行为时序逻辑与自反线性时序逻辑的关系

为了能够将哲学逻辑中的公理系统运用到行为时序逻辑的研究中。对行为时序逻辑公式的语义进行形式化定义．从语义和语法两方面研究行为时序逻辑公理系统和具有自反性质的线性时序逻辑公理系统之间的联系．提出并证明行为时序逻辑公式转换为自反线性时序逻辑公式的定理。按照集合论和模型论的思想,定义行为时序逻辑中项和行为时序逻辑原子公式的概念。定义Lesilie Lamport所提出的行为时序逻辑公式的语义。证明自反线性时序逻辑公理系统适用于行为时序逻辑公理系统．以此为基础证明行为时序逻辑的简单规则、基本规则和附加规则。     

Linear, Branching Time and Joint Closure Semantics for Temporal Logic

Temporal logic can be used to describe processes: their behaviour ischaracterized by a set of temporal models axiomatized by a temporaltheory. Two types of models are most often used for this purpose: linearand branching time models. In this paper a third approach, based onsocalled joint closure models, is studied using models which incorporateall possible behaviour in one model. Relations between this approach andthe other two are studied. In order to define constructions needed torelate branching time models, appropriate algebraic notions are defined(in a category theoretical manner) and exploited. In particular, thenotion of joint closure is used to construct one model subsuming a setof models. Using this universal algebraic construction we show that aset of linear models can be merged to a unique branching time model.Logical properties of the described algebraic constructions are studied.The proposed approach has been successfully aplied to obtain anappropriate semantics for non-monotonic reasoning processes based ondefault logic. References are discussed that show the details of theseapplications.     

基于线性时序逻辑的实时系统建模与求精

线性时序逻辑语言XYZ／E在统一的语义框架下．能表示从高层需求规范到低层实现模型之间的不同抽象层次的系统描述，也适于描述实时系统的模型和逐步求精过程．本文提出了一种基于构件的实时系统求精方法，并给出一个具体实例一电梯控制系统，采用XYZ／E语言描述了该系统的模型及其求精过程．     

An Expressively Complete Linear Time Temporal Logic for Mazurkiewicz Traces

A basic result concerning LTL, the propositional temporal logic of linear time, is that it is expressively complete; it is equal in expressive power to the first order theory of sequences. We present here a smooth extension of this result to the class of partial orders known as Mazurkiewicz traces. These partial orders arise in a variety of contexts in concurrency theory and they provide the conceptual basis for many of the partial order reduction methods that have been developed in connection with LTL-specifications.We show that LTrL, our linear time temporal logic, is equal in expressive power to the first order theory of traces when interpreted over (finite and) infinite traces. This result fills a prominent gap in the existing logical theory of infinite traces. LTrL also constitutes a characterisation of the so-called trace consistent (robust) LTL-specifications. These are specifications expressed as LTL formulas that do not distinguish between different linearisations of the same trace and hence are amenable to partial order reduction methods.     

基于线性时序逻辑的多Agent协商推理模型

在多智能体系统中,协商是Agent交互的主要形式.用形式化方法构建了基于线性时序逻辑的协商推理模型,该模型用线性时序逻辑描述在协商过程中Agent所处环境,自身能力、权力、知识、思维等随时间的变化,以及在系统运行时Agent采取异步行为.进一步完善了多Agent系统中自主的协商机制.     

基于线性时序逻辑的对象文件系统形式化描述

基于线性时序逻辑,给出了对象文件系统特性的形式化描述.对象文件系统时序逻辑(OFSTL)是线性时序逻辑在描述对象文件系统应用中的一个推广.用OFSTL描述对象文件系统的性质,用模型化的状态迁移系统表示对象文件系统的访问行为.试图解决目前对象文件系统研究存在的问题: ①关注提升对象文件系统性能和功能,但是以增加对象文件系统复杂性为代价; ②很少针对对象文件系统精确描述,缺乏形式化的辅助,妨碍从细节上考查对象文件系统的正确性.     

An Until Hierarchy and Other Applications of an Ehrenfeucht–Fraïssé Game for Temporal Logic

We prove there is a strict hierarchy of expressive power according to the Until depth of linear temporal logic (LTL) formulas: for each k, there is a natural property, based on quantitative fairness, that is not expressible with k nestings of Until operators, regardless of the number of applications of other operators, but is expressible by a formula with Until depth k+1. Our proof uses a new Ehrenfeucht–Fraïssé (EF) game designed specifically for LTL. These properties can all be expressed in first-order logic with quantifier depth and size (log k), and we use them to observe some interesting relationships between LTL and first-order expressibility. We note that our Until hierarchy proof for LTL carries over to the branching time logics, CTL and CTL*. We then use the EF game in a novel way to effectively characterize (1) the LTL properties expressible without Until, as well as (2) those expressible without both Until and Next. By playing the game “on finite automata,” we prove that the automata recognizing languages expressible in each of the two fragments have distinctive structural properties. The characterization for the first fragment was originally proved by Cohen, Perrin, and Pin using sophisticated semigroup-theoretic techniques. They asked whether such a characterization exists for the second fragment. The technique we develop is general and can potentially be applied in other contexts.     

基于线性时态逻辑的Petri网模型检测研究

线性时态逻辑Petri网结合了Petri网和时序逻辑的优点,清晰简洁的描述并发系统事件间的时序和因果关系,包括系统的活性和安全性.其中自动机的体积是模型检验的一个关键性问题,为了得到尽可能小体积的自动机,在LTL公式转换为Büchi自动机之前,对LTL公式进行预处理来减少冗余,然后通过布尔技术优化自动机.     

A Fully Automated Framework for Control of Linear Systems from Temporal Logic Specifications

We consider the following problem: given a linear system and a linear temporal logic (LTL) formula over a set of linear predicates in its state variables, find a feedback control law with polyhedral bounds and a set of initial states so that all trajectories of the closed loop system satisfy the formula. Our solution to this problem consists of three main steps. First, we partition the state space in accordance with the predicates in the formula, and construct a transition system over the partition quotient, which captures our capability of designing controllers. Second, using a procedure resembling model checking, we determine runs of the transition system satisfying the formula. Third, we generate the control strategy. Illustrative examples are included.      

Light Linear Logic

The abuse of structural rules may have damaging complexity effects.     

Embedding Alternating-time Temporal Logic in Strategic Logic of Agency

Seeing To It That ()logic is a logic of agency, proposed in the 1990s in the domainof philosophy of action. It is the logic of constructions ofthe form ‘agent a sees to it that ’. We believethat theory can contributeto the logical analysis of multiagent systems. To support thisclaim, we show that there is a close relationship with morerecent logics for multiagent systems. This work extends Broersenet al. (2006, Electron Notes Theor. Comput. Sci., Vol. 157,pp. 23–35) where we presented a translation from Pauly'sCoalition Logic to Chellas' logic. Here we focus on Alur, Henzinger and Kupferman's Alternating-timeTemporal Logic , andthe logic of the ‘fused’ _s[_scstit : _] operatorfor strategic ability, as described by Horty. After a briefpresentation of ATL and the definition of a discrete-time strategic framework slightly adaptedfrom Horty, we give a translation from ATL to the framework, and prove that it determines correctembedding.     

First-Order Logic with Two Variables and Unary Temporal Logic

We investigate the power of first-order logic with only two variables over ω-words and finite words, a logic denoted by FO². We prove that FO² can express precisely the same properties as linear temporal logic with only the unary temporal operators: “next,” “previously,” “sometime in the future,” and “sometime in the past,” a logic we denote by unary-TL Moreover, our translation from FO² to unary-TL converts every FO² formula to an equivalent unary-TL formula that is at most exponentially larger and whose operator depth is at most twice the quantifier depth of the first-order formula. We show that this translation is essentially optimal. While satisfiability for full linear temporal logic, as well as for unary-TL, is known to be PSPACE-complete, we prove that satisfiability for FO² is NEXP-complete, in sharp contrast to the fact that satisfiability for FO³ has nonelementary computational complexity. Our NEXP upper bound for FO² satisfiability has the advantage of being in terms of the quantifier depth of the input formula. It is obtained using a small model property for FO² of independent interest, namely, a satisfiable FO² formula has a model whose size is at most exponential in the quantifier depth of the formula. Using our translation from FO² to unary-TL we derive this small model property from a corresponding small model property for unary-TL. Our proof of the small model property for unary-TL is based on an analysis of unary-TL types.