Characteristic Logics for Behavioural Metrics via Fuzzy Lax Extensions

Behavioural distances provide a fine-grained measure of equivalence in systems involving quantitative data, such as probabilistic, fuzzy, or metric systems. Like in the classical setting of crisp bisimulation-type equivalences, the wide variation found in system types creates a need for generic methods that apply to many system types at once. Approaches of this kind are emerging within the paradigm of universal coalgebra, based either on lifting pseudometrics along set functors or on lifting general real-valued (fuzzy) relations along functors by means of fuzzy lax extensions. An immediate benefit of the latter is that they allow bounding behavioural distance by means of fuzzy bisimulations that need not themselves be (pseudo-)metrics, in analogy to classical bisimulations (which need not be equivalence relations). The known instances of generic pseudometric liftings, specifically the generic Kantorovich and Wasserstein liftings, both can be extended to yield fuzzy lax extensions, using the fact that both are effectively given by a choice of quantitative modalities. Our central result then shows that in fact all fuzzy lax extensions are Kantorovich extensions for a suitable set of quantitative modalities, the so-called Moss modalities. For non-expansive fuzzy lax extensions, this allows for the extraction of quantitative modal logics that characterize behavioural distance, i.e. satisfy a quantitative version of the Hennessy-Milner theorem; equivalently, we obtain expressiveness of a quantitative version of Moss\u27 coalgebraic logic

Characteristic Logics for Behavioural Hemimetrics via Fuzzy Lax Extensions

In systems involving quantitative data, such as probabilistic, fuzzy, or metric systems, behavioural distances provide a more fine-grained comparison of states than two-valued notions of behavioural equivalence or behaviour inclusion. Like in the two-valued case, the wide variation found in system types creates a need for generic methods that apply to many system types at once. Approaches of this kind are emerging within the paradigm of universal coalgebra, based either on lifting pseudometrics along set functors or on lifting general real-valued (fuzzy) relations along functors by means of fuzzy lax extensions. An immediate benefit of the latter is that they allow bounding behavioural distance by means of fuzzy (bi-)simulations that need not themselves be hemi- or pseudometrics; this is analogous to classical simulations and bisimulations, which need not be preorders or equivalence relations, respectively. The known generic pseudometric liftings, specifically the generic Kantorovich and Wasserstein liftings, both can be extended to yield fuzzy lax extensions, using the fact that both are effectively given by a choice of quantitative modalities. Our central result then shows that in fact all fuzzy lax extensions are Kantorovich extensions for a suitable set of quantitative modalities, the so-called Moss modalities. For nonexpansive fuzzy lax extensions, this allows for the extraction of quantitative modal logics that characterize behavioural distance, i.e. satisfy a quantitative version of the Hennessy-Milner theorem; equivalently, we obtain expressiveness of a quantitative version of Moss' coalgebraic logic. All our results explicitly hold also for asymmetric distances (hemimetrics), i.e. notions of quantitative simulation

Kantorovich Functors and Characteristic Logics for Behavioural Distances

Behavioural distances measure the deviation between states in quantitative systems, such as probabilistic or weighted systems. There is growing interest in generic approaches to behavioural distances. In particular, coalgebraic methods capture variations in the system type (nondeterministic, probabilistic, game-based etc.), and the notion of quantale abstracts over the actual values distances take, thus covering, e.g., two-valued equivalences, (pseudo-)metrics, and probabilistic (pseudo-)metrics. Coalgebraic behavioural distances have been based either on liftings of SET-functors to categories of metric spaces, or on lax extensions of SET-functors to categories of quantitative relations. Every lax extension induces a functor lifting but not every lifting comes from a lax extension. It was shown recently that every lax extension is Kantorovich, i.e. induced by a suitable choice of monotone predicate liftings, implying via a quantitative coalgebraic Hennessy-Milner theorem that behavioural distances induced by lax extensions can be characterized by quantitative modal logics. Here, we essentially show the same in the more general setting of behavioural distances induced by functor liftings. In particular, we show that every functor lifting, and indeed every functor on (quantale-valued) metric spaces, that preserves isometries is Kantorovich, so that the induced behavioural distance (on systems of suitably restricted branching degree) can be characterized by a quantitative modal logic

Quantitative Hennessy-Milner Theorems via Notions of Density

The classical Hennessy-Milner theorem is an important tool in the analysis of concurrent processes; it guarantees that any two non-bisimilar states in finitely branching labelled transition systems can be distinguished by a modal formula. Numerous variants of this theorem have since been established for a wide range of logics and system types, including quantitative versions where lower bounds on behavioural distance (e.g. in weighted, metric, or probabilistic transition systems) are witnessed by quantitative modal formulas. Both the qualitative and the quantitative versions have been accommodated within the framework of coalgebraic logic, with distances taking values in quantales, subject to certain restrictions, such as being so-called value quantales. While previous quantitative coalgebraic Hennessy-Milner theorems apply only to liftings of set functors to (pseudo)metric spaces, in the present work we provide a quantitative coalgebraic Hennessy-Milner theorem that applies more widely to functors native to metric spaces; notably, we thus cover, for the first time, the well-known Hennessy-Milner theorem for continuous probabilistic transition systems, where transitions are given by Borel measures on metric spaces, as an instance of such a general result. In the process, we also relax the restrictions imposed on the quantale, and additionally parametrize the technical account over notions of closure and, hence, density, providing associated variants of the Stone-Weierstraß theorem; this allows us to cover, for instance, behavioural ultrametrics.publishe

Fuzzy Logic

Fuzzy Logic is becoming an essential method of solving problems in all domains. It gives tremendous impact on the design of autonomous intelligent systems. The purpose of this book is to introduce Hybrid Algorithms, Techniques, and Implementations of Fuzzy Logic. The book consists of thirteen chapters highlighting models and principles of fuzzy logic and issues on its techniques and implementations. The intended readers of this book are engineers, researchers, and graduate students interested in fuzzy logic systems

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems

Probabilistic logics based on Riesz spaces

We introduce a novel real-valued endogenous logic for expressing properties of probabilistic transition systems called Riesz modal logic. The design of the syntax and semantics of this logic is directly inspired by the theory of Riesz spaces, a mature field of mathematics at the intersection of universal algebra and functional analysis. By using powerful results from this theory, we develop the duality theory of the Riesz modal logic in the form of an algebra-to-coalgebra correspondence. This has a number of consequences including: a sound and complete axiomatization, the proof that the logic characterizes probabilistic bisimulation and other convenient results such as completion theorems. This work is intended to be the basis for subsequent research on extensions of Riesz modal logic with fixed-point operators

Early aspects: aspect-oriented requirements engineering and architecture design

This paper reports on the third Early Aspects: Aspect-Oriented Requirements Engineering and Architecture Design Workshop, which has been held in Lancaster, UK, on March 21, 2004. The workshop included a presentation session and working sessions in which the particular topics on early aspects were discussed. The primary goal of the workshop was to focus on challenges to defining methodical software development processes for aspects from early on in the software life cycle and explore the potential of proposed methods and techniques to scale up to industrial applications

Processamento de eventos complexos como serviço em ambientes multi-nuvem

Orientadores: Luiz Fernando Bittencourt, Miriam Akemi Manabe CapretzTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: O surgimento das tecnologias de dispositivos móveis e da Internet das Coisas, combinada com avanços das tecnologias Web, criou um novo mundo de Big Data em que o volume e a velocidade da geração de dados atingiu uma escala sem precedentes. Por ser uma tecnologia criada para processar fluxos contínuos de dados, o Processamento de Eventos Complexos (CEP, do inglês Complex Event Processing) tem sido frequentemente associado a Big Data e aplicado como uma ferramenta para obter informações em tempo real. Todavia, apesar desta onda de interesse, o mercado de CEP ainda é dominado por soluções proprietárias que requerem grandes investimentos para sua aquisição e não proveem a flexibilidade que os usuários necessitam. Como alternativa, algumas empresas adotam soluções de baixo nível que demandam intenso treinamento técnico e possuem alto custo operacional. A fim de solucionar esses problemas, esta pesquisa propõe a criação de um sistema de CEP que pode ser oferecido como serviço e usado através da Internet. Um sistema de CEP como Serviço (CEPaaS, do inglês CEP as a Service) oferece aos usuários as funcionalidades de CEP aliadas às vantagens do modelo de serviços, tais como redução do investimento inicial e baixo custo de manutenção. No entanto, a criação de tal serviço envolve inúmeros desafios que não são abordados no atual estado da arte de CEP. Em especial, esta pesquisa propõe soluções para três problemas em aberto que existem neste contexto. Em primeiro lugar, para o problema de entender e reusar a enorme variedade de procedimentos para gerência de sistemas CEP, esta pesquisa propõe o formalismo Reescrita de Grafos com Atributos para Gerência de Processamento de Eventos Complexos (AGeCEP, do inglês Attributed Graph Rewriting for Complex Event Processing Management). Este formalismo inclui modelos para consultas CEP e transformações de consultas que são independentes de tecnologia e linguagem. Em segundo lugar, para o problema de avaliar estratégias de gerência e processamento de consultas CEP, esta pesquisa apresenta CEPSim, um simulador de sistemas CEP baseado em nuvem. Por fim, esta pesquisa também descreve um sistema CEPaaS fundamentado em ambientes multi-nuvem, sistemas de gerência de contêineres e um design multiusuário baseado em AGeCEP. Para demonstrar sua viabilidade, o formalismo AGeCEP foi usado para projetar um gerente autônomo e um conjunto de políticas de auto-gerenciamento para sistemas CEP. Além disso, o simulador CEPSim foi minuciosamente avaliado através de experimentos que demonstram sua capacidade de simular sistemas CEP com acurácia e baixo custo adicional de processamento. Por fim, experimentos adicionais validaram o sistema CEPaaS e demonstraram que o objetivo de oferecer funcionalidades CEP como um serviço escalável e tolerante a falhas foi atingido. Em conjunto, esses resultados confirmam que esta pesquisa avança significantemente o estado da arte e também oferece novas ferramentas e metodologias que podem ser aplicadas à pesquisa em CEPAbstract: The rise of mobile technologies and the Internet of Things, combined with advances in Web technologies, have created a new Big Data world in which the volume and velocity of data generation have achieved an unprecedented scale. As a technology created to process continuous streams of data, Complex Event Processing (CEP) has been often related to Big Data and used as a tool to obtain real-time insights. However, despite this recent surge of interest, the CEP market is still dominated by solutions that are costly and inflexible or too low-level and hard to operate. To address these problems, this research proposes the creation of a CEP system that can be offered as a service and used over the Internet. Such a CEP as a Service (CEPaaS) system would give its users CEP functionalities associated with the advantages of the services model, such as no up-front investment and low maintenance cost. Nevertheless, creating such a service involves challenges that are not addressed by current CEP systems. This research proposes solutions for three open problems that exist in this context. First, to address the problem of understanding and reusing existing CEP management procedures, this research introduces the Attributed Graph Rewriting for Complex Event Processing Management (AGeCEP) formalism as a technology- and language-agnostic representation of queries and their reconfigurations. Second, to address the problem of evaluating CEP query management and processing strategies, this research introduces CEPSim, a simulator of cloud-based CEP systems. Finally, this research also introduces a CEPaaS system based on a multi-cloud architecture, container management systems, and an AGeCEP-based multi-tenant design. To demonstrate its feasibility, AGeCEP was used to design an autonomic manager and a selected set of self-management policies. Moreover, CEPSim was thoroughly evaluated by experiments that showed it can simulate existing systems with accuracy and low execution overhead. Finally, additional experiments validated the CEPaaS system and demonstrated it achieves the goal of offering CEP functionalities as a scalable and fault-tolerant service. In tandem, these results confirm this research significantly advances the CEP state of the art and provides novel tools and methodologies that can be applied to CEP researchDoutoradoCiência da ComputaçãoDoutor em Ciência da Computação140920/2012-9CNP

Complex Event Processing as a Service in Multi-Cloud Environments

The rise of mobile technologies and the Internet of Things, combined with advances in Web technologies, have created a new Big Data world in which the volume and velocity of data generation have achieved an unprecedented scale. As a technology created to process continuous streams of data, Complex Event Processing (CEP) has been often related to Big Data and used as a tool to obtain real-time insights. However, despite this recent surge of interest, the CEP market is still dominated by solutions that are costly and inflexible or too low-level and hard to operate. To address these problems, this research proposes the creation of a CEP system that can be offered as a service and used over the Internet. Such a CEP as a Service (CEPaaS) system would give its users CEP functionalities associated with the advantages of the services model, such as no up-front investment and low maintenance cost. Nevertheless, creating such a service involves challenges that are not addressed by current CEP systems. This research proposes solutions for three open problems that exist in this context. First, to address the problem of understanding and reusing existing CEP management procedures, this research introduces the Attributed Graph Rewriting for Complex Event Processing Management (AGeCEP) formalism as a technology- and language-agnostic representation of queries and their reconfigurations. Second, to address the problem of evaluating CEP query management and processing strategies, this research introduces CEPSim, a simulator of cloud-based CEP systems. Finally, this research also introduces a CEPaaS system based on a multi-cloud architecture, container management systems, and an AGeCEP-based multi-tenant design. To demonstrate its feasibility, AGeCEP was used to design an autonomic manager and a selected set of self-management policies. Moreover, CEPSim was thoroughly evaluated by experiments that showed it can simulate existing systems with accuracy and low execution overhead. Finally, additional experiments validated the CEPaaS system and demonstrated it achieves the goal of offering CEP functionalities as a scalable and fault-tolerant service. In tandem, these results confirm this research significantly advances the CEP state of the art and provides novel tools and methodologies that can be applied to CEP research