Mathematics Commons™

All Articles in Mathematics

3,234 full-text articles. Page 1 of 60.

Observing, Reporting, And Deciding In Networks Of Sentences, 2014 University of Massachusetts Boston

Observing, Reporting, And Deciding In Networks Of Sentences, H. Jerome Keisler, Jeffrey M. Keisler

Jeffrey Keisler

In prior work we considered networks of agents who prove facts from their knowledge bases and report them to their neighbors in their common languages in order to help a decider verify a single sentence. In report complete networks, the signatures of the agents and the links between agents are rich enough to verify any decider's sentence that can be proved from the combined knowledge base. This paper introduces a more general setting where new observations may be added to knowledge bases and the decider must choose a sentence from a set of alternatives. We consider the question of ...

Observing, Reporting, And Deciding In Networks Of Sentences, 2014 University of Massachusetts Boston

Observing, Reporting, And Deciding In Networks Of Sentences, H. Jerome Keisler, Jeffrey M. Keisler

Management Science and Information Systems Faculty Publication Series

In prior work we considered networks of agents who prove facts from their knowledge bases and report them to their neighbors in their common languages in order to help a decider verify a single sentence. In report complete networks, the signatures of the agents and the links between agents are rich enough to verify any decider's sentence that can be proved from the combined knowledge base. This paper introduces a more general setting where new observations may be added to knowledge bases and the decider must choose a sentence from a set of alternatives. We consider the question of ...

2013 Kansas State University Libraries

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 ...

Games And Logic, 2013 Kansas State University Libraries

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 ...

Constructive Type Theory And The Dialogical Approach To Meaning, 2013 Kansas State University Libraries

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 ...

Ludics, Dialogue And Inferentialism, 2013 Kansas State University Libraries

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.

Argumentation And Inference: A Unified Approach, 2013 Kansas State University Libraries

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 ...

Antilogic, 2013 Kansas State University Libraries

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 to infer an impossibility (adunaton); we explain why the questioner must not insert any of his own assertions in the scoreboard, as well as the crucial role the Law of Non Contradiction, and why the games end with the inference to an impossibility, as opposed to the assertion of ¬A. In the second part we introduce some specific characteristics of Eleatic Antilogic as a method of enquiry. When Antilogic is used as a method of inquiry, then one must play not only the game beginning with a given thesis A, but also the ...

Trust And Risk In Games Of Partial Information, 2013 Kansas State University Libraries

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)).

Weak Covering Properties And Selection Principles, 2013 Boise State University

Weak Covering Properties And Selection Principles, L. Babinkostova, B. A. Pansera, Marion Scheepers

Mathematics Faculty Publications and Presentations

No convenient internal characterization of spaces that are productively Lindelöf is known. Perhaps the best general result known is Alsterʼs internal characterization, under the Continuum Hypothesis, of productively Lindelöf spaces which have a basis of cardinality at most 1. It turns out that topological spaces having Alsterʼs property are also productively weakly Lindelöf. The weakly Lindelöf spaces form a much larger class of spaces than the Lindelöf spaces. In many instances spaces having Alsterʼs property satisfy a seemingly stronger version of Alsterʼs property and consequently are productively X, where X is a covering property stronger than the Lindelöf property ...

The Effects Of Standards-Based Grading On Student Performance In Algebra 2, 2013 Western Kentucky University

The Effects Of Standards-Based Grading On Student Performance In Algebra 2, Rachel Beth Rosales

Dissertations

The use of standards-based grading in American public schools is increasing, offering students, parents, and teachers a new way of measuring and communicating about student achievement and performance. Parents indicate an appreciation for this method of grading, and students at the elementary grades (K-6) have improved standardized test scores in reading and math as a result of its implementation. This study seeks to determine whether standards-based grading has the same effect on students at the high school level (grades 9-12) by comparing end-of-course test scores and posttest scores of Algebra 2 students enrolled in a standards-based graded classroom with to ...

2013 University of Nebraska - Lincoln

Random Search Models Of Foraging Behavior: Theory, Simulation, And Observation., Ben C. Nolting

Dissertations, Theses, and Student Research Papers in Mathematics

Many organisms, from bacteria to primates, use stochastic movement patterns to find food. These movement patterns, known as search strategies, have recently be- come a focus of ecologists interested in identifying universal properties of optimal foraging behavior. In this dissertation, I describe three contributions to this field. First, I propose a way to extend Charnov's Marginal Value Theorem to the spatially explicit framework of stochastic search strategies. Next, I describe simulations that compare the efficiencies of sensory and memory-based composite search strategies, which involve switching between different behavioral modes. Finally, I explain a new behavioral analysis protocol for identifying ...

Ogden College Of Science & Engineering Newsletter, 2013 Western Kentucky University

Ogden College Of Science & Engineering Newsletter, Odgen College Of Science & Engineering, Western Kentucky University, Cheryl Stevens, Dean

Ogden College of Science & Engineering Publications

No abstract provided.

Leslie Matrices For Logistic Population Modeling, 2013 Western Kentucky University

Leslie Matrices For Logistic Population Modeling, Bruce Kessler

Bruce Kessler

Leslie matrices are taught as a method of modeling populations in a discrete-time fashion with more detail in the tracking of age groups within the population. Leslie matrices have limited use in the actual modeling of populations, since when the age groups are summed, it is basically equivalent to discrete-time modeling assuming exponential population growth. The logistic model of population growth is more realistic, since it takes into account a carrying capacity for the environment of the population. This talk will describe an adjustment to the Leslie matrix approach for population modeling that is both takes into account the carrying ...

An Interface-Capturing Regularization Method For Solving The Equations For Two-Fluid Mixtures, 2013 Boise State University

An Interface-Capturing Regularization Method For Solving The Equations For Two-Fluid Mixtures, Jian Du, Robert D. Guy, Aaron L. Fogelson, Grady B. Wright, James P. Keener

Mathematics Faculty Publications and Presentations

Many problems in biology involve gels which are mixtures composed of a polymer network permeated by a fluid solvent (water). The two-fluid model is a widely used approach to described gel mechanics, in which both network and solvent coexist at each point of space and their relative abundance is described by their volume fractions. Each phase is modeled as a continuum with its own velocity and constitutive law. In some biological applications, free boundaries separate regions of gel and regions of pure solvent, resulting in a degenerate network momentum equation where the network volume fraction vanishes. To overcome this difficulty ...

2013 McMaster University

Solutions Of A Two-Component Ginzburg-Landau System, Qi Gao

Open Access Dissertations and Theses

We study Ginzburg–Landau equations for a complex vector order parameter to a two-component system. We discuss the existence, uniqueness, asymptotics, monotonicity and stability of solutions by extending Alama-Bronsard-Mironescu's results in a more general case.

Immediate Expansions By Valuation Of Fields, 2013 McMaster University

Immediate Expansions By Valuation Of Fields, Jizhan Hong

Open Access Dissertations and Theses

The main subject of investigation is the so-called "immediate expansion''
phenomenon in various first-order valued-field structures over the
corresponding underlying field structures. In particular, certain "valued
o-minimal fields'', certain Henselian valued fields with non-divisible valued
groups, and certain separably closed valued fields of finite imperfection degree, are
shown to have this property.

Equivariant Gauge Theory And Four-Manifolds, 2013 McMaster University

Equivariant Gauge Theory And Four-Manifolds, Nima Anvari

Open Access Dissertations and Theses

Let $p>5$ be a prime and $X_0$ a simply-connected $4$-manifold with boundary the Poincar\'e homology sphere $\Sigma(2,3,5)$ and even negative-definite intersection form $Q_{X_0}=\text{E}_8$ . We obtain restrictions on extending a free $\bZ/p$-action on $\Sigma(2,3,5)$ to a smooth, homologically-trivial action on $X_0$ with isolated fixed points. It is shown that for $p=7$ there is no such smooth extension. As a corollary, we obtain that there does not exist a smooth, homologically-trivial $\bZ/7$-equivariant splitting of \$\#^8 S^2 \times S^2=E_8 \cup_{\Sigma(2 ...

Distribution Of Points On Spherical Objects And Applications, 2013 McMaster University

Distribution Of Points On Spherical Objects And Applications, Alessandro Selvitella, Alessandro Selvitella

Open Access Dissertations and Theses

In this thesis, we discuss some results on the distribution of points on the sphere, asymptotically when both the number of points and the dimension of the sphere tend to infinity. We then give some applications of these results to some statistical problems and especially to hypothesis testing.

Some Results On The Slice-Ribbon Conjecture, 2013 McMaster University

Some Results On The Slice-Ribbon Conjecture, Homayun Karimi

Open Access Dissertations and Theses

Slice-ribbon conjecture has been proved for some special families of knots. In this thesis, we briefly mention some of these results.