3,780 research outputs found

    Graduate Catalog of Studies, 2023-2024

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    Cyclic proof systems for modal fixpoint logics

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    This thesis is about cyclic and ill-founded proof systems for modal fixpoint logics, with and without explicit fixpoint quantifiers.Cyclic and ill-founded proof-theory allow proofs with infinite branches or paths, as long as they satisfy some correctness conditions ensuring the validity of the conclusion. In this dissertation we design a few cyclic and ill-founded systems: a cyclic one for the weak Grzegorczyk modal logic K4Grz, based on our explanation of the phenomenon of cyclic companionship; and ill-founded and cyclic ones for the full computation tree logic CTL* and the intuitionistic linear-time temporal logic iLTL. All systems are cut-free, and the cyclic ones for K4Grz and iLTL have fully finitary correctness conditions.Lastly, we use a cyclic system for the modal mu-calculus to obtain a proof of the uniform interpolation property for the logic which differs from the original, automata-based one

    Southern Adventist University Undergraduate Catalog 2023-2024

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    Southern Adventist University\u27s undergraduate catalog for the academic year 2023-2024.https://knowledge.e.southern.edu/undergrad_catalog/1123/thumbnail.jp

    Fragments and frame classes:Towards a uniform proof theory for modal fixed point logics

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    This thesis studies the proof theory of modal fixed point logics. In particular, we construct proof systems for various fragments of the modal mu-calculus, interpreted over various classes of frames. With an emphasis on uniform constructions and general results, we aim to bring the relatively underdeveloped proof theory of modal fixed point logics closer to the well-established proof theory of basic modal logic. We employ two main approaches. First, we seek to generalise existing methods for basic modal logic to accommodate fragments of the modal mu-calculus. We use this approach for obtaining Hilbert-style proof systems. Secondly, we adapt existing proof systems for the modal mu-calculus to various classes of frames. This approach yields proof systems which are non-well-founded, or cyclic.The thesis starts with an introduction and some mathematical preliminaries. In Chapter 3 we give hypersequent calculi for modal logic with the master modality, building on work by Ori Lahav. This is followed by an Intermezzo, where we present an abstract framework for cyclic proofs, in which we give sufficient conditions for establishing the bounded proof property. In Chapter 4 we generalise existing work on Hilbert-style proof systems for PDL to the level of the continuous modal mu-calculus. Chapter 5 contains a novel cyclic proof system for the alternation-free two-way modal mu-calculus. Finally, in Chapter 6, we present a cyclic proof system for Guarded Kleene Algebra with Tests and take a first step towards using it to establish the completeness of an algebraic counterpart

    UMSL Bulletin 2023-2024

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    The 2023-2024 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1088/thumbnail.jp

    Graduate Catalog of Studies, 2023-2024

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    Modern computing: Vision and challenges

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    Over the past six decades, the computing systems field has experienced significant transformations, profoundly impacting society with transformational developments, such as the Internet and the commodification of computing. Underpinned by technological advancements, computer systems, far from being static, have been continuously evolving and adapting to cover multifaceted societal niches. This has led to new paradigms such as cloud, fog, edge computing, and the Internet of Things (IoT), which offer fresh economic and creative opportunities. Nevertheless, this rapid change poses complex research challenges, especially in maximizing potential and enhancing functionality. As such, to maintain an economical level of performance that meets ever-tighter requirements, one must understand the drivers of new model emergence and expansion, and how contemporary challenges differ from past ones. To that end, this article investigates and assesses the factors influencing the evolution of computing systems, covering established systems and architectures as well as newer developments, such as serverless computing, quantum computing, and on-device AI on edge devices. Trends emerge when one traces technological trajectory, which includes the rapid obsolescence of frameworks due to business and technical constraints, a move towards specialized systems and models, and varying approaches to centralized and decentralized control. This comprehensive review of modern computing systems looks ahead to the future of research in the field, highlighting key challenges and emerging trends, and underscoring their importance in cost-effectively driving technological progress

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    UMSL Bulletin 2022-2023

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    The 2022-2023 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1087/thumbnail.jp
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