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2013

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Full-Text Articles in Physical Sciences and Mathematics

Ancestor Worship In The Logic Of Games. How Foundational Were Aristotle's Contributions?, John Woods Dec 2013

Ancestor Worship In The Logic Of Games. How Foundational Were Aristotle's Contributions?, John Woods

Baltic International Yearbook of Cognition, Logic and Communication

Notwithstanding their technical virtuosity and growing presence in mainstream thinking, game theoretic logics have attracted a sceptical question: "Granted that logic can be done game theoretically, but what would justify the idea that this is the preferred way to do it?'' A recent suggestion is that at least part of the desired support might be found in the Greek dialectical writings. If so, perhaps we could say that those works possess a kind of foundational significance. The relation of being foundational for is interesting in its own right. In this paper, I explore its ancient applicability to relevant, paraconsistent and …

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Games And Logic, Gabriel Sandu Dec 2013

Games And Logic, Gabriel Sandu

Baltic International Yearbook of Cognition, Logic and Communication

The idea behind these games is to obtain an alternative characterization of logical notions cherished by logicians such as truth in a model, or provability (in a formal system). We offer a quick survey of Hintikka's evaluation games, which offer an alternative notion of truth in a model for first-order langauges. These are win-lose, extensive games of perfect information. We then consider a variation of these games, IF games, which are win-lose extensive games of imperfect information. Both games presuppose that the meaning of the basic vocabulary of the language is given. To give an account of the linguistic conventions …

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Constructive Type Theory And The Dialogical Approach To Meaning, Shahid Rahman, Nicolas Clerbout Dec 2013

Constructive Type Theory And The Dialogical Approach To Meaning, Shahid Rahman, Nicolas Clerbout

Baltic International Yearbook of Cognition, Logic and Communication

In its origins Dialogical logic constituted one part of a new movement called the Erlangen School or Erlangen Constructivism. Its goal was to provide a new start to a general theory of language and of science. According to the Erlangen-School, language is not just a fact that we discover, but a human cultural accomplishment whose construction reason can and should control. The resulting project of intentionally constructing a scientific language was called the Orthosprache-project. Unfortunately, the Orthosprache-project was not further developed and seemed to fade away. It is possible that one of the reasons for this fading away is that …

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Ludics, Dialogue And Inferentialism, Alain Lecomte Dec 2013

Ludics, Dialogue And Inferentialism, Alain Lecomte

Baltic International Yearbook of Cognition, Logic and Communication

In this paper, we try to show that Ludics, a (pre-)logical framework invented by J-Y. Girard, enables us to rethink some of the relationships between Philosophy, Semantics and Pragmatics. In particular, Ludics helps to shed light on the nature of dialogue and to articulate features of Brandom's inferentialism.

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Argumentation And Inference: A Unified Approach, Christophe Fouqueré, Myriam Quatrini Dec 2013

Argumentation And Inference: A Unified Approach, Christophe Fouqueré, Myriam Quatrini

Baltic International Yearbook of Cognition, Logic and Communication

We propose in this paper to use Ludics as a unified framework for the analysis of dialogue and the reasoning system. Not only is Ludics a logical theory, but it may also be built by means of concepts of game theory. We first present the main concepts of Ludics. A design is an abstraction and a generalization of the concept of proof. Interaction between designs is equivalent to cut elimination or modus ponens in logical theories. It appears to be a natural means for representing dialogues and also for reasoning. A design is a set of sequences of alternate actions …

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Antilogic, Benoît Castelnérac, Mathieu Marion Dec 2013

Antilogic, Benoît Castelnérac, Mathieu Marion

Baltic International Yearbook of Cognition, Logic and Communication

This paper is an interim report of joint work begun in (Castelnérac & Marion 2009) on dialectic from Parmenides to Aristotle. In the first part we present rules for dialectical games, understood as a specific form of antilogikê developed by philosophers, and explain some of the key concepts of these dialectical games in terms of ideas from game semantics. In the games we describe, for a thesis A asserted by the answerer, a questioner must elicit the answerer’s assent to further assertions B1, B2,…, Bn, which form a scoreboard from which the questioner seeks …

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Trust And Risk In Games Of Partial Information, Robin Clark Dec 2013

Trust And Risk In Games Of Partial Information, Robin Clark

Baltic International Yearbook of Cognition, Logic and Communication

Games of partial information have been used to explicate Gricean implicature; their solution concept has been murky, however. In this paper, I will develop a simple solution concept that can be used to solve games of partial information, depending on the players' mutual trust and tolerance for risk. In addition, I will develop an approach to non-conventional quantity implicatures that relies on "face" (Goffman (1967), Brown and Levinson (1987)).

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A New Approach To The Numerical Solution Of Fractional Order Optimal Control Problems, T. Akbarian, M. Keyanpour Dec 2013

A New Approach To The Numerical Solution Of Fractional Order Optimal Control Problems, T. Akbarian, M. Keyanpour

Applications and Applied Mathematics: An International Journal (AAM)

In this article, a new numerical method is proposed for solving a class of fractional order optimal control problems. The fractional derivative is considered in the Caputo sense. This approach is based on a combination of the perturbation homotopy and parameterization methods. The control function u(t) is approximated by polynomial functions with unknown coefficients. This method converts the fractional order optimal control problem to an optimization problem. Numerical results are included to demonstrate the validity and applicability of the method.

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On The Exact Distribution Of The Maximum Of The Exponential Of The Generalized Normal-Inverse Gaussian Process With Respect To A Martingale Measure, Roman V Ivanov Dec 2013

On The Exact Distribution Of The Maximum Of The Exponential Of The Generalized Normal-Inverse Gaussian Process With Respect To A Martingale Measure, Roman V Ivanov

Communications on Stochastic Analysis

No abstract provided.

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Local Time Of A Multifractional Gaussian Process, Aissa Sghir Dec 2013

Local Time Of A Multifractional Gaussian Process, Aissa Sghir

Communications on Stochastic Analysis

No abstract provided.

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Generalization Of The Anticipative Girsanov Theorem, Hui-Hsiung Kuo, Yun Peng, Benedykt Szozda Dec 2013

Generalization Of The Anticipative Girsanov Theorem, Hui-Hsiung Kuo, Yun Peng, Benedykt Szozda

Communications on Stochastic Analysis

No abstract provided.

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Vertical Martingales, Stochastic Calculus And Harmonic Sections, Simão N Stelmastchuk Dec 2013

Vertical Martingales, Stochastic Calculus And Harmonic Sections, Simão N Stelmastchuk

Communications on Stochastic Analysis

No abstract provided.

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Analytically Weak Solutions To Linear Spdes With Unbounded Time-Dependent Differential Operators And An Application, Benedict Baur, Martin Grothaus, Thanh Tan Mai Dec 2013

Analytically Weak Solutions To Linear Spdes With Unbounded Time-Dependent Differential Operators And An Application, Benedict Baur, Martin Grothaus, Thanh Tan Mai

Communications on Stochastic Analysis

No abstract provided.

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Mathematical Model Of Heavy Diffusion Particles System With Drift, Vitalii Konarovskyi Dec 2013

Mathematical Model Of Heavy Diffusion Particles System With Drift, Vitalii Konarovskyi

Communications on Stochastic Analysis

No abstract provided.

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A New Type Of Reflected Backward Doubly Stochastic Differential Equations, Auguste Aman, Yong Ren Dec 2013

A New Type Of Reflected Backward Doubly Stochastic Differential Equations, Auguste Aman, Yong Ren

Communications on Stochastic Analysis

No abstract provided.

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Reducibility Of Eulerian Graphs And Digraphs, Akram B. Attar Dec 2013

Reducibility Of Eulerian Graphs And Digraphs, Akram B. Attar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper the concept of reducibility in graph theory is discussed, and the deletable vertex (edge) in graph (digraph) is defined. The class of graphs (digraphs) ℛ is called vertex (edge) reducible if for any G∈ ℛ either ℛ is the trivial graph (null graph) or it contains a vertex (edge) v such that G-v∈ ℛ. We introduce some classes of graphs (digraphs) which are reducible and others which are not. The vertex reducibility and edge reducibility of Eulerian graphs and Eulerian digraphs have also been studied.

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Certain Fractional Integral Operators And The Generalized Incomplete Hypergeometric Functions, H. M. Srivastava, Praveen Agarwal Dec 2013

Certain Fractional Integral Operators And The Generalized Incomplete Hypergeometric Functions, H. M. Srivastava, Praveen Agarwal

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we apply a certain general pair of operators of fractional integration involving Appell’s function F3 in their kernel to the generalized incomplete hypergeometric functions pΓq[z] and pɣq [z], which were introduced and studied systematically by Srivastava et al. in the year 2012. Some interesting special cases and consequences of our main results are also considered.

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Relation Between Hilbert Algebras And Be–Algebras, A. Rezaei, A. B. Saeid, R. A. Borzooei Dec 2013

Relation Between Hilbert Algebras And Be–Algebras, A. Rezaei, A. B. Saeid, R. A. Borzooei

Applications and Applied Mathematics: An International Journal (AAM)

Hilbert algebras are introduced for investigations in intuitionistic and other non - classical logics and BE -algebra is a generalization of dual BCK -algebra. In this paper, we investigate the relationship between Hilbert algebras and BE -algebras. In fact, we show that a commutative implicative BE -algebra is equivalent to the commutative self distributive BE -algebra, therefore Hilbert algebras and commutative self distributive BE -algebras are equivalent.

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Generalized Fractional Integral Of The Product Of Two Aleph-Functions, R. K. Saxena, J. Ram, D. Kumar Dec 2013

Generalized Fractional Integral Of The Product Of Two Aleph-Functions, R. K. Saxena, J. Ram, D. Kumar

Applications and Applied Mathematics: An International Journal (AAM)

This paper is devoted to the study and develops the generalized fractional integral operators for a new special function, which is called Aleph-function. The considered generalized fractional integration operators contain the Appell hypergeometric function F3 as a kernel. We establish two results of the product of two Aleph-functions involving Saigo-Maeda operators. On account of the general nature of the Saigo-Maeda operators and the Aleph-function, some results involving Saigo, Riemann-Liouville and Erdélyi-Kober integral operators are obtained as special cases of the main result.

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Using A Pedagogical Content Knowledge Assessment To Inform A Middle Grades Mathematics Teacher Preparation Program, Woong Lim, Paula Guerra Oct 2013

Using A Pedagogical Content Knowledge Assessment To Inform A Middle Grades Mathematics Teacher Preparation Program, Woong Lim, Paula Guerra

Georgia Educational Researcher

This study provided a springboard for teacher preparation evaluation studies by examining what content and pedagogical content knowledge mathematics pre-service teachers demonstrated in the 4 – 8 mathematics teacher preparation program at an urban research university. Twenty nine pre-service students participated in an assessment called Diagnostic Mathematics Assessments for Middle School Teachers. The study found that pre-service teachers displayed the highest scores for Memorized/Factual Knowledge, followed by Conceptual Understanding, Reasoning/Problem Solving, and Pedagogical Content Knowledge. Pre-service teachers had higher Memorized/Factual Knowledge than Pedagogical Content Knowledge. The pre-service teachers’ overall content knowledge was not strong, and the two lowest-performing content knowledge …

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A Clark-Ocone Type Formula Under Change Of Measure For Lévy Processes With L^2-Lévy Measure, Ryoichi Suzuki Sep 2013

A Clark-Ocone Type Formula Under Change Of Measure For Lévy Processes With L^2-Lévy Measure, Ryoichi Suzuki

Communications on Stochastic Analysis

No abstract provided.

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Positive Harris Recurrence Of The Cir Process And Its Applications, Peng Jin, Vidyadhar Mandrekar, Barbara Rüdiger, Chiraz Trabelsi Sep 2013

Positive Harris Recurrence Of The Cir Process And Its Applications, Peng Jin, Vidyadhar Mandrekar, Barbara Rüdiger, Chiraz Trabelsi

Communications on Stochastic Analysis

No abstract provided.

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Identities And Inequalities For Cdo Tranche Sensitivities, Claas Becker, Ambar N Sengupta Sep 2013

Identities And Inequalities For Cdo Tranche Sensitivities, Claas Becker, Ambar N Sengupta

Communications on Stochastic Analysis

No abstract provided.

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Stein's Method For Brownian Approximations, L Coutin, L Decreusefond Sep 2013

Stein's Method For Brownian Approximations, L Coutin, L Decreusefond

Communications on Stochastic Analysis

No abstract provided.

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The Generalized Sub-Fractional Brownian Motion, Aissa Sghir Sep 2013

The Generalized Sub-Fractional Brownian Motion, Aissa Sghir

Communications on Stochastic Analysis

No abstract provided.

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A Bochner-Type Representation Of Positive Definite Mappings On The Dual Of A Compact Group, Herbert Heyer Sep 2013

A Bochner-Type Representation Of Positive Definite Mappings On The Dual Of A Compact Group, Herbert Heyer

Communications on Stochastic Analysis

No abstract provided.

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Itô Formula And Girsanov Theorem For Anticipating Stochastic Integrals, Hui-Hsiung Kuo, Yun Peng, Benedykt Szozda Sep 2013

Itô Formula And Girsanov Theorem For Anticipating Stochastic Integrals, Hui-Hsiung Kuo, Yun Peng, Benedykt Szozda

Communications on Stochastic Analysis

No abstract provided.

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On Optimal Proportional Reinsurance And Investment In A Partial Markovian Regime-Switching Economy, Xin Zhang Sep 2013

On Optimal Proportional Reinsurance And Investment In A Partial Markovian Regime-Switching Economy, Xin Zhang

Communications on Stochastic Analysis

No abstract provided.

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Scitech Book News Reviews, Susan Fingerman Aug 2013

Scitech Book News Reviews, Susan Fingerman

Sci-Tech News

No abstract provided.

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Harmonics In The Library, Charles Coppin Jul 2013

Harmonics In The Library, Charles Coppin

Journal of Humanistic Mathematics

Students of traditional calculus courses can discover significant mathematics original to themselves, especially if these courses are taught in a way that allows shafts of mathematical light to shine through. We tell a story of such an incident in the form of a dialogue between two fictional students. Our students, on their own, discover (or rediscover) a well-known problem based on the harmonic series. We believe opportunities for such discoveries are greater if students have had some experience with inquiry-based learning prior to entering a traditional course. More broadly, we aim to demonstrate what can occur when students feel no …

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