Logic and Foundations Commons^™

(R2127) On 2-Absorbing Hesitant Primary Fuzzy Ideals Of Rings, B. Anitha, M. Vidhya

Applications and Applied Mathematics: An International Journal (AAM)

By presenting 2-absorbing hesitant primary fuzzy ideals, we begin the investigation of a generalisation of hesitant primary fuzzy ideals (HPRFI) in rings in this research. The concepts of a weakly completely 2-absorbing hesitant primary fuzzy ideal (WC2-AHPRFI) and a Weakly completely 2-absorbing hesitant fuzzy ideal (WC2-AHFI) are developed, and their structural features and attributes are examined. We introduce the idea of a 2-absorbing hesitant K-fuzzy ideal (2-AHK-FI), 2-absorbing hesitant K-primary fuzzy ideal (2-AHK-PRFI) and examine a few of its characteristics.

(Si15-017) Modeling Construction Project Uncertainty Using Fuzzy Inference And Nature-Inspired Metaheuristic Knowledge-Based Algorithms, M. Kapoor, B. K. Pathak, R. Kumar

Applications and Applied Mathematics: An International Journal (AAM)

Construction projects are influenced by various uncertain factors, including supervisory knowledge, labor expertise, and weather conditions. These uncertain factors have linguistic properties that are challenging to quantify with the help of traditional set theory. To address this, the study applies fuzzy inference systems, specifically the Mamdani fuzzy inference system, to model and evaluate the impact of these uncertainties on construction projects. This fuzzy inference system provides a more nuanced understanding of these factors compared to traditional set theory methods. Experimental results indicate that uncertainties significantly impact construction projects. These findings establish a valuable framework for developing adaptive strategies, enhancing project …

(Si15-067) Ahp And Moora Decision Making Methods On Bipolar Fuzzy Sets, S. Anita Shanthi, R. Preethi

Applications and Applied Mathematics: An International Journal (AAM)

Decision making, in the present contemporary world, has been inherently complicated. Nowadays, the major challenge is the selection of an appropriate option. The arrival of numerous brands and models makes a purchase challenging. Hence, in this paper, four different models of the same branded laptops are considered, for the selection of an appropriate option, using the Analytic Hierarchy Process (AHP) and Multi-Objective Optimization on the basis of Ratio Analysis (MOORA), with bipolar fuzzy sets, which help decision makers arrive at the most logical choice based on their preferences. The bipolar fuzzy Analytic Hierarchy Process efficaciously supports decision making in cases …

A Dualistic Interpretation Of Mathematical Creation Through Art And Argumentation, Sofia Almpani, Petros Stefaneas, Mihir Chakraborty

Journal of Humanistic Mathematics

Creativity, informal reasoning and dynamic exchange of ideas form the pulsating heart of mathematical creation. In this approach, the concept of a mathematical object surpasses conventional boundaries of formal presentation, as they also encompass the intention to prove, significant creative stages within the proving, and the overall experience of prover's journey, which may involve arguments, debates, discovery insights, aesthetic visualizations, and narrative elements. In this paper we present two conceptual frameworks, namely Argumentation-based Proof-Events Calculus (APEC) and Mathematical RUPAs, in order to provide distinct yet interconnected perspectives on informal thinking, knowledge creation, and proving in mathematics. Following the two perspectives, …

Logic Enriched Over A Quantale, Alexander Kurz

Engineering Faculty Articles and Research

Many-valued logics have a long history in mathematical logic as well as in applications to the semantics of programming languages and to engineering more generally. Typically these logics are rich with features motivated by the particular applications they stem from. In his 1973 article "Metric Spaces, Generalized Logic, and Closed Categories", Lawvere argued that any quantale Ω gives rise to a generalized Ω-valued logic that has as its models the categories enriched over the quantale. This suggests developing a uniform framework for many-valued logics parameterized in a quantale. In this talk we will review some previous and ongoing work in …

Computability Theoretic Aspects Of Profinite Groups And Models Of Presburger Arithmetic, Jason Block

Dissertations, Theses, and Capstone Projects

Profinite groups, which are exactly the Galois groups, are all either finite or uncountable. However, all second countable profinite groups can be presented as the set of paths through a countable tree. We use these tree presentations to find upper bounds on the complexity of the existential theories of profinite groups, as well as to prove sharpness for these bounds. These complexity results enable us to distinguish the class of profinite groups that are isomorphic to a direct product of finite groups, for which we find an upper bound on the complexity of the entire first order theory. Additionally, given …

A Realizability Approach To Constructing Higher Types Via Classifiers, Benjamin Carrick Logsdon

Dartmouth College Ph.D Dissertations

We construct an interpretation of higher types into Peano arithmetic, showing in particular that every model of PA is a model of higher types. This is a reversal of Gödel’s Dialectica construction. We also define the classifier degrees, a degree structure which subsumes the Turing degrees, the enumeration degrees, and the many-one degrees. The classifier degrees boast a rich structure and many well-behaved operations.

Logic's Modern British Up-Enders, Defenders, And Extenders: Whately's Revitalization Of Logic, Calvin Jongsma

Faculty Work Comprehensive List

Logic developed dramatically during the last half of the nineteenth century. The baseline for these transformations in Great Britain was the revival of logic by Richard Whately around 1825. Whately successfully defended syllogistic logic as the science of valid reasoning against potent seventeenth and eighteenth-century detractors—Bacon, Locke, Reid, Campbell, Stewart, and others. In so doing, he made logic an intellectually respectable field of investigation for the next generation of logicians to explore and extend. This included John Stuart Mill (inductive logic), Augustus De Morgan (logic of relations), and George Boole (algebraic logic; propositional logic).

Dedekind-Macneille And Related Completions: Subfitness, Regularity, And Booleanness, G. Bezhanishvili, F. Dashiell Jr., M. A. Moshier, Joanne Walters-Wayland

Mathematics, Physics, and Computer Science Faculty Articles and Research

Completions play an important rôle for studying structure by supplying elements that in some sense “ought to be.” Among these, the Dedekind-MacNeille completion is of particular importance. In 1968 Janowitz provided necessary and sufficient conditions for it to be subfit or Boolean. Another natural separation axiom connected to these is regularity. We explore similar characterizations of when closely related completions are subfit, regular, or Boolean. We are mainly interested in the Bruns-Lakser, ideal, and canonical completions, which (unlike the Dedekind-MacNeille completion) satisfy stronger forms of distributivity. The first two are widely used in pointfree topology, while the latter is of …

Belonging, Lawrence M. Lesser

Journal of Humanistic Mathematics

No abstract provided.

The Making Of Mathematics: An Interview With Carlo Cellucci, Marshall Gordon

Journal of Humanistic Mathematics

Carlo Cellucci is professor emeritus of the Sapienza University of Rome, and has written books on logic, mathematics, and philosophy. In the following interview conducted via back-and-forth email correspondence, he discusses his 2022 book, The Making of Mathematics: Heuristic Philosophy of Mathematics [3], which presents a new paradigm for thinking about, doing, and teaching mathematics.

Modeling Deductive Inference: A Historico-Philosophical Introduction To First-Order Logic, David J. Buller

Faculty Books & Book Chapters

This book is a companion text for lectures on first-order logic and its elementary metatheory (used in Intermediate Logic at Northern Illinois University). It covers the basic concepts of set theory necessary for a mathematical development of first-order logic; develops a formal language of first-order logic; presents a classical Tarskian semantics for the language and the “semantic” conception of logical consequence; presents a Gentzenian proof system and the “syntactic” conception of logical consequence; develops a partial decision procedure for logical consequence in the language; demonstrates applications of the formal system to modeling deductive inference expressed in natural language; and extends …

Local-Neutrosophic Logic And Local-Neutrosophic Sets: Incorporating Locality With Applications, Florentin Smarandache, Takaaki Fujita

Branch Mathematics and Statistics Faculty and Staff Publications

The study of uncertainty has been a significant area of research, with concepts such as fuzzy sets [87], fuzzy graphs [51], and neutrosophic sets [58] receiving extensive attention. In Neutrosophic Logic, indeterminacy often arises from real-world complexities. This paper explores the concept of locality as a key factor in determining indeterminacy, building upon the framework introduced by F. Smarandache in [73]. Locality refers to processes constrained within a specific region, where an object or system is directly influenced by its immediate surroundings. In contrast, nonlocality involves effects that transcend spatial or temporal boundaries, where changes in one location have direct …

Mathematics And Determinism: Chaos, Quantum Mechanics, And The Limits Of Predictive Structure, Jackson T. Salumbides

CMC Senior Theses

This thesis examines the relationship between mathematics and determinism by analyzing how chaos theory, quantum mechanics, and formal mathematical limits challenge traditional conceptions of predictability and causal structure. Chaos theory shows that deterministic systems can exhibit practical unpredictability due to sensitivity to initial conditions. Quantum mechanics introduces probabilistic outcomes that complicate deterministic interpretation, though alternative frameworks such as Bohmian mechanics and superdeterminism attempt to restore determinism at conceptual cost. Additionally, results from mathematical logic, including Gödel’s incompleteness theorems and Turing’s undecidability, demonstrate intrinsic limitations on what can be deduced or computed, even in fully deterministic systems. By synthesizing these areas, …

Significado Neutrosófico: Partes Comunes De Cosas Poco Comunes Y Partes Poco Comunes De Cosas Comunes, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Esta investigación explora la Neutrosofía, un enfoque filosófico que se centra en la identificación de elementos comunes entre conceptos opuestos y en el análisis de las diferencias entre conceptos semejantes. En este contexto, se estudian las Partes Comunes a Cosas No Comunes, que se manifiestan cuando elementos como y < antiA > comparten aspectos en su intersección, y las Partes No Comunes a Cosas Comunes, donde conceptos iguales como y difieren al exhibir elementos únicos. Este análisis permite comprender mejor la neutralidad e indeterminación representada por < neutA > y < neutB >, situados entre sus respectivos opuestos. La investigación abarca diversas áreas como la Dialéctica, el Yin …

Studies On Convexity Of Dnf Formulae, Josue A. Ruiz

Electronic Theses & Dissertations (2024 - present)

In this dissertation, we investigate the problem of determining whether a Boolean formula given in disjunctive normal form (DNF) is convex. Although Boolean formulas have various applications, our research focuses on the practical application for rule-based access control policies, where policies are often expressed as a set of Boolean rules. Understanding the structural properties of such formulas is crucial for determining whether a policy can be efficiently represented within a specific access control model.

The main contribution of this research is the conception and analysis of convexity derived from the “gap problem.” In this context, convexity is characterized by the …