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

Internal Calculi for Separation Logics

We present a general approach to axiomatise separation logics with heaplet semantics with no external features such as nominals/labels. To start with, we design the first (internal) Hilbert-style axiomatisation for the quantifier-free separation logic SL(?, -*). We instantiate the method by introducing a new separation logic with essential features: it is equipped with the separating conjunction, the predicate ls, and a natural guarded form of first-order quantification. We apply our approach for its axiomatisation. As a by-product of our method, we also establish the exact expressive power of this new logic and we show PSpace-completeness of its satisfiability problem

Automating Deductive Verification for Weak-Memory Programs

Writing correct programs for weak memory models such as the C11 memory model is challenging because of the weak consistency guarantees these models provide. The first program logics for the verification of such programs have recently been proposed, but their usage has been limited thus far to manual proofs. Automating proofs in these logics via first-order solvers is non-trivial, due to reasoning features such as higher-order assertions, modalities and rich permission resources. In this paper, we provide the first implementation of a weak memory program logic using existing deductive verification tools. We tackle three recent program logics: Relaxed Separation Logic and two forms of Fenced Separation Logic, and show how these can be encoded using the Viper verification infrastructure. In doing so, we illustrate several novel encoding techniques which could be employed for other logics. Our work is implemented, and has been evaluated on examples from existing papers as well as the Facebook open-source Folly library.Comment: Extended version of TACAS 2018 publicatio

A Complete Axiomatisation for Quantifier-Free Separation Logic

We present the first complete axiomatisation for quantifier-free separation logic. The logic is equipped with the standard concrete heaplet semantics and the proof system has no external feature such as nominals/labels. It is not possible to rely completely on proof systems for Boolean BI as the concrete semantics needs to be taken into account. Therefore, we present the first internal Hilbert-style axiomatisation for quantifier-free separation logic. The calculus is divided in three parts: the axiomatisation of core formulae where Boolean combinations of core formulae capture the expressivity of the whole logic, axioms and inference rules to simulate a bottom-up elimination of separating connectives, and finally structural axioms and inference rules from propositional calculus and Boolean BI with the magic wand

Copy and remove as dynamic operators

In this article, we present a modal logic that extends the basic modal logic ML with two dynamic operators: copy (cp), which replicates the current model, labelling each copy with a different propositional symbol and respecting accessibility relations even between distinct copies; and remove (rm), which deletes paths in the model that satisfy certain intermediate conditions. We call the resulting logic ML(cp,rm). We study its computational complexity, and its relative expressivity with respect to (static) modal logics ML and ML(□−), and the dynamic epistemic Action Model Logic, AML.Fil: Areces, Carlos Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Van Ditmarsch, Hans. Open University; Países BajosFil: Fervari, Raul Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Maubert, Bastien. Università degli Studi di Napoli Federico II; ItaliaFil: Schwarzentruber, François. Universite de Rennes I; Francia. Centre National de la Recherche Scientifique; Francia. Institut de Recherche en Informatique et Systèmes Aléatoires; Franci

SemImput: Bridging Semantic Imputation with Deep Learning for Complex Human Activity Recognition

The recognition of activities of daily living (ADL) in smart environments is a well-known and an important research area, which presents the real-time state of humans in pervasive computing. The process of recognizing human activities generally involves deploying a set of obtrusive and unobtrusive sensors, pre-processing the raw data, and building classification models using machine learning (ML) algorithms. Integrating data from multiple sensors is a challenging task due to dynamic nature of data sources. This is further complicated due to semantic and syntactic differences in these data sources. These differences become even more complex if the data generated is imperfect, which ultimately has a direct impact on its usefulness in yielding an accurate classifier. In this study, we propose a semantic imputation framework to improve the quality of sensor data using ontology-based semantic similarity learning. This is achieved by identifying semantic correlations among sensor events through SPARQL queries, and by performing a time-series longitudinal imputation. Furthermore, we applied deep learning (DL) based artificial neural network (ANN) on public datasets to demonstrate the applicability and validity of the proposed approach. The results showed a higher accuracy with semantically imputed datasets using ANN. We also presented a detailed comparative analysis, comparing the results with the state-of-the-art from the literature. We found that our semantic imputed datasets improved the classification accuracy with 95.78% as a higher one thus proving the effectiveness and robustness of learned models

Logiques pour les réseaux sociaux : annonces asynchrones dans des structures orthogonales

Cette thèse a deux objets d'étude principaux. D'une part, nous proposons et étudions des modèles de transmission et de réception asynchrones de messages. Pour cela, nous nous plaçons dans le cadre des logiques épistémiques dynamiques - un sous-domaine de la logique modale qui formalise les états épistémiques d'un agent (i.e. ce que l'agent sait) et qui caractérise la façon dont ces états évoluent en différentes circonstances. La plus connue des logiques épistémiques dynamiques est la logique des annonces publiques (Plaza, 1989) - une logique dynamique qui considère comme action de base l'action d'effectuer une annonce publique. Dans un système multi-agent, il est dans la connaissance commune des agents que les messages sont reçus par tous les agents au même instant. Dans le chapitre principal de la thèse, nous proposons un modèle d'annonces asynchrones dans lequel les agents peuvent recevoir les annonces à différents instants tout en ignorant si les autres agents ont également reçu ces annonces. D'autre part, nous étudions une classe de structures relationnelles qui apparaissent assez souvent en logique modale : la classe des cadres orthogonaux. Les cadres orthogonaux sont des structures birelationnelles dans lesquelles deux composantes connexes arbitraires déterminées par les deux relations ont au plus un élément en commun. Pour différentes restrictions de la classe des cadres orthogonaux, nous proposons des axiomatisations correctes et complètes des ensembles de formules valides que ces restrictions déterminent et nous proposons quelques résultats de décidabilité de ces ensembles. Pour illustrer l'ubiquité des cadres orthogonaux, nous proposons des exemples de classes de modèles pour les logiques modales qui sont basées sur eux et nous montrons comment les résultats de la thèse peuvent être utilisés pour étudier ces classes du point de vue de leur orthogonalité. Enfin, nous combinons les deux parties précédentes dans le contexte de la logique épistémique sociale (Seligman et al., 2011). Il s'agit d'une logique développée pour l'étude des états épistémiques des agents dans un réseau social. Nous proposons différentes extensions dynamiques de cette logique et, en particulier, nous modélisons la transmission d'annonces asynchrones dans un réseau social.This thesis has two main objects of study, closely related to each other. On the one hand, we provide and study models for asynchronous transmission and reception of messages. To do this, we utilize the framework of Dynamic Epistemic Logic, a branch of Modal Logic which studies the epistemic state of an agent (i.e. what they know) and how this state changes under several circumstances. One of the better known dynamic epistemic logics is Public Announcement Logic (Plaza, 1989), a logic which allows for a notion of recieving a message. In a multi-agent system, this message is received by all agents at the same time, and they all know that the others have received it. In the main chapter of this thesis, we provide a framework for asynchronous announcements, in which the agents might receive the message at different times and be uncertain whether others know the information contained within it. On the other hand, we study a class of relational structures for modal logics which show up quite often in different areas of the literature: this is the class of orthogonal frames. Orthogonal frames are bi-relational structures wherein two distinct points cannot be connected by both relations at the same time. We give a sound and complete logic of orthogonal frames under different restrictions, and we provide decidability results. To illustrate the ubiquity of these structures, we provide multiple examples of frameworks for modal logics which are based on orthogonal frames, and we use some of the results obtained earlier to show how one can further the study of these structures by focusing on their orthogonality. To finish up, we combine the two areas of study, by taking as a case study the orthogonal framework of Social Epistemic Logic (Seligman et al., 2011). This is a framework for studying the epistemic state of agents in a social network. We provide different dynamic extensions, and in particular we give a way to model the transmission of announcements asynchronously in a social networ