Distribution-Based Behavioral Distance for Nondeterministic Fuzzy Transition Systems

We are going to study, from the logical point of view, expressions as “usually ϕ”, “ϕ is probable”, “for many x, ϕ” and similar. We shall handle them both as generalized quantifiers and as modalities. This should not look unnatural since in general modalities can be viewed as hidden quantifiers. We shall try to show how the theory of generalized quantifiers and modal logic can be applied to the above expressions (stressed by Zadeh as items of the specific agenda of fuzzy logic in the narrow sense) and that they admit “classical” logical analysis. We shall offer a logical apparatus, precise definitions, some results and various problems: here much study and development is still necessary. To be able to use and generalize the results and approaches of Boolean logic, we shall have to review and summarize several notions and facts on generalized quantifiers, some modal logics, and also on measures of uncertainty (that will be used to define various quantifiers and modalities). Thus we shall have two preliminary sections in this chapter: Section 1 on generalized quantifiers (with an appendix on uncertainty measures) and Section 2 on modal logics, both sections in the frame of Boolean (two-valued) logic. Generalized quantifiers in fuzzy logic and fuzzy modal logics are studied in Sections 3, 4.

Performing formal verification of concurrent systems involves partial order logics (here MSO with partial orders) for the specification of properties or of the concurrent system itself. A common structure for the verification of concurrent systems is so-called pomset. A pomset is a multiset of partially ordered events. The partial order relation describes causal dependencies of events. We propose a new word based model, namely Pre-Post-Pomset, making the exploration of pomsets space possible. In this paper, our new model stands to be a general model in the sense that some classical models used in the specification of concurrent systems (Synchronized product of systems, Mazurkiewicz traces or parallel series) can be specified within. Besides its general aspect, our model offers decidability results on the verification problem according to an MSO formula on pomsets.

Bisimulation is a central concept in the model theory of modal logic with extensive computational applications. It is a relation between two models in which related states have identical atomic properties and matching transition possibilities. Bisimulation captures the expressive power of propositional modal logic in the sense that bisimilar states are not distinguishable by any propositional modal formula. In recent years, fuzzy modal logic has received much attention because of the connection between uncertainty measures and fuzzy modalities. In this paper, we define the notion of fuzzy bisimulation and prove that, in a fuzzified version, it bears the same relationship to fuzzy modal logic that bisimulation bears to propositional modal logic.

We propose a collection of principles for reasoning about lazy functional programs. These include rules for predicate logic, rules of conversion of programs, and rules for predicates defined in terms of least and greatest fixed points. These rules can be used for reasoning about networks of deterministic computing agents in view of Kahn’s principle. We also propose that certain networks which include non-deterministic agents can be treated in a similar way by viewing such agents as incompletely specified deterministic agents. To illustrate this technique we discuss the specification and correctness of the alternating bit protocol.KeywordsRecursive FunctionPredicate LogicInput StreamFunctional ProgramNatural DeductionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

While waiting for the millennium: Formal specification and verification of concurrent systems now

On undecidability of propositional temporal logics on trace systems

This book is a celebration of Leslie Lamport's work on concurrency, interwoven in four-and-a-half decades of an evolving industry: from the introduction of the first personal computer to an era when parallel and distributed multiprocessors are abundant. His works lay formal foundations for concurrent computations executed by interconnected computers. Some of the algorithms have become standard engineering practice for fault tolerant distributed computing - distributed systems that continue to function correctly despite failures of individual components. He also developed a substantial body of work on the formal specification and verification of concurrent systems, and has contributed to the development of automated tools applying these methods. Part I consists of technical chapters of the book and a biography. The technical chapters of this book present a retrospective on Lamport's original ideas from experts in the field. Through this lens, it portrays their long-lasting impact. The chapters cover timeless notions Lamport introduced: the Bakery algorithm, atomic shared registers and sequential consistency; causality and logical time; Byzantine Agreement; state machine replication and Paxos; temporal logic of actions (TLA). The professional biography tells of Lamport's career, providing the context in which his work arose and broke new grounds, and discusses LaTeX - perhaps Lamport's most influential contribution outside the field of concurrency. This chapter gives a voice to the people behind the achievements, notably Lamport himself, and additionally the colleagues around him, who inspired, collaborated, and helped him drive worldwide impact. Part II consists of a selection of Leslie Lamport's most influential papers. This book touches on a lifetime of contributions by Leslie Lamport to the field of concurrency and on the extensive influence he had on people working in the field. It will be of value to historians of science, and to researchers and students who work in the area of concurrency and who are interested to read about the work of one of the most influential researchers in this field.

As an extension of the traditional modal logic, the fuzzy first-order modal logic is discussed in this paper. A description of fuzzy first-order modal logic based on constant domain semantics is given, and a formal system of fuzzy reasoning based on the semantic information of models of first-order modal logic is established. It is also introduced in this paper the notion of the satisfiability of the reasoning system and some properties associated with the satisfiability are proved.

In the paper we introduce formal calculi which are a generalization of propositional modal logics. These calculi are called fuzzy modal logics. We introduce the concept of a fuzzy Kripke model and consider a semantics of these calculi in the class of fuzzy Kripke models. The main result of the paper is the completeness theorem of a minimal fuzzy modal logic in the class of fuzzy Kripke models.

This paper is concerned with a framework that combines sliding mode control and fuzzy logic systems. This controller is based on the variable structure system control theory and entails the advantages of sliding mode control and fuzzy logic control. The controlled system is a simulated two-links manipulator robot. It is found that the use of sliding mode controller gives good results yielding less coupling between freedom degrees. Moreover, the usage of fuzzy logic applied to the sliding mode controller leads a reduction of the size of the fuzzy inference system.

1 Modal logic: a semantic perspective

Representation of scopes of names is important for analysis and verification of concurrent systems. However, it is difficult to represent the scopes of channel names precisely with models based on process algebra.We introduced a model of concurrent systems with higher-order communication based on graph rewriting in our previous work. A bipartite directed acyclic graph represents a concurrent system that consists of a number of processes and messages in that model. The model can represent the scopes of local names precisely. We defined an equivalence relation such that two systems are equivalent not only in their behavior, but also in extrusion of scopes of names. This paper shows that our equivalence relation is a congruence relation w.r.t. τ-prefix, new-name, replication and composition, even when higher-order communication is allowed. We also show our equivalence relation is not congruent w.r.t. input-prefix though it is congruent w.r.t. input-prefix in the first-order case.

In protocol development for wireless systems, the choice of appropriate mobility models describing the movement patterns of devices has long been recognised as a crucial factor for the successful evaluation of protocols. More recently, wireless protocols have also come into the focus of formal approaches to the modelling and verification of concurrent systems. While in these approaches mobility is also given a central role, the actual mobility modelling remains simplistic since arbitrary node movements are allowed. This leads to a huge behavioural overapproximation that might prevent a successful reasoning about protocol properties. In this paper we describe how to extend a process calculus by realistic mobility models in an orthogonal way. The semantics of our calculus incorporates a notion of global time passing that allows us to express a wide range of mobility models currently used in protocol development practice. Using the behavioural equivalence and pre-order of our calculus, we are furthermore able to compare the strength of these models in our approach.

This paper presents a fuzzy logic control strategy on four-wheel steering(4WS) vehicle based on a multi-body vehicle dynamic model. The multi-body vehicle dynamic model based on ADAMS can accurately predict the dynamics performance of the vehicle. Fuzzy logic is applied to track the yaw velocity of the two degrees of freedom ideal model through the co-simulation of ADAMS and Matlab Fuzzy control unit with the optimized membership function. The fuzzy control parameters are optimized and analyzed by a combined optimization algorithm (Genetic Algorithm (GA) and Nonlinear Programming Quadratic Line search (NLPQL) method) combined with response surface model (RSM). Single lane change test is chosen to validate the fuzzy control logic strategy. Simulation result shows that four-wheel steering vehicle with the fuzzy control logic strategy can improve vehicle handling stability greatly comparing with traditional front wheel steering.

With the increasing need for flexibility and adaptivity in computerized systems, the application of fuzzy expert systems is becoming increasingly commonplace in today's industry. Fuzzy logic expert systems often improve performance by allowing knowledge to generalize without requiring the knowledge engineer to anticipate all possible situations. Thus, for many types of applications, soft such as Fuzzy logic can incur lower overhead in terms of representing and engineering task knowledge. My project investigates the application of fuzzy expert systems to motion tracking. Previous research showed that Fuzzy Logic can be used to track the motion of a brightly colored object against a dark background, with relatively low development and run-time costs. The system I am developing identifies, tracks, and predicts the motion of multiple objects using unique identification patterns against a dark background. My poster will describe the fuzzy inference systems for tracking and motion prediction of such objects. An essential step to obtaining the fuzzy inputs for the motion tracking fuzzy inference system is to use convolution correlation data to obtain the centers of mass of the objects. Image processing information from the region around the center of each object provides good fuzzy inputs for recognizing object patterns and determining orientation. I am investigating two fuzzy inference systems for motion tracking and prediction in order to identify their strengths and weaknesses. In the long run, I hope to exploit the strengths of both by dividing the task between the two approaches. The Adaptive Neuro Fuzzy Inference System (ANFIS) is effective for pattern recognition. Fuzzy Proportional Derivative (FPD) is useful for computing errors and tuning inferences. Cascading the two fuzzy systems allows the system first to acquire generalized patterns and then fine-tune them for error tolerance. To perform this work, I am using the Matlab fuzzy logic toolkit, which is a simple and flexible tool for designing fuzzy inference systems.