Probabilistic Belief Logic and Its Probabilistic Aumann Semantics

In this paper, we present a logic system for probabilistic belief named PBL,which expands the language of belief logic by introducing probabilistic belief. Furthermore, we give the probabilistic Aumann semantics of PBL. We also list some valid properties of belief and probabilistic belief, which form the deduction system of PBL. Finally, we prove the soundness and completeness of these properties with respect to probabilistic Aumann semantics.     

Algebraic approach to linking the semantics of web services

Web services have become more and more important in these years, and BPEL4WS (BPEL) is a de facto standard for the web service composition and orchestration. It contains several distinct features, including the scope-based compensation and fault handling mechanism. We have considered the operational semantics and denotational semantics for BPEL, where a set of algebraic laws can be achieved via these two models, respectively. In this paper, we consider the inverse work, deriving the operational semantics and denotational semantics from algebraic semantics for BPEL. In our model, we introduce four types of typical programs, by which every program can be expressed as the summation of these four types. Based on the algebraic semantics, the strategy for deriving the operational semantics is provided and a transition system is derived by strict proof. This can be considered as the soundness exploration for the operational semantics based on the algebraic semantics. Further, the equivalence between the derivation strategy and the derived transition system is explored, which can be considered as the completeness of the operational semantics. Finally, the derivation of the denotational semantics from algebraic semantics is explored, which can support to reason about more program properties easily.     

Verilog代数语义研究

给出了Verilog的代数语义.这是一个等式公理体系,它将Verilog语义特征通过代数规则简洁而准确地表达出来;并且这个代数语义相对于已经所作的操作语义模型来讲是可靠的,即所有的这些代数规则左右两边的进程在操作语义的观察模型下都是互模拟的.研究了此代数语义的相对完备性,即参照前面的操作语义模型,相对于扩展Verilog语言的一个子集而言,此代数语义是完备的.即所有符合这样语法的程序,如果它们是互模拟等价的,那么它们同样可以在所提出的代数系统中被推导相等.在完备性证明过程中,采用范式方法,即构造一种语法上特殊的程序,任何属于上述子集中的一个程序通过该代数规则都能够被转化为范式程序,而且范式程序在操作语义模型下是互模拟的当且仅当它们是语法相同的.上述结果具有重要的理论意义,因为现有的进程代数理论主要是针对管道通信并行语言而展开的,而对于像Verilog这种以共享变量通信为基础的复杂并行语言研究还是比较少的,对此类复杂的基于共享变量的并行语言的进程代数理论研究提出了一种通用、有效的方法.     

From algebraic semantics to denotational semantics for Verilog

This paper considers how the algebraic semantics for Verilog relates with its denotational semantics. Our approach is to derive the denotational semantics from the algebraic semantics. We first present the algebraic laws for Verilog. Every program can be expressed as a guarded choice that can model the execution of a program. In order to investigate the parallel expansion laws, a sequence is introduced, indicating which instantaneous action is due to which exact parallel component. A head normal form is defined for each program by using a locality sequence. We provide a strategy for deriving the denotational semantics based on head normal form. Using this strategy, the denotational semantics for every program can be calculated. Program equivalence can also be explored by using the derived denotational semantics. A short version of this paper appeared in Proc. ICECCS 2006: 11th IEEE International Conference on Engineering of Complex Computer Systems [48]. This work is partially supported by the National Basic Research Program of China (No. 2005CB321904), the National High Technology Research and Development Program of China (No. 2007AA010302) and the National Natural Science Foundation of China (No. 90718004). Jonathan Bowen is a visiting professor at King’s College London and an emeritus professor at London South Bank University.     

PTSC: probability, time and shared-variable concurrency

Complex software systems typically involve features like time, concurrency and probability, where probabilistic computations play an increasing role. It is challenging to formalize languages comprising all these features. In this paper, we integrate probability, time and concurrency in one single model, where the concurrency feature is modelled using shared-variable-based communication. The probability feature is represented by a probabilistic nondeterministic choice, probabilistic guarded choice and a probabilistic version of parallel composition. We formalize an operational semantics for such an integration. Based on this model we define a bisimulation relation, from which an observational equivalence between probabilistic programs is investigated and a collection of algebraic laws are explored. We also implement a prototype of the operational semantics to animate the execution of probabilistic programs.     

多Agent信念逻辑及其在概率意义下的推广

首先建立了一种多Agent信念逻辑MBL(multi-agentbelieflogic),在经典信念逻辑基础上增加了普遍信念算子和公共信念算子,给出MBL的Kripke语义与广义Aumann语义,讨论了两者的等价性,证明了MBL对于上述两种语义的可靠性和完备性.其次,建立了一种多Agent概率信念逻辑MPBL(multi-agentprobabilisticbelieflogic),通过在广义Aumann语义基础上引入概率空间,给出了MPBL的概率Aumann语义,证明了它的可靠性,并给出MPBL的一些推论.     

基于函数式语义的循环和递归程序结构通用证明技术

各类安全攸关系统的可靠运行离不开软件程序的正确执行.程序的演绎验证技术为程序执行的正确性提供高度保障.程序语言种类繁多,且用途覆盖高可靠性场景的新式语言不断涌现,难以为每种语言设计支撑其程序验证任务的整套逻辑规则,并证明其相对于形式语义的可靠性和完备性.语言无关的程序验证技术提供以程序语言的语义为参数的验证过程及其可靠性结果.对每种程序语言,提供其形式语义后可直接获得面向该语言的程序验证过程.提出一种面向大步操作语义的语言无关演绎验证技术,其核心是对不同语言中循环、递归等可导致无界行为的语法结构进行可靠推理的通用方法.特别地,借助大步操作语义的一种函数式形式化提供表达程序中子结构所执行计算的能力,从而允许借助辅助信息对子结构进行推理.证明所提出验证技术的可靠性和相对完备性,通过命令式、函数式语言中的程序验证实例初步评估了该技术的有效性,并在Coq辅助证明工具中形式化了所有理论结果和验证实例,为基于辅助证明工具实现面向大步语义的语言无关程序验证工具提供了基础.     

A compact fixpoint semantics for term rewriting systems

This work is motivated by the fact that a “compact” semantics for term rewriting systems, which is essential for the development of effective semantics-based program manipulation tools (e.g. automatic program analyzers and debuggers), does not exist. The big-step rewriting semantics that is most commonly considered in functional programming is the set of values/normal forms that the program is able to compute for any input expression. Such a big-step semantics is unnecessarily oversized, as it contains many “semantically useless” elements that can be retrieved from a smaller set of terms. Therefore, in this article, we present a compressed, goal-independent collecting fixpoint semantics that contains the smallest set of terms that are sufficient to describe, by semantic closure, all possible rewritings. We prove soundness and completeness under ascertained conditions. The compactness of the semantics makes it suitable for applications. Actually, our semantics can be finite whereas the big-step semantics is generally not, and even when both semantics are infinite, the fixpoint computation of our semantics produces fewer elements at each step. To support this claim we report several experiments performed with a prototypical implementation.     

补偿通信顺序进程的扩展及失败发散语义

补偿通信顺序进程(cCSP)是通信顺序进程用于长事务建模的扩展,可用来描述服务计算中的编制程序,比如WS-BPEL程序。目前,cCSP只有操作语义和基于迹的指称语义,对死锁和发散行为的推理支持不够。本文扩展了cCSP,引入新的组合操作子,给出扩展cCSP的失败发散语义;并根据该语义,给出新引入组合操作子的重要代数规则,用于语义的理解和佐证。最后,给出一个案例描述用于展示扩展cCSP。     

Trace Semantics and Algebraic Laws for Total Store Order Memory Model

Modern multiprocessors deploy a variety of weak memory models(WMMs).Total Store Order(TSO) is a widely-used weak memory model in SPARC implementations and x86 architecture.It omits the store-load constraint by allowing each core to employ a write buffer.In this paper,we apply Unifying Theories of Programming(abbreviated as UTP) in investigating the trace semantics for TSO,acting in the denotational semantics style.A trace is expressed as a sequence of snapshots,which records the changes in registers,write buffers and the shared memory.All the valid execution results containing reorderings can be described after kicking out those that do not satisfy program order and modification order.This paper also presents a set of algebraic laws for TSO.We study the concept of head normal form,and every program can be expressed in the head normal form of the guarded choice which is able to model the execution of a program with reorderings.Then the linearizability of the TSO model is supported.Furthermore,we consider the linking between trace semantics and algebraic semantics.The linking is achieved through deriving trace semantics from algebraic semantics,and the derivation strategy under the TSO model is provided.     

A formal semantics for debugging synchronous message passing-based concurrent programs

In this paper, we propose a semantic framework to debug synchronous message passing-based con- current programs, which are increasingly useful as parallel computing and distributed systems become more and more pervasive. We first design a concurrent programming language model to uniformly represent exist- ing concurrent programming languages. Compared to sequential programming languages, this model contains communication statements, i.e., sending and receiving statements, and a concurrent structure to represent com- munication and concurrency. We then propose a debugging process consisting of a tracing and a locating procedure. The tracing procedure re-executes a program with a failed test case and uses specially designed data structures to collect useful execution information for locating bugs. We provide for the tracing procedure a struc- tural operational semantics to represent synchronous communication and concurrency. The locating procedure backward locates the ill-designed statement by using information obtained in the tracing procedure, generates a fix equation, and tries to fix the bug by solving the fix equation. We also propose a structural operational semantics for the locating procedure. We supply two examples to test our proposed operational semantics.     

Algebraic and operational semantics of specifications allowing exceptions and errors

The specification of abstract data types requires the possibility to treat exceptions and errors. We present an approach allowing all forms of error handling: error introduction, error propagation and error recovery. The algebraic semantics of our method and a new correctness criterion are given. We also introduce an operational semantics of a subclass of our specifications which coincides with the algebraic semantics.     

Bialgebras for structural operational semantics: An introduction

Bialgebras and distributive laws are an abstract, categorical framework to study various flavors of structural operational semantics. This paper aims to introduce the reader to the basics of bialgebras for operational semantics, and to sketch the state of the art in this research area.     

A Constructor-Based EI-Model Semantics of EI-CTRS

This paper investigates the semantics of conditional term rewriting systems with negation (denoted by EI-CTRS),called constructor-based EI-model semantics.The introduction of “≠” in EI-CTRS make EI-CTRS more difficult to study.This is in part because of a failure of EI-CTRS to guarantee that there exist least Herbrand models in classical logical point of views.The key idea of EI-model is to explain that t≠s” means that the two concepts represented by t and s respectively actually belong to distinguished basic concepts represented by two constructor-ground terms.We define the concept of EI-model,and show that there exist least Herbrand EI-models for EI-satisfiable EI-CTRS.From algebraic and logic point of view,we show that there are very strong reasons for regarding the least Herbrand EI-models as the intended semantics of EI-CTRS.According to fixpoint theory,we develop a method to construct least Herbrand EI-models in a bottom-up manner.Moreover,we discuss soundness and completeness of EI-rewrite for EI-model semantics.     

Event-based operational semantics and a consistency result for real-time concurrent processes with action refinement

In this paper an event-based operational interleaving semantics is proposed for real-time processes,for which action refinement and a denotational true concurrency semantics are developed and defined in terms of timed event structures. The authors characterize the timed event traces that are generated by the operational semantics in a denotational way, and show that this operational semantics is consistent with the denotational semantics in the sense that they generate the same set of timed event traces, thereby eliminating the gap between the true concurrency and interleaving semantics.     

Abstract interpretation of resolution-based semantics

We extend the abstract interpretation point of view on context-free grammars by Cousot and Cousot to resolution-based logic programs and proof systems. Starting from a transition-based small-step operational semantics of Prolog programs (akin to the Warren Machine), we consider maximal finite derivations for the transition system from most general goals. This semantics is abstracted by instantiation to terms and furthermore to ground terms, following the so-called c- and s-semantics approach. Orthogonally, these sets of derivations can be abstracted to SLD-trees, call patterns and models, as well as interpreters providing effective implementations (such as Prolog). These semantics can be presented in bottom–up fixpoint form. This abstract interpretation-based construction leads to classical bottom–up semantics (such as the s-semantics of computed answers, the c-semantics of correct answers of Keith Clark, and the minimal-model semantics of logical consequences of Maarten van Emden and Robert Kowalski). The approach is general and can be applied to infinite and top–down semantics in a straightforward way.     

Semantic theories of programs with nested interrupts

In the design of dependable software for embedded and real-time operating systems, time analysis is a crucial but extremely difficult issue, the challenge of which is exacerbated due to the randomness and nondeterminism of interrupt handling behaviors. Thus research into a theory that integrates interrupt behaviors and time analysis seems to be important and challenging. In this paper, we present a programming language to describe programs with interrupts that is comprised of two essential parts: main program and interrupt handling programs. We also explore a timed operational semantics and a denotational semantics to specify the meanings of our language. Furthermore, a strategy of deriving denotational semantics from the timed operational semantics is provided to demonstrate the soundness of our operational semantics by showing the consistency between the derived denotational semantics and the original denotational semantics.     

Compositional semantics of a real-time prototyping language

The formal semantics of a prototyping language for hard real-time systems, PSDL, is given. PSDL provides a data flow notation augmented by application-orientation timing and control constraints to describe a system as a hierarchy of networks of processing units communicating via data streams. The semantics of PSDL are defined in terms of algebraic high-level Petri nets. This formalism combines algebraic specifications of abstract data types with process and concurrency concepts of Petri nets. Its data abstraction facilities are used to define the meaning of PSDL data types, while high-level Petri nets serve to model the casual and timing behavior of a system. The net model exposes potential concurrency of computation and makes all synchronization needs implied by timing and control constraints explicit and precise. Time is treated as state of clocks, and clocks are modeled as ordinary system components. The net semantics provides the basis for applying analysis techniques and semantic tools available for high-level Petri nets