446 research outputs found

    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

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Higher-Order MSL Horn Constraints

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    Next Generation Business Ecosystems: Engineering Decentralized Markets, Self-Sovereign Identities and Tokenization

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    Digital transformation research increasingly shifts from studying information systems within organizations towards adopting an ecosystem perspective, where multiple actors co-create value. While digital platforms have become a ubiquitous phenomenon in consumer-facing industries, organizations remain cautious about fully embracing the ecosystem concept and sharing data with external partners. Concerns about the market power of platform orchestrators and ongoing discussions on privacy, individual empowerment, and digital sovereignty further complicate the widespread adoption of business ecosystems, particularly in the European Union. In this context, technological innovations in Web3, including blockchain and other distributed ledger technologies, have emerged as potential catalysts for disrupting centralized gatekeepers and enabling a strategic shift towards user-centric, privacy-oriented next-generation business ecosystems. However, existing research efforts focus on decentralizing interactions through distributed network topologies and open protocols lack theoretical convergence, resulting in a fragmented and complex landscape that inadequately addresses the challenges organizations face when transitioning to an ecosystem strategy that harnesses the potential of disintermediation. To address these gaps and successfully engineer next-generation business ecosystems, a comprehensive approach is needed that encompasses the technical design, economic models, and socio-technical dynamics. This dissertation aims to contribute to this endeavor by exploring the implications of Web3 technologies on digital innovation and transformation paths. Drawing on a combination of qualitative and quantitative research, it makes three overarching contributions: First, a conceptual perspective on \u27tokenization\u27 in markets clarifies its ambiguity and provides a unified understanding of the role in ecosystems. This perspective includes frameworks on: (a) technological; (b) economic; and (c) governance aspects of tokenization. Second, a design perspective on \u27decentralized marketplaces\u27 highlights the need for an integrated understanding of micro-structures, business structures, and IT infrastructures in blockchain-enabled marketplaces. This perspective includes: (a) an explorative literature review on design factors; (b) case studies and insights from practitioners to develop requirements and design principles; and (c) a design science project with an interface design prototype of blockchain-enabled marketplaces. Third, an economic perspective on \u27self-sovereign identities\u27 (SSI) as micro-structural elements of decentralized markets. This perspective includes: (a) value creation mechanisms and business aspects of strategic alliances governing SSI ecosystems; (b) business model characteristics adopted by organizations leveraging SSI; and (c) business model archetypes and a framework for SSI ecosystem engineering efforts. The dissertation concludes by discussing limitations as well as outlining potential avenues for future research. These include, amongst others, exploring the challenges of ecosystem bootstrapping in the absence of intermediaries, examining the make-or-join decision in ecosystem emergence, addressing the multidimensional complexity of Web3-enabled ecosystems, investigating incentive mechanisms for inter-organizational collaboration, understanding the role of trust in decentralized environments, and exploring varying degrees of decentralization with potential transition pathways

    The Invention of Truth. Salman Rushdie between Truth and Make-believe

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    [Italiano]: In questo libro, il mondo letterario di Salman Rushdie viene attentamente analizzato con un approccio critico ‘metalettico’. Intrecciando nei suoi romanzi realtà e immaginazione, l’opera dell’autore anglo-indiano testimonia una sensibilità ‘metamoderna’, poiché intreccia senza soluzione di continuità l’esperienza del mondo reale con gli intricati schemi del linguaggio e dell’arte. Partendo dalle contraddizioni e dagli errori presenti nella narrazione del primo capolavoro di Rushdie, I figli della mezzanotte, passando per la fusione di sacro e profano ne I versetti satanici, fino al movimento palindromo o di reciproca convergenza tra vita e scrittura in Quichotte, il volume accompagna chi legge in un viaggio alla scoperta del potere creativo del linguaggio e di come esso plasmi e venga plasmato dalla storia. L’opera di Salman Rushdie offre, infatti, l’opportunità di misurarsi con il rapporto instabile tra realtà storica ed espressione artistica, aspirazioni individuali e bisogni collettivi, identità e disfacimento, verità e finzione./[English]: In this book, the literary world of Salman Rushdie is carefully scrutinised using a ‘metaleptical’ critical approach. Weaving together truth and fiction, reality and fantasy in his novels, the Anglo-Indian author’s work exudes a ‘metamodern’ sensibility as it seamlessly weaves the fabric of real-world experience with the intricate patterns of language and art. Beginning with the contradictions and errors in the narrative of Rushdie’s first masterpiece Midnight’s Children, through the blending of the sacred and the secular in The Satanic Verses, to the palindromic movement of the mutual convergence of life and writing in Quichotte, the volume takes the reader on a journey of discovery of the creative power of language and how it shapes and is shaped by history. Salman Rushdie’s work offers, in fact, the opportunity to engage in a nuanced examination of the balance between historical reality and artistic expression, individual aspirations and collective needs, continuity and decay, truth and make-believe

    Reasoning with Attitude

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    This book presents and develops inferential expressivism, a novel approach to the study of meaning which combines elements of the expressivist and inferentialist programmes. Expressivists explain the meaning of words in terms of the attitudes that they are used to express; inferentialists explain the meaning of words in terms of the inferences that they are used to draw. The book lays out the philosophical foundations of inferential expressivism by articulating and defending the view that the meaning of an expression is to be explained in terms of the inferences we draw involving the attitudes we express. The book, moreover, lays out the logical foundations of inferential expressivism by showing how to implement the view rigorously by means of novel formal systems which can deal with a variety of speech acts. As the book shows, by joining forces expressivism and inferentialism can meet their key challenges whilst retaining their distinctive insights and advantages. The book goes on to demonstrate the fruitfulness of the inferential expressivist approach to meaning by applying it to a diverse range of linguistic phenomena, including epistemic modals, probability operators, conditionals, moral predicates, the truth predicate, and propositional attitude predicates

    Logics of Responsibility

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    The study of responsibility is a complicated matter. The term is used in different ways in different fields, and it is easy to engage in everyday discussions as to why someone should be considered responsible for something. Typically, the backdrop of these discussions involves social, legal, moral, or philosophical problems. A clear pattern in all these spheres is the intent of issuing standards for when---and to what extent---an agent should be held responsible for a state of affairs. This is where Logic lends a hand. The development of expressive logics---to reason about agents' decisions in situations with moral consequences---involves devising unequivocal representations of components of behavior that are highly relevant to systematic responsibility attribution and to systematic blame-or-praise assignment. To put it plainly, expressive syntactic-and-semantic frameworks help us analyze responsibility-related problems in a methodical way. This thesis builds a formal theory of responsibility. The main tool used toward this aim is modal logic and, more specifically, a class of modal logics of action known as stit theory. The underlying motivation is to provide theoretical foundations for using symbolic techniques in the construction of ethical AI. Thus, this work means a contribution to formal philosophy and symbolic AI. The thesis's methodology consists in the development of stit-theoretic models and languages to explore the interplay between the following components of responsibility: agency, knowledge, beliefs, intentions, and obligations. Said models are integrated into a framework that is rich enough to provide logic-based characterizations for three categories of responsibility: causal, informational, and motivational responsibility. The thesis is structured as follows. Chapter 2 discusses at length stit theory, a logic that formalizes the notion of agency in the world over an indeterministic conception of time known as branching time. The idea is that agents act by constraining possible futures to definite subsets. On the road to formalizing informational responsibility, Chapter 3 extends stit theory with traditional epistemic notions (knowledge and belief). Thus, the chapter formalizes important aspects of agents' reasoning in the choice and performance of actions. In a context of responsibility attribution and excusability, Chapter 4 extends epistemic stit theory with measures of optimality of actions that underlie obligations. In essence, this chapter formalizes the interplay between agents' knowledge and what they ought to do. On the road to formalizing motivational responsibility, Chapter 5 adds intentions and intentional actions to epistemic stit theory and reasons about the interplay between knowledge and intentionality. Finally, Chapter 6 merges the previous chapters' formalisms into a rich logic that is able to express and model different modes of the aforementioned categories of responsibility. Technically, the most important contributions of this thesis lie in the axiomatizations of all the introduced logics. In particular, the proofs of soundness & completeness results involve long, step-by-step procedures that make use of novel techniques

    Quantum fine-grained complexity

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    Selected Topics in Gravity, Field Theory and Quantum Mechanics

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    Quantum field theory has achieved some extraordinary successes over the past sixty years; however, it retains a set of challenging problems. It is not yet able to describe gravity in a mathematically consistent manner. CP violation remains unexplained. Grand unified theories have been eliminated by experiment, and a viable unification model has yet to replace them. Even the highly successful quantum chromodynamics, despite significant computational achievements, struggles to provide theoretical insight into the low-energy regime of quark physics, where the nature and structure of hadrons are determined. The only proposal for resolving the fine-tuning problem, low-energy supersymmetry, has been eliminated by results from the LHC. Since mathematics is the true and proper language for quantitative physical models, we expect new mathematical constructions to provide insight into physical phenomena and fresh approaches for building physical theories
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