Relation-changing modal operators

We study dynamic modal operators that can change the accessibility relation of a model during the evaluation of a formula. In particular, we extend the basic modal language with modalities that are able to delete, add or swap an edge between pairs of elements of the domain. We define a generic framework to characterize this kind of operations. First, we investigate relation-changing modal logics as fragments of classical logics. Then, we use the new framework to get a suitable notion of bisimulation for the logics introduced, and we investigate their expressive power. Finally, we show that the complexity of the model checking problem for the particular operators introduced is PSpace-complete, and we study two subproblems of model checking: formula complexity and program complexity.Fil: Areces, Carlos Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Fervari, Raul Alberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Hoffmann, Guillaume Emmanuel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Relation-Changing Logics as Fragments of Hybrid Logics

Relation-changing modal logics are extensions of the basic modal logic that allow changes to the accessibility relation of a model during the evaluation of a formula. In particular, they are equipped with dynamic modalities that are able to delete, add, and swap edges in the model, both locally and globally. We provide translations from these logics to hybrid logic along with an implementation. In general, these logics are undecidable, but we use our translations to identify decidable fragments. We also compare the expressive power of relation-changing modal logics with hybrid logics.Comment: In Proceedings GandALF 2016, arXiv:1609.0364

Bisimulation for reactive frames

Reactive frames are those whose structure is not fi xed but can vary according to the path chosen. This kind of frame has been study and both a logic and an axiomatization for it were already developed. In this paper we take this study further and de fine a notion of bisimulation for reactive models. We show that the logic introduced by Marcelino for these frames is invariant under our notion of bisimulation. Finally, we proof the Hennessy-Milner theorem for a class of reactive models

Reuse and integration of specification logics: the hybridisation perspective

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. It also captures the construction of first-order encodings of such hybridised institutions into theories in first-order logic. The method was originally developed to build suitable logics for the specification of reconfigurable software systems on top of whatever logic is used to describe local requirements of each system’s configuration. Hybridisation has, however, a broader scope, providing a fresh example of yet another development in combining and reusing logics driven by a problem from Computer Science. This paper offers an overview of this method, proposes some new extensions, namely the introduction of full quantification leading to the specification of dynamic modalities, and exemplifies its potential through a didactical application. It is discussed how hybridisation can be successfully used in a formal specification course in which students progress from equational to hybrid specifications in a uniform setting, integrating paradigms, combining data and behaviour, and dealing appropriately with systems evolution and reconfiguration.This work is financed by the ERDF—European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation—COMPETE 2020 Programme, and by National Funds through the FCT (Portuguese Foundation for Science and Technology) within project POCI-01-0145-FEDER-006961. M. Martins was further supported by project UID/MAT/04106/2013. A. Madeira and R. Neves research was carried out in the context of a post-doc and a Ph.D. grant with references SFRH/BPD/103004/2014 and SFRH/BD/52234/2013, respectively. L.S. Barbosa is also supported by SFRH/BSAB/ 113890/2015

rPrism: a software for reactive weighted state transition models

In this work we introduce the software rPrism, as a branch of the software PRISM model checker, in order to be able to study weighted reactive state transition models. This kind of model gathers together the concepts of reactivity { which consists of the capacity of a state transition model to alter its accessibility relation { and weights, which can be seen as costs, rates, etc.. Given a speci c model, the tool performs a simulation based on a Continuous Time Markov Chain. In particular, we show an example of its application for biological systems.This work was supported by ERDF - The 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 Ciência e a Tecnologia, within project POCI-01-0145-FEDER-030947 and project with reference UID/MAT/04106/2019 at CIDMA. The authors acknowledge the support given by a France-Portugal partnership PHC PESSOA 2018 between M. Chaves (Campus France #40823SD) and M. A. Martins. D. Figueiredo also acknowledges the support given by FCT via the PhD scholarship PD/BD/114186/2016.publishe

Reactive models for biological regulatory networks

A reactive model, as studied by D. Gabbay and his collaborators, can be regarded as a graph whose set of edges may be altered whenever one of them is crossed. In this paper we show how reactive models can describe biological regulatory networks and compare them to Boolean networks and piecewise-linear models, which are some of the most common kinds of models used nowadays. In particular, we show that, with respect to the identification of steady states, reactive Boolean networks lie between piecewise linear models and the usual, plain Boolean networks. We also show this ability is preserved by a suitable notion of bisimulation, and, therefore, by network minimisation.ERDF - The 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 Ciência e a Tecnologia, within project POCI-01-0145-FEDER-030947. and project with reference UID/MAT/04106/2019 at CIDMA. D. Figueiredo also acknowledges the support given by FCT via the PhD scholarship PD/BD/114186/201

Axiomatising logics with separating conjunctions and modalities

International audienceModal separation logics are formalisms that combine modal operators to reason locally, with separating connectives that allow to perform global updates on the models. In this work, we design Hilbert-style proof systems for the modal separation logics MSL(⇤, h6 =i) and MSL(⇤, 3), where ⇤ is the separating conjunction, 3 is the standard modal operator and h6 =i is the di↵erence modality. The calculi only use the logical languages at hand (no external features such as labels) and take advantage of new normal forms and of their axiomatisation