Results for 'Eyvind Briseid'

9 found
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  1.  28
    A Functional Interpretation for Nonstandard Arithmetic.Benno van den Berg, Eyvind Briseid & Pavol Safarik - 2012 - Annals of Pure and Applied Logic 163 (12):1962-1994.
    We introduce constructive and classical systems for nonstandard arithmetic and show how variants of the functional interpretations due to Gödel and Shoenfield can be used to rewrite proofs performed in these systems into standard ones. These functional interpretations show in particular that our nonstandard systems are conservative extensions of E-HAω and E-PAω, strengthening earlier results by Moerdijk and Palmgren, and Avigad and Helzner. We will also indicate how our rewriting algorithm can be used for term extraction purposes. To conclude the (...)
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  2.  7
    Logical Aspects of Rates of Convergence in Metric Spaces.Eyvind Martol Briseid - 2009 - Journal of Symbolic Logic 74 (4):1401 - 1428.
    In this paper we develop a method for finding, under general conditions, explicit and highly uniform rates of convergence for the Picard iteration sequences for selfmaps on bounded metric spaces from ineffective proofs of convergence to a unique fixed point. We are able to extract full rates of convergence by extending the use of a logical metatheorem recently proved by Kohlenbach. In recent case studies we were able to find such explicit rates of convergence in two concrete cases. Our novel (...)
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  3.  19
    The Strength of Countable Saturation.Benno van den Berg, Eyvind Briseid & Pavol Safarik - 2017 - Archive for Mathematical Logic 56 (5-6):699-711.
    In earlier work we introduced two systems for nonstandard analysis, one based on classical and one based on intuitionistic logic; these systems were conservative extensions of first-order Peano and Heyting arithmetic, respectively. In this paper we study how adding the principle of countable saturation to these systems affects their proof-theoretic strength. We will show that adding countable saturation to our intuitionistic system does not increase its proof-theoretic strength, while adding it to the classical system increases the strength from first- to (...)
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  4.  44
    Everyday Reasoning with Inducements and Advice.Eyvind Ohm & Valerie A. Thompson - 2004 - Thinking and Reasoning 10 (3):241 – 272.
    In two experiments, we investigated how people interpret and reason with realistic conditionals in the form of inducements (i.e., promises and threats) and advice (i.e., tips and warnings). We found that inducements and advice differed with respect to the degree to which the speaker was perceived to have (a) control over the consequent, (b) a stake in the outcome, and (c) an obligation to ensure that the outcome occurs. Inducements and advice also differed with respect to perceived sufficiency and necessity, (...)
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  5.  80
    Conditional Probability and Pragmatic Conditionals: Dissociating Truth and Effectiveness.Eyvind Ohm & Valerie A. Thompson - 2006 - Thinking and Reasoning 12 (3):257 – 280.
    Recent research (e.g., Evans & Over, 2004) has provided support for the hypothesis that people evaluate the probability of conditional statements of the form if p then q as the conditional probability of q given p , P( q / p ). The present paper extends this approach to pragmatic conditionals in the form of inducements (i.e., promises and threats) and advice (i.e., tips and warnings). In so doing, we demonstrate a distinction between the truth status of these conditionals and (...)
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  6. The Problem of Knowledge in the Ethics of Kierkegaard's Works of Love.Kjell Eyvind Johansen - 1994 - Kierkegaardiana 17:52-65.
     
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  7.  23
    Fear and Trembling-the Problem of Justification.Kjell Eyvind Johansen - 2002 - British Journal for the History of Philosophy 10 (2):261 – 276.
  8.  11
    Nonstandard Functional Interpretations and Categorical Models.Amar Hadzihasanovic & Benno van den Berg - 2017 - Notre Dame Journal of Formal Logic 58 (3):343-380.
    Recently, the second author, Briseid, and Safarik introduced nonstandard Dialectica, a functional interpretation capable of eliminating instances of familiar principles of nonstandard arithmetic—including overspill, underspill, and generalizations to higher types—from proofs. We show that the properties of this interpretation are mirrored by first-order logic in a constructive sheaf model of nonstandard arithmetic due to Moerdijk, later developed by Palmgren, and draw some new connections between nonstandard principles and principles that are rejected by strict constructivism. Furthermore, we introduce a variant (...)
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  9. Contributors to the Present Issue.Jacob Boggild, Jacob Golomb, Povl Gotke, Kjell Eyvind Johansen, George Pattison, Joachim Ringleben, Jon Stewart, Soren Bruun, Jacob Beggild & Niels Nymann Eriksen - 1998 - Kierkegaardiana 19:242.
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