Logic and Foundations Commons^™

Canonical Extensions Of Quantale Enriched Categories, Alexander Kurz

MPP Research Seminar

No abstract provided.

Formalization Of A Security Framework Design For A Health Prescription Assistant In An Internet Of Things System, Thomas Rolando Mellema

Electronic Theses and Dissertations

Security system design flaws will create greater risks and repercussions as the systems being secured further integrate into our daily life. One such application example is incorporating the powerful potential of the concept of the Internet of Things (IoT) into software services engineered for improving the practices of monitoring and prescribing effective healthcare to patients. A study was performed in this application area in order to specify a security system design for a Health Prescription Assistant (HPA) that operated with medical IoT (mIoT) devices in a healthcare environment. Although the efficiency of this system was measured, little was presented to …

(R2082) Two New Operations And Extended Modal Operators On Bipolar Pythagorean Fuzzy Matrices, S. Sriram, K. Sivaranjani

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, two novel binary operations concerning bipolar Pythagorean fuzzy matrices are delineated. Several algebraic properties, such as commutativity and associativity, are explored. Additionally, extended modal operators for Bipolar Pythagorean fuzzy matrices are introduced. Subsequently, these methodologies are applied to a decision-making scenario wherein a scoring matrix is formulated and alternatives are ranked according to their cumulative score values.

Towards Erasing The Distinction Between The Computational And Syntactic Accounts Of Scientific Theories, Timothy Luft

Theses

One of the main goals of philosophy of science is to give a proper account of scientific theories and their structure. One way that accounts of the structure of scientific theories can be distinguished is by the mathematical or logical structures that they involve. For instance, syntactic accounts of scientific theories hold that theories are axioms in a logical framework, whereas semantic accounts are more liberal in the range of mathematical and logical structures they take as pertinent to the structure of scientific theories. Paul Thagard (1988) offers a computational account of scientific theories, which holds that theories are complex …

Breve Introducción A Los Conjuntos Y A La Lógica Neutrosófica Estándar Y No Estándar, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Se recuerdan las definiciones de Conjunto Neutrosófico de Valor Único (SVNS), Conjunto Neutrosófico de Valor Intervalo (IVNS), Conjunto Neutrosófico de Valor Subconjunto (SVNS) y, respectivamente, Conjunto Neutrosófico No Estándar [Con Valor Único ( SVNS NoS ), Con Valor Intervalo ( IVNS NoS ) y Con Valor Subconjunto ( SVNS NoS )], junto con sus operadores. De manera similar, para Conjunto Neutrosófico Estándar y No Estándar.

Introduction To Upside-Down Logic: Its Deep Relation To Neutrosophic Logic And Applications, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In the study of uncertainty, concepts such as fuzzy sets [113], fuzzy graphs [79], and neutrosophic sets [88] have been extensively investigated. This paper focuses on a novel logical framework known as Upside-Down Logic, which systematically transforms truths into falsehoods and vice versa by altering contexts, meanings, or perspectives. The concept was first introduced by F. Smarandache in [99]. To contribute to the growing interest in this area, this paper presents a mathematical definition of Upside-Down Logic, supported by illustrative examples, including applications related to the Japanese language. Additionally, it introduces and explores Contextual Upside-Down Logic, an advanced extension that …

New Trends In Neutrosophic Theories And Applications, Volume Iii, Florentin Smarandache, Surapati Pramanik

Branch Mathematics and Statistics Faculty and Staff Publications

The field of neutrosophic set theory and its applications has been rapidly expanding, particularly since the introduction of the journal "Neutrosophic Sets and Systems." New theories, techniques, and algorithms are being developed at a very high rate. One of the most notable trends in neutrosophic theory is its hybridization with other set theories such as rough set theory, bipolar set theory, soft set theory, hesitant fuzzy set theory, and more. Various hybrid structures like rough neutrosophic sets, neutrosophic soft set, single valued neutrosophic hesitant fuzzy sets, among others, have been proposed in a short period. Neutrosophic sets have proven to …

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen

Theses and Dissertations (Comprehensive)

The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Many-Valued Coalgebraic Logic: From Boolean Algebras To Primal Varieties, Alexander Kurz, Wolfgang Poiger

Engineering Faculty Articles and Research

We study many-valued coalgebraic logics with primal algebras of truth-degrees. We describe a way to lift algebraic semantics of classical coalgebraic logics, given by an endofunctor on the variety of Boolean algebras, to this many-valued setting, and we show that many important properties of the original logic are inherited by its lifting. Then, we deal with the problem of obtaining a concrete axiomatic presentation of the variety of algebras for this lifted logic, given that we know one for the original one. We solve this problem for a class of presentations which behaves well with respect to a lattice structure …

Soundness And Completeness Results For The Logic Of Evidence Aggregation And Its Probability Semantics, Eoin Moore

Dissertations, Theses, and Capstone Projects

The Logic of Evidence Aggregation (LEA), introduced in 2020, offers a solution to the problem of evidence aggregation, but LEA is not complete with respect to the intended probability semantics. This left open the tasks to find sound and complete semantics for LEA and a proper axiomatization for probability semantics. In this thesis we do both. We also develop the proof theory for some LEA-related logics and show surprising connections between LEA-related logics and Lax Logic.

One Formula For Non-Prime Numbers: Motivations And Characteristics, Mahmoud Mansour, Kamal Hassan Prof.

Basic Science Engineering

Primes are essential for computer encryption and cryptography, as they are fundamental units of whole numbers and are of the highest importance due to their mathematical qualities. However, identifying a pattern of primes is not easy. Thinking in a different way may get benefits, by considering the opposite side of the problem which means focusing on non-prime numbers. Recently, researchers introduced, the pattern of non-primes in two maximal sets while in this paper, non-primes are presented in one formula. Getting one-way formula for non-primes may pave the way for further applications based on the idea of primes.

Platonism, De Re, And (Philosophy Of) Mathematical Practice, Marco Panza

MPP Published Research

The chapter advances a reformulation of the classical problem of the nature of mathematical objects (if any), here called “Plato’s problem,” in line with the program of a philosophy of mathematical practice. It then provides a sketch of a platonist solution, following the same perspective. This solution disregards as nonsensical the question of the existence of abstract, and specifically mathematical, objects, by rather focusing on the modalities of our access to them: objects (in general, both concrete and abstract) are regarded as individual contents that we have (or can have) a de re epistemic access to. The question of the …

(R1986) Neutrosophic Soft Contra E-Continuous Maps, Contra E-Irresolute Maps And Application Using Distance Measure, P. Revathi, K. Chitirakala, A. Vadivel

Applications and Applied Mathematics: An International Journal (AAM)

We introduce and investigate neutrosophic soft contra e-continuous maps and contra e-irresolute maps in neutrosophic soft topological spaces with examples. Also, neutrosophic soft contra econtinuous maps are compared with neutrosophic soft continuous maps, δ-continuous maps, δ- semi continuous maps, δ-pre continuous maps and e∗ continuous maps in neutrosophic soft topological spaces. We derive some useful results and properties related to them. An application in decision making problem using distance measure is given. An example of a candidate selection from a company interview is formulated as neutrosophic soft model problem and the hamming distance measure is applied to calculate the distance …

(R1957) Some Types Of Continuous Function Via N-Neutrosophic Crisp Topological Spaces, A. Vadivel, C. John Sundar

Applications and Applied Mathematics: An International Journal (AAM)

The aim of this article is to introduced a new type of continuous functions such as N-neutrosophic crisp gamma continuous and weakly N-neutrosophic crisp gamma continuous functions in a N-neutrosophic crisp topological space and also discuss a relation between them in a N-neutrosophic crisp topological spaces. We also investigate some of their properties in N-neutrosophic crisp gamma continuous function via N-neutrosophic crisp topological spaces. Further, a contra part of continuity called N-neutrosophic crisp gamma-contra continuous map in a N-neutrosophic crisp topology is also initiated. Finally, an application based on neutrosophic score function of medical diagnosis is examined with graphical representation.

(R1997) Distance Measures Of Complex Fermatean Fuzzy Number And Their Application To Multi-Criteria Decision-Making Problem, V. Chinnadurai, S. Thayalan, A. Bobin

Applications and Applied Mathematics: An International Journal (AAM)

Multi-criteria decision-making (MCDM) is the most widely used decision-making method to solve many complex problems. However, classical MCDM approaches tend to make decisions when the parameters are imprecise or uncertain. The concept of a complex fuzzy set is new in the field of fuzzy set theory. It is a set that can collect and interpret the membership grades from the unit circle in a plane instead of the interval [0,1]. CFS cannot deal with membership and non-membership grades, while complex intuitionistic fuzzy set and complex Pythagorean fuzzy set works only for a limited range of values. The concept of a …

(R1965) Some More Properties On Generalized Double Fuzzy Z Alpha Open Sets, K. Jayapandian, A. Saivarajan, O. Uma Maheswari, J. Sathiyaraj

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a new class of sets termed as double fuzzy generalized Z alpha closed sets and double fuzzy generalized Z alpha open sets are introduced with the help of double fuzzy Z alpha open and double fuzzy Z alpha closed sets, respectively. Using these sets double fuzzy generalized Z alpha border, double fuzzy generalized Z alpha exterior and double fuzzy generalized Z alpha frontier of a fuzzy set in double fuzzy topological spaces are introduced. Also, the topological properties and characterizations of these sets and operators are studied. Furthermore, suitable examples have been provided to illustrate the theory.

Deep Learning Recommendations For The Acl2 Interactive Theorem Prover, Robert K. Thompson, Robert K. Thompson

Master's Theses

Due to the difficulty of obtaining formal proofs, there is increasing interest in partially or completely automating proof search in interactive theorem provers. Despite being a theorem prover with an active community and plentiful corpus of 170,000+ theorems, no deep learning system currently exists to help automate theorem proving in ACL2. We have developed a machine learning system that generates recommendations to automatically complete proofs. We show that our system benefits from the copy mechanism introduced in the context of program repair. We make our system directly accessible from within ACL2 and use this interface to evaluate our system in …

Reverse Mathematics Of Ramsey's Theorem, Nikolay Maslov

Electronic Theses, Projects, and Dissertations

Reverse mathematics aims to determine which set theoretic axioms are necessary to prove the theorems outside of the set theory. Since the 1970’s, there has been an interest in applying reverse mathematics to study combinatorial principles like Ramsey’s theorem to analyze its strength and relation to other theorems. Ramsey’s theorem for pairs states that for any infinite complete graph with a finite coloring on edges, there is an infinite subset of nodes all of whose edges share one color. In this thesis, we introduce the fundamental terminology and techniques for reverse mathematics, and demonstrate their use in proving Kőnig's lemma …

Generations Of Reason: A Family’S Search For Meaning In Post-Newtonian England (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: Generations of Reason: A Family's Search for Meaning in Post-Newtonian England by Joan L. Richards. New Haven, CT: Yale University Press, 2021. 456 pp. ISBN: 9780300255492.