Completeness and decidability results for hybrid(ised) logics

Adding to the modal description of transition structures the ability to refer to specific states, hybrid(ised) logics provide an interesting framework for the specification of reconfigurable systems. The qualifier ‘hybrid(ised)’ refers to a generic method of developing, on top of whatever specification logic is used to model software configurations, the elements of an hybrid language, including nominals and modalities. In such a context, this paper shows how a calculus for a hybrid(ised) logic can be generated from a calculus of the base logic and that, moreover, it preserves soundness and completeness. A second contribution establishes that hybridising a decidable logic also gives rise to a decidable hybrid(ised) one. These results pave the way to the development of dedicated proof tools for such logics used in the design of reconfigurable systems

Dynamic logic with binders and its application to the development of reactive systems

Publicado em "Theoretical aspects of computing - ICTAC 2016: 13th International Colloquium, Taipei, Taiwan, ROC, October 24–31, 2016, Proceedings". ISBN 978-3-319-46749-8This paper introduces a logic to support the specification and development of reactive systems on various levels of abstraction, from property specifications, concerning e.g. safety and liveness requirements, to constructive specifications representing concrete processes. This is achieved by combining binders of hybrid logic with regular modalities of dynamic logics in the same formalism, which we call D↓-logic. The semantics of our logic focuses on effective processes and is therefore given in terms of reachable transition systems with initial states. The second part of the paper resorts to this logic to frame stepwise development of reactive systems within the software development methodology proposed by Sannella and Tarlecki. In particular, we instantiate the generic concepts of constructor and abstractor implementations by using standard operators on reactive components, like relabelling and parallel composition, as constructors, and bisimulation for abstraction. We also study vertical composition of implementations which relies on the preservation of bisimularity by the constructions on labeleld transition systems.FCT individual grants SFRH/BPD/103004/2014 and SFRH/BSAB/113890/2015ERDF European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT - Fundação para a Cência e a Tecnologia within project POCI-01-0145-FEDER-016692 and UID/MAT/04106/2013 at CIDM

Dual Logic Concepts based on Mathematical Morphology in Stratified Institutions: Applications to Spatial Reasoning

Several logical operators are defined as dual pairs, in different types of logics. Such dual pairs of operators also occur in other algebraic theories, such as mathematical morphology. Based on this observation, this paper proposes to define, at the abstract level of institutions, a pair of abstract dual and logical operators as morphological erosion and dilation. Standard quantifiers and modalities are then derived from these two abstract logical operators. These operators are studied both on sets of states and sets of models. To cope with the lack of explicit set of states in institutions, the proposed abstract logical dual operators are defined in an extension of institutions, the stratified institutions, which take into account the notion of open sentences, the satisfaction of which is parametrized by sets of states. A hint on the potential interest of the proposed framework for spatial reasoning is also provided.Comment: 36 page

Proof theory for hybrid(ised) logics

Hybridisation is a systematic process along which the characteristic features of hybrid logic, both at the syntactic and the semantic levels, are developed on top of an arbitrary logic framed as an institution. In a series of papers this process has been detailed and taken as a basis for a specification methodology for reconfigurable systems. The present paper extends this work by showing how a proof calculus (in both a Hilbert and a tableau based format) for the hybridised version of a logic can be systematically generated from a proof calculus for the latter. Such developments provide the basis for a complete proof theory for hybrid(ised) logics, and thus pave the way to the development of (dedicated) proof support.The authors are grateful to Torben Bräuner for helpful, inspiring discussions, and to the anonymous referees for their detailed comments. This work is funded by ERDF—European Regional Development Fund, through the COMPETE Programme, and by National Funds through Fundação para a Ciência e a Tecnologia(FCT) within project PTDC/EEI-CTP/4836/2014. Moreover, the first and the second authors are sponsored by FCT grants SFRH/BD/52234/2013 and SFRH/BPD/103004/2014, respectively. M. Mar-tins is also supported by the EU FP7 Marie Curie PIRSES-GA-2012-318986 project GeTFun: Generalizing Truth-Functionality and FCT project UID/MAT/04106/2013 through CIDMA. L.Barbosa is further supported by FCT in the context of SFRH/B-SAB/113890/2015

A logic for the stepwise development of reactive systems

D↓is a new dynamic logic combining regular modalities with the binder constructor typical of hybrid logic, which provides a smooth framework for the stepwise development of reactive systems. Actually, the logic is able to capture system properties at different levels of abstraction, from high-level safety and liveness requirements, to constructive specifications representing concrete processes. The paper discusses its semantics, given in terms of reachable transition systems with initial states, its expressive power and a proof system. The methodological framework is in debt to the landmark work of D.Sannella and A.Tarlecki, instantiating the generic concepts of constructor and abstractor implementations by standard operators on reactive components, e.g. relabelling and parallel composition, as constructors, and bisimulation for abstraction.This work was funded by ERDF European Regional Development Fund, through the COMPETE Programme, and by National Funds through FCT – Portuguese Foundation for Science and Technology – within projects POCI-01-0145-FEDER-016692 (DaLí – Dynamic logics for cyber-physical systems: towards contract based design) and UID/MAT/04106/2013 at CIDMA. Further support was given by the project SmartEGOV, NORTE-01-0145-FEDER000037, supported by Norte Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement, through the EFDR. The first author is also supported by a FCT individual grant SFRH/BPD/103004/201

Proof support for hybridised logics

Dissertação de mestrado em Engenharia InformáticaFormal methods are mathematical techniques used to certify safe systems. Such methods abound and have been successfully used in classical Engineering domains, yet informatics is the exception. There, they are still immature and costly; furthermore, software engineers frequently view them with "fear". Thus, the use of formal methods is typically restricted to cases where they are essential. In other words, they are mostly used in the class of systems where safety is imperative, as the lack of it can lead to significant losses (material or human). We denote such systems critical. The present is leading us to a future where critical systems are ubiquitous. Recent research in the Mondrian project emphasises the need for expressive logics to formally specify reconfigurable systems, i.e., systems capable of evolving in order to adapt to the different contexts induced by the dynamics of their surroundings. In the same project, theoretical foundations for the formal specification of reconfigurable systems, were developed in a sound, generic, and systematic way, resorting for this to hybrid logics – their intrinsic properties make them natural candidates for such job. From those foundations a methodology for specifying reconfigurable systems was built and proposed: Instead of choosing a logic for the specification, build an hybrid ad-hoc one, by taking into account the particular characteristics of each reconfigurable system to be specified. The purpose of this dissertation is to bring the proposed methodology into practice, by creating suitable tools for it, and by illustrating its application to relevant case studies.Métodos formais são técnicas matemáticas usadas para certificar sistemas fiáveis. Tais métodos são comuns e usados com sucesso nas engenharias clássicas. No entanto, informática é a excepção. No que respeita este campo, os métodos formais são prematuros e relativamente dispendiosos; para além disso, os engenheiros de software vêem estas técnicas com alguma apreensão. Assim, o emprego de métodos formais está tipicamente restrito a casos onde são absolutamente essenciais. Por outras palavras, são maioritariamente usados na classe de sistemas, cujas falhas têm o potencial de tragédia, seja ela material ou humana; tais sistemas têm a denominação de críticos. O presente leva-nos para um futuro em que os sistemas críticos são ubíquos. Investigação recente no project Mondrian enfatiza a necessidade de lógicas expressivas, para especificar formalmente sistemas reconfiguráveis, i.e., sistemas que evoluem de modo a se adaptarem aos diferentes contextos, induzidos pela dinâmica do meio que os rodeia. No mesmo projecto, bases teóricas para a especificação formal de sistemas reconfiguráveis foram establecidas de forma sólida, genérica e sistemática, recorrendo-se para isso às lógicas híbridas – as suas propriedades intrínsecas, fazem delas candidatos naturais para a especificação de sistemas reconfiguráveis. Dessas teorias foi inferida e proposta uma metodologia para especificar sistemas reconfiguráveis: Em vez de escolher uma lógica para a especificação, construir uma outra, híbrida ad-hoc, tendo em conta as características particulares de cada sistema reconfigurável a especificar. O propósito desta dissertação é de trazer a metodologia proposta à práctica, criando-se para isso, ferramentas que a suportem, e ilustrando a sua aplicação a casos de estudo relevantes

Heterogeneous verification of model transformations

Esta tesis trata sobre la verificación formal en el contexto de la Ingeniería Dirigida por Modelos (MDE por sus siglas en inglés). El paradigma propone un ciclo de vida de la ingeniería de software basado en una abstracción de su complejidad a través de la definición de modelos y en un proceso de construcción (semi)automático guiado por transformaciones de estos modelos. Nuestro propósito es abordar la verificación de transformaciones de modelos la cual incluye, por extensión, la verificación de sus modelos. Comenzamos analizando la literatura relacionada con la verificación de transformaciones de modelos para concluir que la heterogeneidad de las propiedades que interesa verificar y de los enfoques para hacerlo, sugiere la necesidad de utilizar diversos dominios lógicos, lo cual es la base de nuestra propuesta. En algunos casos puede ser necesario realizar una verificación heterogénea, es decir, utilizar diferentes formalismos para la verificación de cada una de las partes del problema completo. Además, es beneficioso permitir a los expertos formales elegir el dominio en el que se encuentran más capacitados para llevar a cabo una prueba formal. El principal problema reside en que el mantenimiento de múltiples representaciones formales de los elementos de MDE en diferentes dominios lógicos, puede ser costoso si no existe soporte automático o una relación formal clara entre estas representaciones. Motivados por esto, definimos un entorno unificado que permite la verificación formal transformaciones de modelos mediante el uso de métodos de verificación heterogéneos, de forma tal que es posible automatizar la traducción formal de los elementos de MDE entre dominios logicos. Nos basamos formalmente en la Teoría de Instituciones, la cual proporciona una base sólida para la representación de los elementos de MDE (a través de instituciones) sin depender de ningúningún dominio lógico específico. También proporciona una forma de especificar traducciones (a través de comorfismos) que preservan la semántica entre estos elementos y otros dominios lógicos. Nos basamos en estándares para la especificación de los elementos de MDE. De hecho, definimos una institución para la buena formación de los modelos especificada con una versión simplificada del MetaObject Facility y otra institución para transformaciones utilizando Query/View/Transformation Relations. No obstante, la idea puede ser generalizada a otros enfoques de transformación y lenguajes.Por último, demostramos la viabilidad del entorno mediante el desarrollo de un prototipo funcional soportado por el Heterogeneous Tool Set (HETS). HETS permite realizar una especificación heterogénea y provee facilidades para el monitoreo de su corrección global. Los elementos de MDE se conectan con otras lógicas ya soportadas en HETS (por ejemplo: lógica de primer orden, lógica modal, entre otras) a través del Common Algebraic Specification Language (CASL). Esta conexión se expresa teóricamente mediante comorfismos desde las instituciones de MDE a la institución subyacente en CASL. Finalmente, discutimos las principales contribuciones de la tesis. Esto deriva en futuras líneas de investigación que contribuyen a la adopción de métodos formales para la verificación en el contexto de MDE.This thesis is about formal verification in the context of the Model-Driven Engineering (MDE) paradigm. The paradigm proposes a software engineering life-cycle based on an abstraction from its complexity by defining models, and on a (semi)automatic construction process driven by model transformations. Our purpose is to address the verification of model transformations which includes, by extension, the verification of their models. We first review the literature on the verification of model transformations to conclude that the heterogeneity we find in the properties of interest to verify, and in the verification approaches, suggests the need of using different logical domains, which is the base of our proposal. In some cases it can be necessary to perform a heterogeneous verification, i.e. using different formalisms for the verification of each part of the whole problem. Moreover, it is useful to allow formal experts to choose the domain in which they are more skilled to address a formal proof. The main problem is that the maintenance of multiple formal representations of the MDE elements in different logical domains, can be expensive if there is no automated assistance or a clear formal relation between these representations. Motivated by this, we define a unified environment that allows formal verification of model transformations using heterogeneous verification approaches, in such a way that the formal translations of the MDE elements between logical domains can be automated. We formally base the environment on the Theory of Institutions, which provides a sound basis for representing MDE elements (as so called institutions) without depending on any specific logical domain. It also provides a way for specifying semantic-preserving translations (as so called comorphisms) from these elements to other logical domains. We use standards for the specification of the MDE elements. In fact, we define an institution for the well-formedness of models specified with a simplified version of the MetaObject Facility, and another institution for Query/View/Transformation Relations transformations. However, the idea can be generalized to other transformation approaches and languages. Finally, we evidence the feasibility of the environment by the development of a functional prototype supported by the Heterogeneous Tool Set (HETS). HETS supports heterogeneous specifications and provides capabilities for monitoring their overall correctness. The MDE elements are connected to the other logics already supported in HETS (e.g. first-order logic, modal logic, among others) through the Common Algebraic Specification Language (CASL). This connection is defined by means of comorphisms from the MDE institutions to the underlying institution of CASL. We carry out a final discussion of the main contributions of this thesis. This results in future research directions which contribute with the adoption of formal tools for the verification in the context of MDE