213,927 research outputs found

    Virtual Evidence: A Constructive Semantics for Classical Logics

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    This article presents a computational semantics for classical logic using constructive type theory. Such semantics seems impossible because classical logic allows the Law of Excluded Middle (LEM), not accepted in constructive logic since it does not have computational meaning. However, the apparently oracular powers expressed in the LEM, that for any proposition P either it or its negation, not P, is true can also be explained in terms of constructive evidence that does not refer to "oracles for truth." Types with virtual evidence and the constructive impossibility of negative evidence provide sufficient semantic grounds for classical truth and have a simple computational meaning. This idea is formalized using refinement types, a concept of constructive type theory used since 1984 and explained here. A new axiom creating virtual evidence fully retains the constructive meaning of the logical operators in classical contexts. Key Words: classical logic, constructive logic, intuitionistic logic, propositions-as-types, constructive type theory, refinement types, double negation translation, computational content, virtual evidenc

    Harnessing Collaborative Technologies: Helping Funders Work Together Better

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    This report was produced through a joint research project of the Monitor Institute and the Foundation Center. The research included an extensive literature review on collaboration in philanthropy, detailed analysis of trends from a recent Foundation Center survey of the largest U.S. foundations, interviews with 37 leading philanthropy professionals and technology experts, and a review of over 170 online tools.The report is a story about how new tools are changing the way funders collaborate. It includes three primary sections: an introduction to emerging technologies and the changing context for philanthropic collaboration; an overview of collaborative needs and tools; and recommendations for improving the collaborative technology landscapeA "Key Findings" executive summary serves as a companion piece to this full report

    Establishing a resource center: A guide for organizations supporting community foundations

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    Maintaining a resource center such as a library is a central tasks of an association to serve its members, though one of the first to be neglected. WINGS-CF commissioned this guide to assist organizations supporting community foundations to review and organize their resource items, and to propose several classification systems / taxonomies

    New Media Art/ New Funding Models

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    Investigates the current state of funding for new media artists, with an emphasis on the support structures for innovative creative work that utilizes advanced technologies as the main vehicle for artistic practice

    Mathematical Foundations of Consciousness

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    We employ the Zermelo-Fraenkel Axioms that characterize sets as mathematical primitives. The Anti-foundation Axiom plays a significant role in our development, since among other of its features, its replacement for the Axiom of Foundation in the Zermelo-Fraenkel Axioms motivates Platonic interpretations. These interpretations also depend on such allied notions for sets as pictures, graphs, decorations, labelings and various mappings that we use. A syntax and semantics of operators acting on sets is developed. Such features enable construction of a theory of non-well-founded sets that we use to frame mathematical foundations of consciousness. To do this we introduce a supplementary axiomatic system that characterizes experience and consciousness as primitives. The new axioms proceed through characterization of so- called consciousness operators. The Russell operator plays a central role and is shown to be one example of a consciousness operator. Neural networks supply striking examples of non-well-founded graphs the decorations of which generate associated sets, each with a Platonic aspect. Employing our foundations, we show how the supervening of consciousness on its neural correlates in the brain enables the framing of a theory of consciousness by applying appropriate consciousness operators to the generated sets in question
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