2,795 research outputs found

    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

    On Wondering: The Epistemology of A Questioning Attitude

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    An emerging trend in contemporary epistemology departs from the traditional preoccupation with the nature of knowledge, belief, evidence, justification, and the problems of skepticism. This trend focuses instead on the nature of inquiry itself and especially on the role of questions and questioning attitudes that arise in and define that activity. Naturally, this emerging trend calls for a philosophical exploration of the nature of questioning attitudes like curiosity and wondering, and of the various epistemological considerations pertaining to them. Consequently, this project primarily addresses two questions: what does it mean to wonder? And what is required to wonder well? The project is thus both descriptive and normative, aiming to pin down the place that wondering has in our ontology of epistemologically significant mental states and to determine what kinds of prescriptive norms it is subject to in the course of rational inquiry

    Deep Clustering for Data Cleaning and Integration

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    Deep Learning (DL) techniques now constitute the state-of-theart for important problems in areas such as text and image processing, and there have been impactful results that deploy DL in several data management tasks. Deep Clustering (DC) has recently emerged as a sub-discipline of DL, in which data representations are learned in tandem with clustering, with a view to automatically identifying the features of the data that lead to improved clustering results. While DC has been used to good effect in several domains, particularly in image processing, the potential of DC for data management tasks remains unexplored. In this paper, we address this gap by investigating the suitability of DC for data cleaning and integration tasks, specifically schema inference, entity resolution and domain discovery, from the perspective of tables, rows and columns, respectively. In this setting, we compare and contrast several DC and non-DC clustering algorithms using standard benchmarks. The results show, among other things, that the most effective DC algorithms consistently outperform non-DC clustering algorithms for data integration tasks. Experiments also show consistently strong performance compared with state-of-the-art bespoke algorithms for each of the data integration tasks

    Polynomial time and dependent types

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    We combine dependent types with linear type systems that soundly and completely capture polynomial time computation. We explore two systems for capturing polynomial time: one system that disallows construction of iterable data, and one, based on the LFPL system of Martin Hofmann, that controls construction via a payment method. Both of these are extended to full dependent types via Quantitative Type Theory, allowing for arbitrary computation in types alongside guaranteed polynomial time computation in terms. We prove the soundness of the systems using a realisability technique due to Dal Lago and Hofmann. Our long-term goal is to combine the extensional reasoning of type theory with intensional reasoning about the resources intrinsically consumed by programs. This paper is a step along this path, which we hope will lead both to practical systems for reasoning about programs’ resource usage, and to theoretical use as a form of synthetic computational complexity theory

    Current and Future Challenges in Knowledge Representation and Reasoning

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    Knowledge Representation and Reasoning is a central, longstanding, and active area of Artificial Intelligence. Over the years it has evolved significantly; more recently it has been challenged and complemented by research in areas such as machine learning and reasoning under uncertainty. In July 2022 a Dagstuhl Perspectives workshop was held on Knowledge Representation and Reasoning. The goal of the workshop was to describe the state of the art in the field, including its relation with other areas, its shortcomings and strengths, together with recommendations for future progress. We developed this manifesto based on the presentations, panels, working groups, and discussions that took place at the Dagstuhl Workshop. It is a declaration of our views on Knowledge Representation: its origins, goals, milestones, and current foci; its relation to other disciplines, especially to Artificial Intelligence; and on its challenges, along with key priorities for the next decade

    A Theistic Critique of Secular Moral Nonnaturalism

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    This dissertation is an exercise in Theistic moral apologetics. It will be developing both a critique of secular nonnaturalist moral theory (moral Platonism) at the level of metaethics, as well as a positive form of the moral argument for the existence of God that follows from this critique. The critique will focus on the work of five prominent metaethical theorists of secular moral non-naturalism: David Enoch, Eric Wielenberg, Russ Shafer-Landau, Michael Huemer, and Christopher Kulp. Each of these thinkers will be critically examined. Following this critique, the positive moral argument for the existence of God will be developed, combining a cumulative, abductive argument that follows from filling in the content of a succinct apagogic argument. The cumulative abductive argument and the apagogic argument together, with a transcendental and modal component, will be presented to make the case that Theism is the best explanation for the kind of moral, rational beings we are and the kind of universe in which we live, a rational intelligible universe

    On Internal Merge

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    Bootstrapping extensionality

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    Intuitionistic type theory is a formal system designed by Per Martin-Loef to be a full-fledged foundation in which to develop constructive mathematics. One particular variant, intensional type theory (ITT), features nice computational properties like decidable type-checking, making it especially suitable for computer implementation. However, as traditionally defined, ITT lacks many vital extensionality principles, such as function extensionality. We would like to extend ITT with the desired extensionality principles while retaining its convenient computational behaviour. To do so, we must first understand the extent of its expressive power, from its strengths to its limitations. The contents of this thesis are an investigation into intensional type theory, and in particular into its power to express extensional concepts. We begin, in the first part, by developing an extension to the strict setoid model of type theory with a universe of setoids. The model construction is carried out in a minimal intensional type theoretic metatheory, thus providing a way to bootstrap extensionality by ``compiling'' it down to a few building blocks such as inductive families and proof-irrelevance. In the second part of the thesis we explore inductive-inductive types (ITTs) and their relation to simpler forms of induction in an intensional setting. We develop a general method to reduce a subclass of infinitary IITs to inductive families, via an encoding that can be expressed in ITT without any extensionality besides proof-irrelevance. Our results contribute to further understand IITs and the expressive power of intensional type theory, and can be of practical use when formalizing mathematics in proof assistants that do not natively support induction-induction
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