94 research outputs found

    Quantitative Graded Semantics and Spectra of Behavioural Metrics

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    Behavioural metrics provide a quantitative refinement of classical two-valued behavioural equivalences on systems with quantitative data, such as metric or probabilistic transition systems. In analogy to the classical linear-time/branching-time spectrum of two-valued behavioural equivalences on transition systems, behavioural metrics come in various degrees of granularity, depending on the observer's ability to interact with the system. Graded monads have been shown to provide a unifying framework for spectra of behavioural equivalences. Here, we transfer this principle to spectra of behavioural metrics, working at a coalgebraic level of generality, that is, parametrically in the system type. In the ensuing development of quantitative graded semantics, we discuss presentations of graded monads on the category of metric spaces in terms of graded quantitative equational theories. Moreover, we obtain a canonical generic notion of invariant real-valued modal logic, and provide criteria for such logics to be expressive in the sense that logical distance coincides with the respective behavioural distance. We thus recover recent expressiveness results for coalgebraic branching-time metrics and for trace distance in metric transition systems; moreover, we obtain a new expressiveness result for trace semantics of fuzzy transition systems. We also provide a number of salient negative results. In particular, we show that trace distance on probabilistic metric transition systems does not admit a characteristic real-valued modal logic at all

    CLARIN

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    The book provides a comprehensive overview of the Common Language Resources and Technology Infrastructure – CLARIN – for the humanities. It covers a broad range of CLARIN language resources and services, its underlying technological infrastructure, the achievements of national consortia, and challenges that CLARIN will tackle in the future. The book is published 10 years after establishing CLARIN as an Europ. Research Infrastructure Consortium

    Coalgebra for the working software engineer

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    Often referred to as ‘the mathematics of dynamical, state-based systems’, Coalgebra claims to provide a compositional and uniform framework to spec ify, analyse and reason about state and behaviour in computing. This paper addresses this claim by discussing why Coalgebra matters for the design of models and logics for computational phenomena. To a great extent, in this domain one is interested in properties that are preserved along the system’s evolution, the so-called ‘business rules’ or system’s invariants, as well as in liveness requirements, stating that e.g. some desirable outcome will be eventually produced. Both classes are examples of modal assertions, i.e. properties that are to be interpreted across a transition system capturing the system’s dynamics. The relevance of modal reasoning in computing is witnessed by the fact that most university syllabi in the area include some incursion into modal logic, in particular in its temporal variants. The novelty is that, as it happens with the notions of transition, behaviour, or observational equivalence, modalities in Coalgebra acquire a shape . That is, they become parametric on whatever type of behaviour, and corresponding coinduction scheme, seems appropriate for addressing the problem at hand. In this context, the paper revisits Coalgebra from a computational perspective, focussing on three topics central to software design: how systems are modelled, how models are composed, and finally, how properties of their behaviours can be expressed and verified.Fuzziness, as a way to express imprecision, or uncertainty, in computation is an important feature in a number of current application scenarios: from hybrid systems interfacing with sensor networks with error boundaries, to knowledge bases collecting data from often non-coincident human experts. Their abstraction in e.g. fuzzy transition systems led to a number of mathematical structures to model this sort of systems and reason about them. This paper adds two more elements to this family: two modal logics, framed as institutions, to reason about fuzzy transition systems and the corresponding processes. This paves the way to the development, in the second part of the paper, of an associated theory of structured specification for fuzzy computational systems

    Kantorovich Functors and Characteristic Logics for Behavioural Distances

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    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

    Automated Reasoning

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    This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book

    CLARIN. The infrastructure for language resources

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    CLARIN, the "Common Language Resources and Technology Infrastructure", has established itself as a major player in the field of research infrastructures for the humanities. This volume provides a comprehensive overview of the organization, its members, its goals and its functioning, as well as of the tools and resources hosted by the infrastructure. The many contributors representing various fields, from computer science to law to psychology, analyse a wide range of topics, such as the technology behind the CLARIN infrastructure, the use of CLARIN resources in diverse research projects, the achievements of selected national CLARIN consortia, and the challenges that CLARIN has faced and will face in the future. The book will be published in 2022, 10 years after the establishment of CLARIN as a European Research Infrastructure Consortium by the European Commission (Decision 2012/136/EU)

    Dualities in modal logic

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    Categorical dualities are an important tool in the study of (modal) logics. They offer conceptual understanding and enable the transfer of results between the different semantics of a logic. As such, they play a central role in the proofs of completeness theorems, Sahlqvist theorems and Goldblatt-Thomason theorems. A common way to obtain dualities is by extending existing ones. For example, Jonsson-Tarski duality is an extension of Stone duality. A convenient formalism to carry out such extensions is given by the dual categorical notions of algebras and coalgebras. Intuitively, these allow one to isolate the new part of a duality from the existing part. In this thesis we will derive both existing and new dualities via this route, and we show how to use the dualities to investigate logics. However, not all (modal logical) paradigms fit the (co)algebraic perspective. In particular, modal intuitionistic logics do not enjoy a coalgebraic treatment, and there is a general lack of duality results for them. To remedy this, we use a generalisation of both algebras and coalgebras called dialgebras. Guided by the research field of coalgebraic logic, we introduce the framework of dialgebraic logic. We show how a large class of modal intuitionistic logics can be modelled as dialgebraic logics and we prove dualities for them. We use the dialgebraic framework to prove general completeness, Hennessy-Milner, representation and Goldblatt-Thomason theorems, and instantiate this to a wide variety of modal intuitionistic logics. Additionally, we use the dialgebraic perspective to investigate modal extensions of the meet-implication fragment of intuitionistic logic. We instantiate general dialgebraic results, and describe how modal meet-implication logics relate to modal intuitionistic logics

    Proceedings of the 19th Sound and Music Computing Conference

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    Proceedings of the 19th Sound and Music Computing Conference - June 5-12, 2022 - Saint-Étienne (France). https://smc22.grame.f

    Effectful program distancing

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    International audienceSemantics is traditionally concerned with program equivalence, in which all pairs of programs which are not equivalent are treated the same, and simply dubbed as incomparable. In recent years, various forms of program metrics have been introduced such that the distance between non-equivalent programs is measured as an element of an appropriate quantale. By letting the underlying quantale vary as the type of the compared programs become more complex, the recently introduced framework of differential logical relations allows for a new contextual form of reasoning. In this paper, we show that all this can be generalised to effectful higher-order programs, in which not only the values , but also the effects computations produce can be appropriately distanced in a principled way. We show that the resulting framework is flexible, allowing various forms of effects to be handled, and that it provides compact and informative judgments about program differences

    Mathematics in Software Reliability and Quality Assurance

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    This monograph concerns the mathematical aspects of software reliability and quality assurance and consists of 11 technical papers in this emerging area. Included are the latest research results related to formal methods and design, automatic software testing, software verification and validation, coalgebra theory, automata theory, hybrid system and software reliability modeling and assessment
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