4,397 research outputs found

    Ramsey's Theorem for Pairs and kk Colors as a Sub-Classical Principle of Arithmetic

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    The purpose is to study the strength of Ramsey's Theorem for pairs restricted to recursive assignments of kk-many colors, with respect to Intuitionistic Heyting Arithmetic. We prove that for every natural number k2k \geq 2, Ramsey's Theorem for pairs and recursive assignments of kk colors is equivalent to the Limited Lesser Principle of Omniscience for Σ30\Sigma^0_3 formulas over Heyting Arithmetic. Alternatively, the same theorem over intuitionistic arithmetic is equivalent to: for every recursively enumerable infinite kk-ary tree there is some i<ki < k and some branch with infinitely many children of index ii.Comment: 17 page

    Constructing failure: a frame analysis of entrepreneurial failure blogs

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    Constructing failure: a frame analysis of entrepreneurial failure blog

    An Intuitionistic Analysis of Size-change Termination

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    In 2001 Lee, Jones and Ben-Amram introduced the notion of size-change termination (SCT) for first order functional programs, a sufficient condition for termination. They proved that a program is size-change terminating if and only if it has a certain property which can be statically verified from the recursive definition of the program. Their proof of the size-change termination theorem used Ramsey\u27s Theorem for pairs, which is a purely classical result. In 2012 Vytiniotis, Coquand and Wahlsteldt intuitionistically proved a classical variant of the size-change termination theorem by using the Almost-Full Theorem instead of Ramsey\u27s Theorem for pairs. In this paper we provide an intuitionistic proof of another classical variant of the SCT theorem: our goal is to provide a statement and a proof very similar to the original ones. This can be done by using the H-closure Theorem, which differs from Ramsey\u27s Theorem for pairs only by a contrapositive step. As a side result we obtain another proof of the characterization of the functions computed by a tail-recursive SCT program, by relating the SCT Theorem with the Termination Theorem by Podelski and Rybalchenko. Finally, by investigating the relationship between them, we provide a property in the "language" of size-change termination which is equivalent to Podelski and Rybalchenko\u27s termination

    Connecticut College News Vol. 29 No. 10

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    Spartan Daily, May 3, 1962

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    Volume 49, Issue 111https://scholarworks.sjsu.edu/spartandaily/4298/thumbnail.jp

    The God-World Relationship Between Joseph Bracken, Philip Clayton, and the Open Theism

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    This dissertation investigates the God-world relationship between Joseph Bracken as a process theologian, Philip Clayton as a panentheist, and the open theism. They have affinities and differences as conversational partners in their multilayered relations. Their common question must be as follows: “What does it mean to believe in God today?” In this dissertation I compare their respectively theological perspectives and explore their affinities and differences. Many scholars have already noted more affinities than untenable differences among Bracken’s theology, Clayton’s panentheism, and the open theism. On the one hand, even though theological perspectives of Bracken and Clayton are obviously different from each other, they are both influenced in specific ways by Whitehead. On the other hand, open theism is a movement that emphasizes “the openness of God,” from within evangelical theism. The fact that there is even within classical theism the pursuit of new models of God such as revised classical theism or modified classical theism might suggest the need for contemporary models of God in philosophical theology. This dissertation will thus explore philosophical theologies that are proper both to the biblical faith and intellectual earnestness, that is, 居敬窮理 (geo (to live) kyeong (piety) kung (to acknowledge) li (reason)) in Eastern philosophy, which means distinctions but not separation between piety and intelligence, and that stand between classical theism and “orthodox” process theism. If there is no consistency among biblical, rational and existential descriptions of God, how can we establish philosophical theologies? Our theological task is to frame a new constructive theology whose primary aspect must synthesize both classical theism and process theology in the hermeneutical circle. For example, this new theism admits an infinitely qualitative difference between God and the world, as well as a really radical relation between God and the world. Aspects and domains do not encroach upon each other

    The Cord Weekly (February 17, 1983)

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    Seaman v. YouTube

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    Six Inversion Strategies for Avoiding Rejection in Academic Publishing: Lessons from the IS Discipline

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    The publication process in many academic disciplines, including in Information Systems (IS), can seem arduous and unpredictable, particularly for early career researchers. While the literature offers plentiful guidance on how to pursue a paper acceptance, this paper offers a crisp summary of common mistakes that lead to rejection and how to avoid them. We provide six actionable inversion strategies for avoiding common mistakes that often lead to paper rejection. Namely, when preparing a paper, we recommend you (1) abstain from methodological promiscuity and (2) never overclaim (but try not to underclaim either); When submitting a paper, it is a good idea to (3) steer clear of bootlicking and (3) avoid sloppiness; And, after receiving the reviews, you should (5) forego belligerence, and (6) stop flogging a dead horse. These inversion strategies can help early career researchers better navigate the review process, increasing the chances of their papers maturing, and helping to avoid mistakes that lower the chance of publishing in high quality IS journals
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