Mathematics Commons^™

Pruebas Entimemáticas Y Pruebas Canónicas En La Geometría Plana De Euclides, Marco Panza, Abel Lassalle Casanave

MPP Published Research

Dado que la aplicación del Postulado I.2 no es uniforme en Elementos, ¿de qué manera debería ser aplicado en la geometría plana de Euclides? Además de legitimar la pregunta misma desde la perspectiva de una filosofía de la práctica matemática, nos proponemos esbozar una perspectiva general de análisis conceptual de textos matemáticos que involucra una noción ampliada de la teoría matemática como sistema de autorizaciones o potestades y una noción de prueba que depende del auditorio.

Since the application of Postulate I.2 in the Elements is not uniform, one could wonder in what way should it be applied in Euclid’s …

Extensions Of Functors From Set To V-Cat, Adriana Balan, Alexander Kurz, Jirí Velebil

Engineering Faculty Articles and Research

We show that for a commutative quantale V every functor Set --> V-cat has an enriched left- Kan extension. As a consequence, coalgebras over Set are subsumed by coalgebras over V-cat. Moreover, one can build functors on V-cat by equipping Set-functors with a metric.

Coalgebraic Semantics Of Reflexive Economics (Dagstuhl Seminar 15042), Samson Abramsky, Alexander Kurz, Pierre Lescanne, Viktor Winschel

Engineering Faculty Articles and Research

This report documents the program and the outcomes of Dagstuhl Seminar 15042 “Coalgebraic Semantics of Reflexive Economics”.

Neutrosophic Graphs: A New Dimension To Graph Theory, Florentin Smarandache, Wb. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time have made a through study of neutrosophic graphs. This study reveals that these neutrosophic graphs give a new dimension to graph theory. The important feature of this book is it contains over 200 neutrosophic graphs to provide better understanding of this concepts. Further these graphs happen to behave in a unique way inmost cases, for even the edge colouring problem is different from the classical one. Several directions and dimensions in graph theory are obtained from this study. Finally certainly these new notions of neutrosophic graphs in general and in particular the …

Philosophy Of Mathematics: Theories And Defense, Amy E. Maffit

Williams Honors College, Honors Research Projects

In this paper I discuss six philosophical theories of mathematics including logicism, intuitionism, formalism, platonism, structuralism, and moderate realism. I also discuss problems that arise within these theories and attempts to solve them. Finally, I attempt to harmonize the best features of moderate realism and structuralism, presenting a theory that I take to best describe current mathematical practice.

Quaestiones Neutrosophicae, Florentin Smarandache, Yale Landsberg

Branch Mathematics and Statistics Faculty and Staff Publications

The following dialogue contains cuts from different non-protocolar conversations, initially not intended for publication, held by the authors by email during the beginning of 2015 – on Neutrosophy and related topics.

Many thanks to all friends and dialogue partners who payed attention to Neutrosophy and connected areas, in emails, yahoo groups, social media, letters, private discussions.

Euclid Squares On Infinite Planes, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book for the first time the authors study the new type of Euclid squares in various planes like real plane, complex plane, dual number plane, special dual like number plane and special quasi dual number plane. There are six such planes and they behave distinctly. From the study it is revealed that each type of squares behave in a different way depending on the plane. We define several types of algebraic structures on them. Such study is new, innovative and interesting. However for some types of squares; one is not in a position to define product. Further under …

Techno-Art Of Selariu Supermathematics Functions, 2nd Volume, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

An ALBUM, according to the dictionary, is defined as "notebook for storing photos, postcards, stamps, lyrics, quotes etc.", which, in other words, means gatherings of "pieces" of the same "species". Or, in the new Techno-Art of Selariu SuperMathematics Functions ALBUM (the second book of Selariu SuperMathematics Functions), one contemplates a unique COMPOSITION, INTER-, INTRA- and TRANS-DISCIPLINARY. (Capitalizing here is not a futility, but a harmony with the TRUTH.) One caveat I am indebted to do, as a consequent "reader" – over time, I received the ALBUM, chapter by chapter, pace by pace, which gave me the time to analyze / …

N-Valued Interval Neutrosophic Sets And Their Application In Medical Diagnosis, Said Broumi, Irfan Deli, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper a new concept is called n-valued interval neutrosophic sets is given. The basic operations are introduced on n-valued interval neutrosophic sets such as; union, intersection, addition, multiplication, scalar multiplication, scalar division, truthfavorite and false-favorite. Then, some distances between n-valued interval neutrosophic sets (NVINS) are proposed. Also, we propose an efficient approach for group multi-criteria decision making based on n-valued interval neutrosophic sets. An application of n-valued interval neutrosophic sets in medical diagnosis problem is given.

(T, I, F)-Neutrosophic Structures, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we introduce for the first time a new type of structures, called (T, I, F)-Neutrosophic Structures, presented from a neutrosophic logic perspective, and we show particular cases of such structures in geometry and in algebra. In any field of knowledge, each structure is composed from two parts: a space, and a set of axioms (or laws) acting (governing) on it. If the space, or at least one of its axioms (laws), has some indeterminacy, that structure is a (T, I, F)-Neutrosophic Structure.

Neutrosophic Axiomatic System, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we introduce for the first time the notions of Neutrosophic Axiom, Neutrosophic Axiomatic System, Neutrosophic Deducibility and Neutrosophic Inference, Neutrosophic Proof, Neutrosophic Tautologies, Neutrosophic Quantifiers, Neutrosophic Propositional Logic, Neutrosophic Axiomatic Space, Degree of Contradiction (Dissimilarity) of Two Neutrosophic Axioms, and Neutrosophic Model. A class of neutrosophic implications is also introduced. A comparison between these innovatory neutrosophic notions and their corresponding classical notions is made. Then, three concrete examples of neutrosophic axiomatic systems, describing the same neutrosophic geometrical model, are presented at the end of the paper.

Symbolic Neutrosophic Theory, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Symbolic (or Literal) Neutrosophic Theory is referring to the use of abstract symbols (i.e. the letters T, I, F, or their refined indexed letters T_j, I_k, F_l) in neutrosophics.

In the first chapter we extend the dialectical triad thesis-antithesis-synthesis (dynamics of A and antiA, to get a synthesis) to the neutrosophic tetrad thesis-antithesis-neutrothesis-neutrosynthesis (dynamics of A, antiA, and neutA, in order to get a neutrosynthesis).

In the second chapter we introduce the neutrosophic system and neutrosophic dynamic system. A neutrosophic system is a quasi- or –classical system, in the sense that the neutrosophic …

Special Type Of Topological Spaces Using [0, N), Florentin Smarandache, W.B Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the notion of special type of topological spaces using the interval [0, n). They are very different from the usual topological spaces. Algebraic structure using the interval [0, n) have been systemically dealt by the authors. Now using those algebraic structures in this book authors introduce the notion of special type of topological spaces. Using the super subset interval semigroup special type of super interval topological spaces are built. Several interesting results in this direction are obtained. Next six types of topological spaces using subset interval pseudo ring semiring of type …

Neutrosophic Crisp Set Theory, Florentin Smarandache, A.A. Salama

Branch Mathematics and Statistics Faculty and Staff Publications

Since the world is full of indeterminacy, the Neutrosophics found their place into contemporary research. We now introduce for the first time the notions of Neutrosophic Crisp Sets and Neutrosophic Topology on Crisp Sets. We develop the 2012 notion of Neutrosophic Topological Spaces and give many practical examples. Neutrosophic Science means development and applications of Neutrosophic Logic, Set, Measure, Integral, Probability etc., and their applications in any field. It is possible to define the neutrosophic measure and consequently the neutrosophic integral and neutrosophic probability in many ways, because there are various types of indeterminacies, depending on the problem we need …

Fuzzy Abel Grassmann Groupoids, Florentin Smarandache, Madad Khan, Tariq Aziz

Branch Mathematics and Statistics Faculty and Staff Publications

Usually the models of real world problems in almost all disciplines like engineering, medical sciences, mathematics, physics, computer science, management sciences, operations research and articial intelligence are mostly full of complexities and consist of several types of uncertainties while dealing them in several occasion. To overcome these di¢ culties of uncertainties, many theories have been developed such as rough sets theory, probability theory, fuzzy sets theory, theory of vague sets, theory of soft ideals and the theory of intuitionistic fuzzy sets, theory of neutrosophic sets, Dezert-Smarandache Theory (DSmT), etc. Zadeh introduced the degree of membership/truth (t) in 1965 and dened …

Theory Of Abel Grassmann's Groupoids, Florentin Smarandache, Madad Khan

Branch Mathematics and Statistics Faculty and Staff Publications

It is common knowledge that common models with their limited boundaries of truth and falsehood are not su¢ cient to detect the reality so there is a need to discover other systems which are able to address the daily life problems. In every branch of science problems arise which abound with uncertainties and impaction. Some of these problems are related to human life, some others are subjective while others are objective and classical methods are not su¢ cient to solve such problems because they can not handle various ambiguities involved. To overcome this problem, Zadeh [67] introduced the concept of …

Probleme De Geometrie Și Trigonometrie, Compilate Și Rezolvate, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Α-Discounting Method For Multi-Criteria Decision Making (Α-D Mcdm), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this book we introduce a new procedure called αDiscounting Method for Multi-Criteria Decision Making (α-D MCDM), which is as an alternative and extension of Saaty’s Analytical Hierarchy Process (AHP). It works for any number of preferences that can be transformed into a system of homogeneous linear equations. A degree of consistency (and implicitly a degree of inconsistency) of a decision-making problem are defined. α-D MCDM is afterwards generalized to a set of preferences that can be transformed into a system of linear and/or non-linear homogeneous and/or nonhomogeneous equations and/or inequalities. Many consistent, weak inconsistent, and strong inconsistent examples are …

255 Compiled And Solved Problems In Geometry And Trigonometry, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Readup Buildup. Thync - Instant Α-Readings, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Some Observations On Scientific Epistemology With Applications To Conflict Resolution And Constructive Controversy, Judith Puncochar, Don Faust

Other Presentations

An overview, by Judy and Don (published in 2013 in the BULLETIN OF SYMBOLIC LOGIC):

Explorationism is a perspective wherein all of our knowledge is (so far) less than certain, and naturally would come equipped with a base logic entailing machinery for representing and processing evidential knowledge. One such base logic is Evidence Logic, which strives to deal with the phenomenon of the gradational presence of both confirmatory and refutatory evidence. From this perspective, we will address questions surrounding sociological problem areas that we see as deeply infused with substantial epistemological factors. By defining a framework as any theory, …

On The Indispensable Premises Of The Indispensability Argument, Andrea Sereni, Marco Panza

MPP Published Research

We identify four different minimal versions of the indispensability argument, falling under four different varieties: an epistemic argument for semantic realism, an epistemic argument for platonism and a non-epistemic version of both. We argue that most current formulations of the argument can be reconstructed by building upon the suggested minimal versions. Part of our discussion relies on a clarification of the notion of (in)dispensability as relational in character. We then present some substantive consequences of our inquiry for the philosophical significance of the indispensability argument, the most relevant of which being that both naturalism and confirmational holism can be dispensed …

A Quasi-Classical Logic For Classical Mathematics, Henry Nikogosyan

Honors College Theses

Classical mathematics is a form of mathematics that has a large range of application; however, its application has boundaries. In this paper, I show that Sperber and Wilson’s concept of relevance can demarcate classical mathematics’ range of applicability by demarcating classical logic’s range of applicability. Furthermore, I introduce how to systematize Sperber and Wilson’s concept of relevance into a quasi-classical logic that can explain classical logic’s and classical mathematics’ range of applicability.

Distance And Similarity Measures Of Interval Neutrosophic Soft Sets, Said Broumi, Irfan Deli, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper several distance and similarity measures of interval neutrosophic soft sets are introduced. The measures are examined based on the geometric model, the set theoretic approach and the matching function. Finally, we have successfully shown an application of this similarity measure of interval neutrosophic soft sets.

New Distance And Similarity Measures Of Interval Neutrosophic Sets, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we proposed a new distance and several similarity measures between interval neutrosophic sets.

Reichenbach Fuzzy Set Of Transitivity, Samina Ashraf, Muhammad A. Javed

Applications and Applied Mathematics: An International Journal (AAM)

Fuzzy implicators are the basic ingredients of many applications. So it becomes essential to study the various features of an implicator before implementing it in any practical application. This paper discusses the properties of transitivity of a fuzzy relation on a given universe and measure of fuzzy transitivity defined in terms of the Reichenbach fuzzy implicator which is an s-implicator.

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 when …

Multi-Criteria Decision Making Based On Dsmt-Ahp, Jean Dezert, Jean Marc Tacnet, Mireille Batton-Hubert, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we present an extension of the multicriteria decision making based on the Analytic Hierarchy Process (AHP) which incorporates uncertain knowledge matrices for generating basic belief assignments (bba’s). The combination of priority vectors corresponding to bba’s related to each (sub)- criterion is performed using the Proportional Conflict Redistribution rule no. 5 proposed in Dezert-Smarandache Theory (DSmT) of plausible and paradoxical reasoning. The method presented here, called DSmT-AHP, is illustrated on very simple examples.

Euler, Reader Of Newton: Mechanics And Algebraic Analysis, Sébastien Maronne, Marco Panza

MPP Published Research

We follow two of the many paths leading from Newton’s to Euler’s scientific productions, and give an account of Euler’s role in the reception of some of Newton’s ideas, as regards two major topics: mechanics and algebraic analysis. Euler contributed to a re-appropriation of Newtonian science, though transforming it in many relevant aspects. We study this re-appropriation with respect to the mentioned topics and show that it is grounded on the development of Newton’s conceptions within a new conceptual frame also influenced by Descartes’s views sand Leibniz’s formalism.

A Proof-Theoretic Semantic Analysis Of Dynamic Epistemic Logic, Sabine Frittella, Giuseppe Greco, Alexander Kurz, Alessandra Palmigiano, Vlasta Sikimić

Engineering Faculty Articles and Research

The present paper provides an analysis of the existing proof systems for dynamic epistemic logic from the viewpoint of proof-theoretic semantics. Dynamic epistemic logic is one of the best known members of a family of logical systems which have been successfully applied to diverse scientific disciplines, but the proof theoretic treatment of which presents many difficulties. After an illustration of the proof-theoretic semantic principles most relevant to the treatment of logical connectives, we turn to illustrating the main features of display calculi, a proof-theoretic paradigm which has been successfully employed to give a proof-theoretic semantic account of modal and substructural …