Logic and Foundations of Mathematics Commons^™

Polynomial Invariants For Classical Invariant Groups, John Diller

UNF Graduate Theses and Dissertations

The classical invariant theory of matrix groups plays a fundamental role in modern algebra and geometry, with origins in Hilbert’s Fourteenth Problem concerning the finite generation of rings of invariants. In this thesis, we study polynomial functions on spaces of matrices and investigate their invariants under natural actions of classical groups. After recalling the geometric and algebraic motivations behind Hilbert’s question, we focus on invariants for several complex Lie groups, including the general linear group GL(V), the symplectic group Sp(V), the orthogonal group O(V), and the special orthogonal group SO(V). Building on foundational work of Hermann Weyl and a modern …

Intuitionism, Justification Logic, And Doxastic Reasoning, Vincent A. Peluce

Dissertations, Theses, and Capstone Projects

In this Dissertation, we examine a handful of related themes in the philosophy of logic and mathematics. We take as a starting point the deeply philosophical, and—as we argue, deeply Kantian—views of L.E.J. Brouwer, the founder of intuitionism. We examine his famous first act of intuitionism. Therein, he put forth both a critical and a constructive idea. This critical idea involved digging a philosophical rift between what he thought of himself as doing and what he thought of his contemporaries, specifically Hilbert, as doing. He sought to completely separate mathematics from mathematical language, and thereby logic. In chapter 3, we …

Avoiding Pragmatic Oddity: A Bottom-Up Defeasible Deontic Logic, Guido Governatori, Silvano Colombo Tosatto, Antonio Rotolo

Centre for Computational Law (2022-2025)

This paper presents an extension of Defeasible Deontic Logic to deal with the Pragmatic Oddity problem. The logic applies three general principles: (i) the Pragmatic Oddity problem must be solved within a general logical treatment of contrary-to-duty (CTD) reasoning; (ii) non-monotonic methods must be adopted to handle CTD reasoning; (iii) logical models of CTD reasoning must be computationally feasible and, if possible, efficient. The proposed extension of Defeasible Deontic Logic elaborates a preliminary version of the model proposed by Governatori and Rotolo [15]. The previous solution was based on particular characteristics of the (constructive, top-down) proof theory of the logic. …

A Thesis, Or Digressions On Sculptural Practice: In Which, Concepts & Influences Thereof Are Explained, Set Forth, Catalogued, Or Divulged By Way Of Commentaries To A Poem, First Conceived By The Artist, Fed Through Chatg.P.T., And Re-Edited By The Artist, To Which Are Added, Annotated References, Impressions And Ruminations Thereof, Also Including Private Thoughts & Personal Accounts Of The Artist, Jaimie An

Masters Theses

This thesis is an exercise in, perhaps a futile, attempt to trace just some of the ideas, stories, and musings I might meander through in my process. It’s not quite a map, nor is it a neat catalogue; it is a haphazard collection of tickets and receipts from a travel abroad, carelessly tossed in a carry-on, only to be stashed upon returning home. These ideas are derived from much greater thinkers and authors than myself; I am a mere collector or a translator, if that, and not a very good one, for much is lost. I do not claim comprehensive …

Canonical Extensions Of Quantale Enriched Categories, Alexander Kurz

MPP Research Seminar

No abstract provided.

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 …

“What Line Can’T Be Measured With A Ruler?” Riddles And Concept-Formation In Mathematics And Aesthetics, William H. Brenner, Samuel J. Wheeler

Philosophy Faculty Publications

We analyze two problems in mathematics – the first (stated in our title) is extracted from Wittgenstein’s “Philosophy for Mathematicians”; the second (“What set of numbers is non-denumerable?”) is taken from Cantor. We then consider, by way of comparison, a problem in musical aesthetics concerning a Brahms variation on a theme by Haydn. Our aim is twofold: first, to bring out and elucidate the essentially riddle-like character of these problems; second, to show that the comparison with riddles does not reduce their solution to an exercise in bare subjectivity

Deontic Meta-Rules, Francesco Olivieri, Guido Governatori, Matteo Cristani, Antonino Rotolo, Abdul Sattar

Centre for Computational Law (2022-2025)

The use of meta-rules in logic, i.e., rules whose content includes other rules, has recently gained attention in the setting of non-monotonic reasoning: a first logical formalisation and efficient algorithms to compute the (meta)-extensions of such theories were proposed in Olivieri et al. (2021, Computing defeasible meta-logic. In JELIA 2021, LNCS, vol. 12678, pp. 69-84. Springer.). This work extends such a logical framework by considering the deontic aspect. The resulting logic will not just be able to model policies but also tackle well-known aspects that occur in numerous legal systems. The use of Defeasible Logic to model meta-rules in the …

Spatial Relations Between Conscious And Unconscious Thought, John Shannon Hendrix

Architecture, Art, and Historic Preservation Faculty Publications

No abstract provided.

Alternative Ontology For Ante Rem Structuralism Based On Huayan Buddhist Metaphysics, Chul Soon Hwang

CMC Senior Theses

Ante rem structuralism is a version of mathematical structuralism presented by Shapiro (1997) that asserts the existence of mathematical objects. It stands out amongst other structuralist views in that it secures a face value semantics for mathematical statements. In this paper, I propose an alternative ontology where structures are fully explained by relations. I argue that this alternative ontology avoids arguments against ante rem structuralism’s endorsement of indiscernible entities while retaining the convenience of a face value semantics for mathematical expressions.

This ontology is based on mereological nihilism and the Huayan Buddhist argument that an object can be fully described …

Reflections On Williamson On Logic And Validity, Graham Priest

Publications and Research

Over many years now, Tim Williamson and I have engaged in debates over fundamental issues concerning logic. On some things, we have disagreed strongly; on others, we have agreed.

Networking For Mid-Level Administrators In Higher Education: Increase Job Performance And Reduce Burnout, Laura Glasbrenner

All-Inclusive List of Electronic Theses and Dissertations

Mid-level administrators occupy a complex position within higher education institutions, a role defined by “middleness” (Gleeson & Shain, 1999, p. 488), which characterizes their place in institutional hierarchies between superiors and subordinates. Mid-level administrators often feel isolated since they cannot be seen as having close personal relationships with those above or below them in the rankings. Consequently, mid-level administrators are subject to burnout, a psychological condition resulting from isolation compounded by working long hours reconciling the competing and conflicting needs of supervisors and subordinates, which leaves them emotionally exhausted, physically depleted, and feeling like they have reached a professional dead-end. …

Adolescent Well-Being And Exclusionary Discipline: A Resiliency Model, Rachel Ballard

All-Inclusive List of Electronic Theses and Dissertations

Adolescents, especially those with a mental illness, often behave in ways judged to be impulsive, overly emotional, and irresponsible (Gogtay et al., 2004; Lawrence et al., 2015; Tamnes et al., 2010). Many teen behaviors which concern adults can be related to underdeveloped skills or competencies, rate of brain development, or expressions of mental disorders (Casey et al., 2011; Serbin et al., 2011; Spear, 2000). Behaviors commonly associated with adolescence, such as impulsivity, risk-taking, and efforts to fit in with peers, are often seen as a serious threat to school harmony, learning, and student safety, necessitating a disciplinary response from school …

The Hidden Quality Cost Resulting From Food And Drug Administration Inspection Failures In Mid To Large Companies, Jonathan Walston

All-Inclusive List of Electronic Theses and Dissertations

An approach to identify and validate hidden quality costs associated with regulatory non-compliance from inspections by the Food and Drug Administration (FDA) has not been previously researched. This dissertation presents a robust quantitative methodology to analyze the daily cumulative abnormal returns (CAR) on populations of publicly traded mid-to-large cap companies around FDA inspection events having negative outcomes. Three hypotheses have been tested focusing only on inspection events from companies falling under the biologics product type category. Hypothesis 1 states that there is no statistically significant correlation between the sum of CAR around inspection windows for such companies when a negative …

The Relationship Between Principal Perceptions On Leadership And Inclusive Education With Growth Model Outcomes For Students With Disabilities, Jason Bletzinger

All-Inclusive List of Electronic Theses and Dissertations

Now more than ever, school principals play a critical role in effective implementation of inclusive education programs in their schools, as inclusive practices are becoming tightly embedded in a school’s culture (Sailor, 2016; Shogren et al., 2015). The success of inclusive education programs has been primarily supported by school principals’ positive attitudes toward inclusion (Romanuck Murphy, 2018; Urton et al., 2014). With increasing pressure to provide legally compliant and quality inclusive special education services in schools, it has become more critical than ever that school principals not only recognize the roles and responsibilities they play in leading inclusive education programs …

Deontics And Time In Contracts: An Executable Semantics For The L4 Dsl, Seng Joe Watt, Oliver Goodenough, Meng Weng (Huang Mingrong) Wong

Research Collection Yong Pung How School Of Law

Existing approaches to modelling contracts often rely on deontic logic to reason about norms, and only treat time qualitatively. Using L4, a textual domain specific language (DSL) for the law, we offer a more operational interpretation of norms, based on states and transitions, that also accounts for the granular timing of events. In this paper, we present a higher-level rendering of the loan agreement from Flood & Goodenough in L4, and an accompanying operational semantics amenable to execution and static analysis. We also implement this semantics in Maude and show how this lets us visualize the execution of the loan …

Japanese-English Translation: Miki Kiyoshi —Thinking With Master Nishida (First Published In Fujin Kōron, August 1941) Complete Draft; Translated, Edited, And Revised By Christopher Southward, October 2022-September 2023 「西田先生のことども」、三木清著（初発 婦人公論、昭和十六年八月）, Christopher Southward

Comparative Literature Faculty and Student Scholarship

Japanese-English Translation: Miki Kiyoshi —Thinking with Master Nishida (First Published in Fujin Kōron, August 1941) Complete Draft; Translated, Edited, and Revised by Christopher Southward, October 2022-September 2023「西田先生のことども」、三木清著（初発 婦人公論、昭和十六年八月）

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Tarski And Bachmann In Regina: A Magical Connection, James T. Smith

Journal of Humanistic Mathematics

This is a personal account of an intersection of the schools of research in foundations of geometry founded by Alfred Tarski and Friedrich Bachmann. Their academic lineages and the origins of the schools are also described, as well as the mathematics that resulted from this intersection.

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 …

Toys As Tools For Good Science, Joshua Luczak

Research Collection College of Integrative Studies

The primary aim of this paper is to elevate the status of toy models, toy model based reasoning, and to encourage more focused discussions of them. This paper attempts to satisfy this aim by achieving two, secondary goals. First, it attempts elevate the status of toy models by making clear and elaborating on the distinction between them and representational models, and by discussing the connection between user intentionality and scientific representation (i.e. when a model represents something). And second, this paper attempts to elevate the status of toy models by highlighting, through some important historical examples, how they have been …