了正则可换双剩余格的概念,并给出了基于正则可换双剩余格的广义模糊粗糙上、下近似算子的公理系统,推广了多个文献中已有的结果。     

基于量子逻辑的下推自动机与上下文无关文法

给出基于量子逻辑的下推自动机(e-VPDA)的概念,提出广义的子集构造方法,进而证明了一般的e-VPDA与状态转移为分明函数且具有量子终态的e-VPDA的等价性.利用此等价性,给出了量子上下文无关语言的代数刻画与层次刻画,并籍此证明了量子上下文无关语言关于正则运算的封闭性.最后,说明了量子下推自动机和量子上下文无关文法(e-VCFG)的等价性.     

粗代数研究

在粗糙集的代数方法研究中,一个重要的方面是从粗糙集的偶序对((下近似集,上近似集()表示入手,通过定义偶序对的基本运算,从而构造出相应粗代数,并寻找能够抽象刻画偶序对性质的一般代数结构.其中最有影响的粗代数分别是粗双Stone代数、粗Nelson代数和近似空间代数,它们对应的一般代数结构分别是正则双Stone代数、半简单Nelson代数和预粗代数.通过建立这些粗代数中算子之间的联系,证明了:(a) 近似空间代数可转化为半简单Nelson代数和正则双Stone代数;(b) 粗Nelson代数可转化为预粗代数和正则双Stone代数;(c) 粗双Stone代数可化为预粗代数和半简单Nelson代数,从而将3个不同角度的研究统一了起来.     

基于语言值格蕴涵代数的偏好顺序结构评估决策方法

针对具有可比性和不可比性语言值信息的决策问题,提出基于语言值格蕴涵代数(L_V(n×2))的多属性决策方法.讨论L_(n×2)上的语言值评价矩阵及其性质,提出L_V(n×2)上的优先函数和格值程度差,充分考虑属性值差距信息,将格值程度差应用到择优排序上.通过语言值向量,建立语言值向量合成矩阵,处理决策问题中的多专家多属性信息.引入语言值评价矩阵加权聚合算子对语言值评价矩阵进行聚合,利用偏好顺序结构评估(PROMETHEE)决策方法的非补偿性,构建基于语言值格蕴涵代数的PROMETHEE决策模型,并通过网络商品评价实例说明文中方法的有效性和实用性.     

-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).     

Rough implication operator based on strong topological rough algebras

The role of topological De Morgan algebra in the theory of rough sets is investigated. The rough implication operator is introduced in strong topological rough algebra that is a generalization of classical rough algebra and a topological De Morgan algebra. Several related issues are discussed. First, the two application directions of topological De Morgan algebras in rough set theory are described, a uniform algebraic depiction of various rough set models are given. Secondly, based on interior and closure operators of a strong topological rough algebra, an implication operator (called rough implication) is introduced, and its important properties are proved. Thirdly, a rough set interpretation of classical logic is analyzed, and a new semantic interpretation of ?ukasiewicz continuous-valued logic system ?uk is constructed based on rough implication. Finally, strong topological rough implication algebra (STRI-algebra for short) is introduced. The connections among STRI-algebras, regular double Stone algebras and RSL-algebras are established, and the completeness theorem of rough logic system RSL is discussed based on STRI-algebras.     

Notes on automata theory based on quantum logic

The main results are as follows: (1) it deals with a number of basic operations (concatenation, Kleene closure, homomorphism, complement); (2) due to a condition imposed on the implication operator for discussing some basic issues in orthomodular lattice-valued automata, this condition is investigated in detail, and it is discovered that all the relatively reasonable five implication operators in quantum logic do not satisfy this condition, and that one of the five implications satisfies such a condition iff the truth-value lattice is indeed a Boolean algebra; (3) it deals further with orthomodular lattice-valued successor and source operators; (4) an example is provided, implying that some negative results obtained in the literature may still hold in some typical orthomodular lattice-valued automata.     

Lattice pseudoeffect algebras as double residuated structures

Pseudoeffect algebras are partial algebraic structures which are non-commutative generalizations of effect algebras. The main result of the paper is a characterization of lattice pseudoeffect algebras in terms of so-called pseudo Sasaki algebras. In contrast to pseudoeffect algebras, pseudo Sasaki algebras are total algebras. They are obtained as a generalization of Sasaki algebras, which in turn characterize lattice effect algebras. Moreover, it is shown that lattice pseudoeffect algebras are a special case of double CI-posets, which are algebraic structures with two pairs of residuated operations, and which can be considered as generalizations of residuated posets. For instance, a lattice ordered pseudoeffect algebra, regarded as a double CI-poset, becomes a residuated poset if and only if it is a pseudo MV-algebra. It is also shown that an arbitrary pseudoeffect algebra can be described as a special case of conditional double CI-poset, in which case the two pairs of residuated operations are only partially defined.     

正则FI-代数的刻画及成为Boole代数的条件

正则FI-代数是仅基于蕴涵算子在一般集合上建立的逻辑代数。基于正则FI-代数的公理组以及诸多性质之间的内部联系,给出了正则FI-代数的两个公理组条件更少的刻画定理,简化了正则FI-代数的定义形式。在正则FI-代数中引入蕴涵分配性,探讨了蕴涵分配正则FI-代数的若干性质,证明了蕴涵分配正则FI-代数与Boole代数是相互等价的代数系统,给出了Boole代数的一种新的刻画,使其在形式上更接近于二值逻辑代数。     

基于量子逻辑的下推自动机的代数刻画

首先,本文提出量子下推自动机（简记为L-VPDA）的概念,从代数角度出发详细研究了此类自动机的性质,同时建立此类自动机的代数刻画,即利用量子状态构造证明了任意L-VPDA与状态转移为经典函数且具有量子终状态的L-VPDA间的相互等价性;其次详细研究了量子上下文无关语言的代数刻画以及对于正则运算的封闭性。     

Peirce algebras

We present a two-sorted algebra, called aPeirce algebra, of relations and sets interacting with each other. In a Peirce algebra, sets can combine with each other as in a Boolean algebra, relations can combine with each other as in a relation algebra, and in addition we have both a set-forming operator on relations (the Peirce product of Boolean modules) and a relation-forming operator on sets (a cylindrification operation). Two applications of Peirce algebras are given. The first points out that Peirce algebras provide a natural algebraic framework for modelling certain programming constructs. The second shows that the so-calledterminological logics arising in knowledge representation have evolved a semantics best described as a calculus of relations interacting with sets.     

Isomorphism theorems on generalized effect algebras based on atoms

A well-known fact is that every generalized effect algebra can be uniquely extended to an effect algebra in which it becomes a sub-generalized effect algebra and simultaneously a proper order ideal, the set-theoretic complement of which is its dual poset. We show that two non-isomorphic generalized effect algebras (even finite ones) may have isomorphic effect algebraic extensions. For Archimedean atomic lattice effect algebras we prove “Isomorphism theorem based on atoms”. As an application we obtain necessary and sufficient conditions for isomorphism of two prelattice Archimedean atomic generalized effect algebras with common (or isomorphic) effect algebraic extensions.