A SOLUTION TO THE SURPRISE EXAM PARADOX IN CONSTRUCTIVE MATHEMATICS

2012 ◽  
Vol 5 (4) ◽  
pp. 679-686 ◽  
Author(s):  
MOHAMMAD ARDESHIR ◽  
RASOUL RAMEZANIAN
Keyword(s):  
The Other ◽  
Backward Induction ◽  
Constructive Mathematics ◽  
Constructive Logic ◽  
Extensive Form ◽  
Turing Computability ◽  
Extensive Form Games ◽  
Continuity Principle ◽  
Classical Mathematics

AbstractWe represent the well-known surprise exam paradox in constructive and computable mathematics and offer solutions. One solution is based on Brouwer’s continuity principle in constructive mathematics, and the other involves type 2 Turing computability in classical mathematics. We also discuss the backward induction paradox for extensive form games in constructive logic.

scholarly journals The Refined Best Reply Correspondence and Backward Induction

2019 ◽  
Vol 20 (1) ◽  
pp. 52-66
Author(s):  
Dieter Balkenborg ◽  
Christoph Kuzmics ◽  
Josef Hofbauer
Keyword(s):  
Normal Form ◽  
Fixed Points ◽  
The Other ◽  
Backward Induction ◽  
Perfect Recall ◽  
Extensive Form ◽  
Remarkable Property ◽  
Extensive Form Games ◽  
Other Hand ◽  
Perfect Equilibria

Abstract Fixed points of the (most) refined best reply correspondence, introduced in Balkenborg et al. (2013), in the agent normal form of extensive form games with perfect recall have a remarkable property. They induce fixed points of the same correspondence in the agent normal form of every subgame. Furthermore, in a well-defined sense, fixed points of this correspondence refine even trembling hand perfect equilibria, while, on the other hand, reasonable equilibria that are not weak perfect Bayesian equilibria are fixed points of this correspondence.

scholarly journals Non-altruistic Equilibria

2019 ◽  
Vol 67 (3-4) ◽  
pp. 185-195
Author(s):  
Kazuhiro Ohnishi
Keyword(s):  
Normal Form ◽  
Cooperative Games ◽  
The Other ◽  
Extensive Form ◽  
Extensive Form Games ◽  
Normal Form Games ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria ◽  
Non Cooperative Games

Which choice will a player make if he can make one of two choices in which his own payoffs are equal, but his rival’s payoffs are not equal, that is, one with a large payoff for his rival and the other with a small payoff for his rival? This paper introduces non-altruistic equilibria for normal-form games and extensive-form non-altruistic equilibria for extensive-form games as equilibrium concepts of non-cooperative games by discussing such a problem and examines the connections between their equilibrium concepts and Nash and subgame perfect equilibria that are important and frequently encountered equilibrium concepts.

scholarly journals Rationality in Extensive-Form Games

1992 ◽  
Vol 6 (4) ◽  
pp. 103-118 ◽  
Author(s):  
Philip J Reny
Keyword(s):  
Point Of View ◽  
Backward Induction ◽  
Rational Behavior ◽  
Rational Decision ◽  
Extensive Form ◽  
Extensive Form Games ◽  
Classical Point

Let us adopt the classical point of view that a theory of games is a description of “rational” behavior. Consequently, equipped with a book entitled “Theory of Games,” any individual in any strategic situation need only consult the book to make a “rational” decision. One of the questions to address in this context is indeed whether or not strategies other than those provided by backward induction can ever appear in such a book. In offering an answer, we shall also explore the logical limits within which any “Theory of Games” must operate.

Extensive Form Rationalizability

2014 ◽  
Author(s):  
Herbert Gintis
Keyword(s):  
Normal Form ◽  
Nash Equilibria ◽  
Common Knowledge ◽  
Backward Induction ◽  
Forward Induction ◽  
Extensive Form ◽  
Extensive Form Games ◽  
Dominated Strategies ◽  
Extensive Form Game ◽  
Common Knowledge Of Rationality

The extensive form of a game is informationally richer than the normal form since players gather information that allows them to update their subjective priors as the game progresses. For this reason, the study of rationalizability in extensive form games is more complex than the corresponding study in normal form games. There are two ways to use the added information to eliminate strategies that would not be chosen by a rational agent: backward induction and forward induction. The latter is relatively exotic (although more defensible). Backward induction, by far the most popular technique, employs the iterated elimination of weakly dominated strategies, arriving at the subgame perfect Nash equilibria—the equilibria that remain Nash equilibria in all subgames. An extensive form game is considered generic if it has a unique subgame perfect Nash equilibrium. This chapter develops the tools of modal logic and presents Robert Aumann's famous proof that common knowledge of rationality (CKR) implies backward induction. It concludes that Aumann is perfectly correct, and the real culprit is CKR itself. CKR is in fact self-contradictory when applied to extensive form games.

scholarly journals Classical mathematics for a constructive world

2011 ◽  
Vol 21 (4) ◽  
pp. 861-882 ◽  
Author(s):  
RUSSELL O'CONNOR
Keyword(s):  
Classical Logic ◽  
Type Theory ◽  
Function Spaces ◽  
Constructive Mathematics ◽  
Constructive Logic ◽  
Dependent Type Theory ◽  
Interactive Theorem Provers ◽  
Classical Function ◽  
Classical Mathematics ◽  
Dependent Type

Interactive theorem provers based on dependent type theory have the flexibility to support both constructive and classical reasoning. Constructive reasoning is supported natively by dependent type theory, and classical reasoning is typically supported by adding additional non-constructive axioms. However, there is another perspective that views constructive logic as an extension of classical logic. This paper will illustrate how classical reasoning can be supported in a practical manner inside dependent type theory without additional axioms. We will show several examples of how classical results can be applied to constructive mathematics. Finally, we will show how to extend this perspective from logic to mathematics by representing classical function spaces using a weak value monad.

The pseudomalachite-ludjibaite-reichenbachite conundrum: OD description

2019 ◽  
Vol 57 (5) ◽  
pp. 571-581
Author(s):  
Emil Makovicky
Keyword(s):  
Crystal Structures ◽  
Current Knowledge ◽  
The Other ◽  
Crystal Chemical ◽  
Layer System ◽  
Coordination Polyhedra

Abstract Crystal structures of the three polymorphs of Cu5(PO4)2(OH)4, namely pseudomalachite, ludjibaite, and reichenbachite, can be described as being composed of rods perpendicular to their crystal-chemical layering. Two different sorts of rods can be defined. Type 1 rods share rows of Cu coordination polyhedra, forming a series of slabs. Slab boundaries and slab interiors represent alternating geometric OD layers of two kinds, with layer symmetries close to P21/m and , which make up two different stacking schemes of geometric OD layers in the structures of ludjibaite and pseudomalachite. Such OD layers, however, are not developed in reichenbachite. Type 2 rods are defined as having columns of PO4 tetrahedra in the corners of the rods. In the Type 2 slabs composed of these rods, geometric Pg OD layers of glide-arrayed tetrahedra alternate with more complex OD layers; in ludjibaite this system of layers is oriented diagonally with respect to the Type 1 OD layer system. Two different OD stackings of Type 2 OD layers form the ludjibaite and reichenbachite structures but not that of pseudomalachite. Thus, ludjibaite might form disordered intergrowths with either of the other two members of the triplet but reichenbachite and pseudomalachite should not form oriented intergrowths. Current knowledge concerning formation of the three polymorphs is considered.

The Effects of Smoking Cessation on Diabetes Mellitus Patients

2020 ◽  
Vol 16 (2) ◽  
pp. 137-142
Author(s):  
Ali Alshahrani
Keyword(s):  
Smoking Cessation ◽  
The Other ◽  
Data Sources ◽  
Controlled Trials ◽  
Effective Management ◽  
Tailored Intervention ◽  
Randomized Controlled ◽  
Increased Risk ◽  
Diabetes Progression

Background: Smoking is an established predictor of type 2 diabetes. However, the link between smoking cessation and diabetes progression remains a subject of scholarly investigation. Objective: The objective of this systematic review is to establish the link between smoking cessation and diabetes. Data Sources: The study utilized conference abstracts and peer-reviewed journals that reported randomized controlled trials smoking cessation interventions for diabetes patients. Results: Results from the review were inconclusive on the link between smoking cessation and diabetes. On one hand, several researchers have confirmed a positive correlation between smoking cessation and decreased risk of diabetes. On the other hand, some researchers have demonstrated that immediate withdrawal of nicotine resulted in increased risk of diabetes; however, this risk reduces with time. Conclusion: The result of this review did not estblish a clear relationship between smoking cessation and diabates. Limitations: Compared to other studies examining the implication of smoking on chronic diseases, this study identified a very small number of trials evaluating the effect of smoking cessation on diabetes. The small number of studies implies that the results may not be suitable for generalization. Implication: Results from the review can help in the development of a tailored intervention for effective management of diabetes in smoking patients.

scholarly journals Development of Type 2 Diabetes Mellitus Phenotyping Framework Using Expert Knowledge and Machine Learning Approach

2016 ◽  
Vol 11 (4) ◽  
pp. 791-799 ◽  
Author(s):  
Rina Kagawa ◽  
Yoshimasa Kawazoe ◽  
Yusuke Ida ◽  
Emiko Shinohara ◽  
Katsuya Tanaka ◽  
...  
Keyword(s):  
Diabetes Mellitus ◽  
Machine Learning ◽  
Type 2 Diabetes ◽  
Type 2 Diabetes Mellitus ◽  
Expert Knowledge ◽  
The Other ◽  
Learning Approach ◽  
Research Subjects ◽  
Machine Learning Approach

Background: Phenotyping is an automated technique that can be used to distinguish patients based on electronic health records. To improve the quality of medical care and advance type 2 diabetes mellitus (T2DM) research, the demand for T2DM phenotyping has been increasing. Some existing phenotyping algorithms are not sufficiently accurate for screening or identifying clinical research subjects. Objective: We propose a practical phenotyping framework using both expert knowledge and a machine learning approach to develop 2 phenotyping algorithms: one is for screening; the other is for identifying research subjects. Methods: We employ expert knowledge as rules to exclude obvious control patients and machine learning to increase accuracy for complicated patients. We developed phenotyping algorithms on the basis of our framework and performed binary classification to determine whether a patient has T2DM. To facilitate development of practical phenotyping algorithms, this study introduces new evaluation metrics: area under the precision-sensitivity curve (AUPS) with a high sensitivity and AUPS with a high positive predictive value. Results: The proposed phenotyping algorithms based on our framework show higher performance than baseline algorithms. Our proposed framework can be used to develop 2 types of phenotyping algorithms depending on the tuning approach: one for screening, the other for identifying research subjects. Conclusions: We develop a novel phenotyping framework that can be easily implemented on the basis of proper evaluation metrics, which are in accordance with users’ objectives. The phenotyping algorithms based on our framework are useful for extraction of T2DM patients in retrospective studies.

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