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Dissertations / Theses on the topic 'Mathematical Logic'

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1

Wedin, Hanna. "Mathematical Induction." Thesis, Uppsala universitet, Algebra och geometri, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-414099.

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2

Moreno, Dávila Julio Moreno Davila Julio. "Mathematical programming for logic inference /." [S.l.] : [s.n.], 1990. http://library.epfl.ch/theses/?nr=784.

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3

Cerami, Marco. "Fuzzy Description Logics from a Mathematical Fuzzy Logic point of view." Doctoral thesis, Universitat de Barcelona, 2012. http://hdl.handle.net/10803/113374.

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Description Logic is a formalism that is widely used in the framework of Knowledge Representation and Reasoning in Artificial Intelligence. They are based on Classical Logic in order to guarantee the correctness of the inferences on the required reasoning tasks. It is indeed a fragment of First Order Predicate Logic whose language is strictly related to the one of Modal Logic. Fuzzy Description Logic is the generalization of the classical Description Logic framework thought for reasoning with vague concepts that often arise in practical applications. Fuzzy Description Logic has been investigated since the last decade of the 20th century. During the first fifteen years of investigation their semantics has been based on Fuzzy Set Theory. A semantics based on Fuzzy Set Theory, however, has been shown to have some counter-intuitive behavior, due to the fact that the truth function for the implication used is not the residuum of the truth function for the conjunction. In the meanwhile, Fuzzy Logic has been given a formal framework based on Many-valued Logic. This framework, called Mathematical Fuzzy Logic, has been proposed has the kernel of a mathematically well founded Fuzzy Logic. In this dissertation we propose a Fuzzy Description Logic whose semantics is based on Mathematical Fuzzy Logic as its mathematically well settled kernel. To this end we provide a novel notation that is strictly related to the notation that is used in Mathematical Fuzzy Logic. After having settled the notation, we investigate the hierarchies of description languages over different-“t” norm based semantics and the reductions that can be performed between reasoning tasks. The new framework that we establish gives us the possibility to systematically investigate the relation of Fuzzy Description Logic to Fuzzy First Order Logic and Fuzzy Modal Logic. Next we provide some (un)decidability results for the case of infinite “t”-norm based semantics with or without knowledge bases. Finally we investigate the complexity bounds of reasoning tasks without knowledge bases for basic Fuzzy Description Logics over finite “t”-norms.
El trabajo desarrollado en esta tesis es una propuesta de sistematizar la formalización de las Lógicas de la Descripción Fuzzy a partir de la Lógica Difusa Matemática. Para ello se define un lenguaje para las Lógicas de la Descripción Fuzzy que extiende el lenguaje de la primera tradición de esta disciplina para adaptarlo al lenguaje más propio de la Lógica Difusa Matemática. Desde el punto de vista semántico, la teoría de conjuntos borrosos cede el paso a una semántica algebraica, que es la que se utiliza en la Lógica Difusa Matemática y que resuelve las consecuencias poco intuitivas que tenía la semántica tradicional. A partir de esta formalización, se tratan temas que eran tradicionales en las Lógicas de la Descripción clásicas como son las jerarquías de inclusiones entre lenguajes de la descripción y la relación de las Lógicas de la Descripción Fuzzy con la Lógica Difusa de primer orden por un lado y la Lógica Difusa Multi-modal por el otro. En relación a problemas de decidibilidad se demuestra que la satisfacción y la subsunción de conceptos en el lenguaje ALE bajo una semántica basada en la Lógica del Producto son problemas decidibles. También se demuestra que la consistencia de bases de conocimiento en el lenguaje ALC bajo una semántica basada en la Lógica de Lukasiewicz es un problema indecidible. En relación a problemas de complejidad computacional se demuestra que satisfacción y validez de fórmulas en la Lógica Modal minimal de Lukasiewicz con valores finitos son problemas PSPACE-completos. También se demuestra que la satisfacción y subsunción de conceptos en el lenguaje IALCED bajo una semántica basada en cualquier lógica difusa con valores finitos son problemas PSPACE-completos. Otra contribución de nuestro trabajo es el estudio sistemático de algoritmos de decisión para la satisfacción y subsunción de conceptos en el lenguaje IALCED, respecto a modelos “witnessed", basados en una reducción de es- tos problemas a los problemas de satisfacción y consecuencia en la lógica proposicional correspondiente.
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4

Greer, Deirdre C. Silvern Steven B. "Logic-mathematical processes in beginning reading." Auburn, Ala., 2005. http://repo.lib.auburn.edu/2005%20Summer/doctoral/GREER_DEIRDRE_28.pdf.

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5

Friend, Michèle Indira. "Second-order logic is logic." Thesis, University of St Andrews, 1997. http://hdl.handle.net/10023/14753.

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"Second-order logic" is the name given to a formal system. Some claim that the formal system is a logical system. Others claim that it is a mathematical system. In the thesis, I examine these claims in the light of some philosophical criteria which first motivated Frege in his logicist project. The criteria are that a logic should be universal, it should reflect our intuitive notion of logical validity, and it should be analytic. The analysis is interesting in two respects. One is conceptual: it gives us a purchase on where and how to draw a distinction between logic and other sciences. The other interest is historical: showing that second-order logic is a logical system according to the philosophical criteria mentioned above goes some way towards vindicating Frege's logicist project in a contemporary context.
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6

Collazo, Antonio. "The Mathematical Landscape." Scholarship @ Claremont, 2011. http://scholarship.claremont.edu/cmc_theses/116.

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The intent of this paper is to present the reader will enough information to spark a curiosity in to the subject. By no means is the following a complete formulation of any of the topics covered. I want to give the reader a tour of the mathematical landscape. There are plenty of further details to explore in each section, I have just touched the tip the iceberg. The work is basically in four sections: Numbers, Geometry, Functions, Sets and Logic, which are the basic building blocks of Math. The first sections are a exposition into the mathematical objects and their algebras. The last section dives into the foundation of math, sets and logic, and develops the ``language'' of Math. My hope is that after this, the reader will have the necessary (maybe not sufficient) information needed to talk the language of Math.
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7

Fors, Mikael. "Elementary Discrete Sets in Martin-Löf Type Theory." Thesis, Uppsala universitet, Algebra och geometri, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-175717.

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8

Wiklund, Tilo. "Locally cartesian closed categories, coalgebras, and containers." Thesis, Uppsala universitet, Algebra och geometri, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-197556.

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9

Yim, Austin Vincent. "On Galois correspondences in formal logic." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:b47d1dda-8186-4c81-876c-359409f45b97.

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This thesis examines two approaches to Galois correspondences in formal logic. A standard result of classical first-order model theory is the observation that models of L-theories with a weak form of elimination of imaginaries hold a correspondence between their substructures and automorphism groups defined on them. This work applies the resultant framework to explore the practical consequences of a model-theoretic Galois theory with respect to certain first-order L-theories. The framework is also used to motivate an examination of its underlying model-theoretic foundations. The model-theoretic Galois theory of pure fields and valued fields is compared to the algebraic Galois theory of pure and valued fields to point out differences that may hold between them. The framework of this logical Galois correspondence is also applied to the theory of pseudoexponentiation to obtain a sketch of the Galois theory of exponential fields, where the fixed substructure of the complex pseudoexponential field B is an exponential field with the field Qrab as its algebraic subfield. This work obtains a partial exponential analogue to the Kronecker-Weber theorem by describing the pure field-theoretic abelian extensions of Qrab, expanding upon work in the twelfth of Hilbert’s problems. This result is then used to determine some of the model-theoretic abelian extensions of the fixed substructure of B. This work also incorporates the principles required of this model-theoretic framework in order to develop a model theory over substructural logics which is capable of expressing this Galois correspondence. A formal semantics is developed for quantified predicate substructural logics based on algebraic models for their propositional or nonquantified fragments. This semantics is then used to develop substructural forms of standard results in classical first-order model theory. This work then uses this substructural model theory to demonstrate the Galois correspondence that substructural first-order theories can carry in certain situations.
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10

Eliasson, Jonas. "Ultrasheaves." Doctoral thesis, Uppsala : Matematiska institutionen, Univ. [distributör], 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3762.

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11

May, Bruce Matthew. "Elementary Logic as a Tool in Proving Mathematical Statements." Thesis, University of the Western Cape, 2008. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_1025_1263170321.

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The findings of the study indicate that knowledge of logic does help to improve the ability of students to make logical connections (deductions) between and from
statements. The results of the study, however, do not indicate that knowledge and understanding of logic translates into improved proving ability of mathematical
statements by students.

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12

Gorman, Judith A. "Aspects of coherent logic." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=63868.

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13

Purser, David Thurman. "A Leibnizian Approach to Mathematical Relationships: A New Look at Synthetic Judgments in Mathematics." University of Toledo / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1264612988.

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14

Levy, Bat-Sheva. "Fuzzy logic, a model to explain students' mathematical decision-making." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape7/PQDD_0026/MQ51391.pdf.

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15

McDonald, Kevin. "Modelling multi-layered network and security architectures using mathematical logic." Thesis, University of Aberdeen, 2014. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=214154.

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Complex systems, be they natural or synthetic, are ubiquitous. In particular, complex networks of devices and services underpin most of society's operations. By their very nature, such systems are di cult to conceptualize and reason about e ectively. One seemingly natural notion, which helps to manage complexity and which is commonly found in discussions of complex systems, is that of layering: the system is considered to consist of a collection of interconnected layers that have distinct, identi able roles in the overall operations of the system. Noting that graphs are a key formalism in the description of complex systems, this thesis establishes a notion of a layered graph. A logical characterization of this notion of layering using a non-associative, non-commutative substructural, sepa- rating logic is provided. In addition, soundness and completeness results for a class of algebraic models that includes layered graphs are provided, which give a math- ematically substantial semantics to this very weak logic. Examples in information processing and security are used to show the applicability of the logic. The examples given use an informal notion of action. The thesis also presents a discussion of a number of possible languages that could be used to provide a dynamic extension of the logic. The key components of each language are identi ed and the semantics that would be required in the case of a full, theoretical, development are presented. Examples, mainly in access control, are used to illustrate situations where each extension could be applied. The logic is then used to describe a uniform logical framework for reasoning compositionally about access control policy models. The approach takes account of the underlying system architecture, and so provides a way to identify and reason about how vulnerabilities may arise (and be removed) as a result of the architecture of the system. The logic is then used to describe a uniform logical framework for reasoning compositionally about access control policy models. The approach takes account of the underlying system architecture, and so provides a way to identify and reason about how vulnerabilities may arise (and be removed) as a result of the architecture of the system. Using frame rules, it is also considered how local properties of access control policies are maintained as the system architecture evolves.
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16

Farias, Pablo Mayckon Silva. "A study about the origins of Mathematical Logic and the limits of its applicability to the formalization of Mathematics." Universidade Federal do CearÃ, 2007. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=1516.

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Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico
Este trabalho à um estudo sobre as origens da LÃgica MatemÃtica e os limites da sua aplicabilidade ao desenvolvimento formal da MatemÃtica. Primeiramente, à apresentada a teoria aritmÃtica de Dedekind, a primeira teoria a fornecer uma definiÃÃo precisa para os nÃmeros naturais e com base nela demonstrar todos os fatos comumente conhecidos a seu respeito. à tambÃm apresentada a axiomatizaÃÃo da AritmÃtica feita por Peano, que de certa forma simplificou a teoria de Dedekind. Em seguida, à apresentada a ome{german}{Begriffsschrift} de Frege, a linguagem formal que deu origem à LÃgica moderna, e nela sÃo representadas as definiÃÃes bÃsicas de Frege a respeito da noÃÃo de nÃmero. Posteriormente, à apresentado um resumo de questÃes importantes em fundamentos da MatemÃtica durante as primeiras trÃs dÃcadas do sÃculo XX, iniciando com os paradoxos na Teoria dos Conjuntos e terminando com a doutrina formalista de Hilbert. Por fim, sÃo apresentados, em linhas gerais, os teoremas de incompletude de GÃdel e o conceito de computabilidade de Turing, que apresentaram respostas precisas Ãs duas mais importantes questÃes do programa de Hilbert, a saber, uma prova direta de consistÃncia para a AritmÃtica e o problema da decisÃo, respectivamente.
This work is a study about the origins of Mathematical Logic and the limits of its applicability to the formal development of Mathematics. Firstly, Dedekindâs arithmetical theory is presented, which was the first theory to provide a precise definition for natural numbers and to demonstrate relying on it all facts commonly known about them. Peanoâs axiomatization for Arithmetic is also presented, which in a sense simplified Dedekindâs theory. Then, Fregeâs Begriffsschrift is presented, the formal language from which modern Logic originated, and in it are represented Fregeâs basic definitions concerning the notion of number. Afterwards, a summary of important topics on the foundations of Mathematics from the first three decades of the twentieth century is presented, beginning with the paradoxes in Set Theory and ending with Hilbertâs formalist doctrine. At last, are presented, in general terms, GÃdelâs incompleteness. theorems and Turingâs computability concept, which provided precise answers to the two most important points in Hilbertâs program, to wit, a direct proof of consistency for Arithmetic and the decision problem, respectively. Keywords: 1. Mathematical Logic 2. Foundations of Mathematics 3. GÃdelâs incompleteness theorems
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17

Brierley, William. "Undecidability of intuitionistic theories." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66016.

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18

Boskovitz, Agnes. "Data editing and logic : the covering set method from the perspective of logic /." View thesis entry in Australian Digital Theses, 2008. http://thesis.anu.edu.au/public/adt-ANU20080314.163155/index.html.

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19

Lim, Jia Wei. "Parisian excursions of Brownian motion and their applications in mathematical finance." Thesis, London School of Economics and Political Science (University of London), 2013. http://etheses.lse.ac.uk/795/.

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In this thesis, we study Parisian excursions, which are defined as excursions of Brownian motion above or below a pre-determined barrier, exceeding a certain time length. Employing a new method, a recursion formula for the densities of single barrier and double barrier Parisian stopping times are computed. This new approach allows us to obtain a semi-closed form solution for the density of the one-sided stopping times, and does not require any numerical inversions of Laplace transforms. Further, it is backed by an intuitive argument which is premised on the recursive nature of the excursions and the strong Markov property of the Brownian motion. The same method is also employed in our computation of the two-sided and the double barrier Parisian stopping times. In turn, the resultant densities are used to price Parisian options. In particular, we provide numerical expressions for down-and-in Parisian calls. Additionally, we study the tail of the distribution of the two-sided Parisian stopping time. Based on the asymptotic properties of its distribution, we propose an approximation for the option prices, alleviating the heavy computational load arising from the recursions. Finally, we use the infinitesimal generator to obtain several results on other variations of Parisian excursions. Specifically, apart from the length, we are interested in the number of excursions and the maximum height achieved during an excursion. Using the same generator, we derive the joint Laplace transform of the occupation times of the Brownian motion above and below zero, but only starting the clock each time after a certain length.
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20

Fleury, Arnaud. "La règle d'échange : Logique linéaire multiplicative tressée." Paris 7, 1996. http://www.theses.fr/1996PA077055.

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Nous presentons ici un calcul des sequents et une structure de reseaux planaires pour la logique lineaire multiplicative classique et intuitionniste. L'echange est interprete comme echange tresse. Du point de vue semantique les reseaux sont des classes d'isotopie de graphes plonges dans r#3
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21

Bishop, Joyce Wolfer Otto Albert D. Lubinski Cheryl Ann. "Middle school students' understanding of mathematical patterns and their symbolic representations." Normal, Ill. Illinois State University, 1997. http://wwwlib.umi.com/cr/ilstu/fullcit?p9803721.

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Thesis (Ph. D.)--Illinois State University, 1997.
Title from title page screen, viewed June 1, 2006. Dissertation Committee: Albert D. Otto, Cheryl A. Lubinski (co-chairs), John A. Dossey, Cynthia W. Langrall, George Padavil. Includes bibliographical references (leaves 119-123) and abstract. Also available in print.
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22

Trybus, Adam. "An axiom system for a spatial logic with convexity." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/an-axiom-system-for-a-spatial-logic-with-convexity(cd19b55f-b4e5-4782-90f2-d3c0ad79891b).html.

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A spatial logic is any formal language with geometric interpretation. Research on region-based spatial logics, where variables are set to range over certain subsets of geometric space, have been investigated recently within the qualitative spatial reasoning paradigm in AI. We axiomatised the theory of (ROQ(R 2), conv, ≤) , where ROQ(R 2) is the set of regular open rational polygons of the real plane; conv is the convexity property and ≤ is the inclusion relation. We proved soundness and completeness theorems. We also proved several expressiveness results. Additionally, we provide a historical and philosophical overview of the topic and present contemporary results relating to affine spatial logics.
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23

Yu, Chaoran. "A study on relational databases through mathematical theories of relations and logic." Virtual Press, 1988. http://liblink.bsu.edu/uhtbin/catkey/539627.

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The purpose of this study is to explore that mathematics provides a convenient formalism for studying classical database management system problems. There are two main parts in this study, devoted respectively to using mathematical theory of relations and using logical theory to study database management systems. In the first part we focus on relational model and relational algebra. The second part deals with the application of mathematical logic to database management systems, where logic may be used both as a inference system and as a representation language. The features and logical mechanisms of Prolog programming language have been studied. A sample logical database model is developed and tested, using the logic programming language Prolog.
Department of Computer Science
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24

Revenko, Artem. "Automatic Construction of Implicative Theories for Mathematical Domains." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-197794.

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Implication is a logical connective corresponding to the rule of causality "if ... then ...". Implications allow one to organize knowledge of some field of application in an intuitive and convenient manner. This thesis explores possibilities of automatic construction of all valid implications (implicative theory) in a given field. As the main method for constructing implicative theories a robust active learning technique called Attribute Exploration was used. Attribute Exploration extracts knowledge from existing data and offers a possibility of refining this knowledge via providing counter-examples. In frames of the project implicative theories were constructed automatically for two mathematical domains: algebraic identities and parametrically expressible functions. This goal was achieved thanks both pragmatical approach of Attribute Exploration and discoveries in respective fields of application. The two diverse application fields favourably illustrate different possible usage patterns of Attribute Exploration for automatic construction of implicative theories.
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25

Quine, W. V. "The logic of sequences a generalization of Principia mathematica /." New York : Garland Pub, 1990. http://catalog.hathitrust.org/api/volumes/oclc/20797392.html.

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26

Peron, Newton Marques 1982. "Logicas da inconsistencia deontica." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/278895.

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Orientador: Marcelo Esteban Coniglio
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas
Made available in DSpace on 2018-08-13T04:53:14Z (GMT). No. of bitstreams: 1 Peron_NewtonMarques_M.pdf: 601027 bytes, checksum: 5828adda31c6102b730941a14056d7d9 (MD5) Previous issue date: 2009
Resumo: Esse trabalho expõe brevemente o que são as Lógicas da Inconsistência Formal ¿Observação: O resumo, na íntegra poderá ser visualizado no texto completo da tese digital.
Abstract: This work expose briefly what are the Logics of Formal Inconsistency ...Note: The complete abstract is available with the full electronic digital thesis or dissertations.
Mestrado
Filosofia
Mestre em Filosofia
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27

Baysal, Onur Alizde Rarail. "Lower-top and upper-bottom points for any formula in temporal logic/." [s.l.]: [s.n.], 2006. http://library.iyte.edu.tr/tezler/master/matematik/T000549.pdf.

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28

Horsfall, Benjamin Robert. "The logic of bunched implications : a memoir /." Connect to thesis, 2007. http://eprints.unimelb.edu.au/archive/00002633.

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29

Rossberg, Marcus. "Second-order logic : ontological and epistemological problems." Thesis, University of St Andrews, 2006. http://hdl.handle.net/10023/6407.

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In this thesis I provide a survey over different approaches to second-order logic and its interpretation, and introduce a novel approach. Of special interest are the questions whether (a particular form of) second-order logic can count as logic in some (further to be specified) proper sense of logic, and what epistemic status it occupies. More specifically, second-order logic is sometimes taken to be mathematical, a mere notational variant of some fragment of set theory. If this is the case, it might be argued that it does not have the "epistemic innocence" which would be needed for, e.g., foundational programmes in (the philosophy of) mathematics for which second-order logic is sometimes used. I suggest a Deductivist conception of logic, that characterises logical consequence by means of inference rules, and argue that on this conception second-order logic should count as logic in the proper sense.
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30

Weiss, Bernhard. "Intuitionistic semantics and the revision of logic." Thesis, University of St Andrews, 1992. http://hdl.handle.net/10023/14755.

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In this thesis I investigate the implications, for one's account of mathematics, of holding an anti-realist view. The primary aim is to appraise the scope of revision imposed by anti-realism on classical inferential practice in mathematics. That appraisal has consequences both for our understanding of the nature of mathematics and for our attitude towards anti-realism itself. If an anti-realist position seems inevitably to be absurdly revisionary then we have grounds for suspecting the coherence of arguments canvassed in favour of anti-realism. I attempt to defend the anti-realist position by arguing, i) that it is not internally incoherent for anti-realism to be a potentially revisionary position, and ii) that an anti-realist position can, plausibly, be seen to result in a stable intuitionistic position with regard to the logic it condones. The use of impredicative methods in classical mathematics is a site of traditional intuitionistic attacks. I undertake an examination of what the anti-realist attitude towards such methods should be. This question is of interest both because such methods are deeply implicated in classical mathematical theory of analysis and because intuitionistic semantic theories make use of impredicative methods. I attempt to construct the outlines of a set theory which is anti-realistically acceptable but which, although having no antecedent repugnance for impredicative methods as such, appears to be too weak to offer an anti-realistic vindication of impredicative methods in general. I attempt to exonerate intuitionistic semantic theories in their use of impredicative methods by showing that a partial order relying on the nature of our grasp of the intuitionistic meaning stipulations for the logical constants precludes a possible circularity.
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31

Blakely, Scott. "Probabilistic Analysis for Reliable Logic Circuits." PDXScholar, 2014. https://pdxscholar.library.pdx.edu/open_access_etds/1860.

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Continued aggressive scaling of electronic technology poses obstacles for maintaining circuit reliability. To this end, analysis of reliability is of increasing importance. Large scale number of inputs and gates or correlations of failures render such analysis computationally complex. This paper presents an accurate framework for reliability analysis of logic circuits, while inherently handling reconvergent fan-out without additional complexity. Combinational circuits are modeled stochastically as Discrete-Time Markov Chains, where propagation of node logic levels and error probability distributions through circuitry are used to determine error probabilities at nodes in the circuit. Model construction is scalable, as it is done so on a gate-by-gate basis. The stochastic nature of the model lends itself to allow various properties of the circuit to be formally analyzed by means of steady-state properties. Formal verifying the properties against the model can circumvent strenuous simulations while exhaustively checking all possible scenarios for given properties. Small combinational circuits are used to explain model construction, properties are presented for analysis of the system, more example circuits are demonstrated, and the accuracy of the method is verified against an existing simulation method.
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32

Tabachnikova, Olga Markovna. "Fresh orderings of groups." Thesis, University of Bath, 1995. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.295448.

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33

Delaney, Aidan. "Defining star-free regular languages using diagrammatic logic." Thesis, University of Brighton, 2012. https://research.brighton.ac.uk/en/studentTheses/d1c53bda-f520-4807-9de9-8de12eda3d9e.

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Spider diagrams are a recently developed visual logic that make statements about relationships between sets, their members and their cardinalities. By contrast, the study of regular languages is one of the oldest active branches of computer science research. The work in this thesis examines the previously unstudied relationship between spider diagrams and regular languages. In this thesis, the existing spider diagram logic and the underlying semantic theory is extended to allow direct comparison of spider diagrams and star-free regular languages. Thus it is established that each spider diagram defines a commutative star-free regular language. Moreover, we establish that every com- mutative star-free regular language is definable by a spider diagram. From the study of relationships between spider diagrams and commutative star-free regular languages, an extension of spider diagrams is provided. This logic, called spider diagrams of order, increases the expressiveness of spider di- agrams such that the language of every spider diagram of order is star-free and regular, but not-necessarily commutative. Further results concerning the expres- sive power of spider diagrams of order are gained through the use of a normal form for the diagrams. Sound reasoning rules which take a spider diagram of order and produce a semantically equivalent diagram in the normal form are pro- vided. A proof that spider diagrams of order define precisely the star-free regular languages is subsequently presented. Further insight into the structure and use of spider diagrams of order is demonstrated by restricting the syntax of the logic. Specifically, we remove spiders from spider diagrams of order. We compare the expressiveness of this restricted fragment of spider diagrams of order with the unrestricted logic.
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Lindroth, Olof. "A random formula lower bound for ordered DLL extended with local symmetry recognition /." Uppsala, 2004. http://www.math.uu.se/research/pub/Lindroth1.pdf.

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35

Farnsworth, Michael Arlington. "Improvements in the theory of confirmation as improvability by incorporating mathematical simplicity." Laramie, Wyo. : University of Wyoming, 2008. http://proquest.umi.com/pqdweb?did=1798480851&sid=1&Fmt=2&clientId=18949&RQT=309&VName=PQD.

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36

Oliveira, Antonio Marmo da Cunha 1969. "Sistemas, pressuposições e implicaturas = uma investigação exploratória, lógica e filosófica." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/279513.

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Orientador: Walter Alexandre Carnielli
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas
Made available in DSpace on 2018-08-19T13:14:11Z (GMT). No. of bitstreams: 1 Oliveira_AntonioMarmodaCunha_M.pdf: 7643012 bytes, checksum: 1904b2b114fcf86253069cc0fe63eedb (MD5) Previous issue date: 2011
Resumo: Neste trabalho investigaremos, do ponto de vista da lógica e da filosofia, os fenômenos pragmáticos conhecidos como pressuposição e implicatura, relacionando-os a traços mais gerais da racionalidade humana, como economia e consistência, e ao pluralismo da lógica atual, incluindo alguns tópicos de contenda entre a tradição clássica e as propostas alternativas recentes. Grice articulou uma análise destes fenômenos assentes em princípios para a conversação ou interação entre entes racionais e cooperativos. Divergimos da tradição griceana, postulando que as implicaturas são processadas por "clivagem de informações", ou por verificação de outros critérios lógicos, ao invés da mera exploração de máximas. Partindo de conceitos precisamente definidos, como pressuposição e implicatura, é possível construir um arcabouço lógico, a denominar sistemas pressuposicionais, que estendem outros sistemas lógicos (como, por exemplo, o cálculo proposicional) e cujos resultados exporemos
Abstract: In this work we shall, from the logical and philosophical standpoint, investigate two pragmatic phenomena known as presupposition and implicature, associating them to more general features of human rationality, such as economy and consistency, and to the current logical pluralism, including some controversies between the classical tradition and more recent alternative approaches. Grice has articulated an analysis of such phenomena based on principles governing conversation or interaction between cooperative and rational beings. We dissent from the gricean tradition, and proposing that implicatures are processed by the 'sieving of information', rather than by the mere exploitation of maxims. By providing precise definitions to the concepts of presupposition and implicature, it is possible to build a logical framework, to be called presuppositional systems, which either extend or generalise other logical systems (such as the propositional calculus, for instance), the results of which we shall present hereinafter
Mestrado
Filosofia
Mestre em Filosofia
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37

Kerber, Manfred. "On the representation of mathematical concepts and their translation into first-order logic /." Kaiserslautern : Univ., Fachbereich Informatik, 1992. http://kluedo.ub.uni-kl.de/volltexte/2000/336/.

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Strobach, Niko. "Alternativen in der Raumzeit eine Studie zur philosophischen Anwendung multimodaler Aussagenlogiken." Berlin Logos, 2007. http://deposit.d-nb.de/cgi-bin/dokserv?id=2907736&prov=M&dok_var=1&dok_ext=htm.

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39

Corfield, David Neil. "Research programmes, logic, and analogy : three aspects of mathematics and its development." Thesis, King's College London (University of London), 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.306938.

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40

Lindman, Phillip A. (Phillip Anthony). "Intuition versus Formalization: Some Implications of Incompleteness on Mathematical Thought." Thesis, University of North Texas, 1994. https://digital.library.unt.edu/ark:/67531/metadc277970/.

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This paper describes the tension between intuition about number theory and attempts to formalize it. I will first examine the root of the dilemma, Godel's First Incompleteness Theorem, which demonstrates that in any reasonable formalization of number theory, there will be independent statements. After proving the theorem, I consider some of its consequences on intuition, focusing on Freiling's "Dart Experiment" which is based on our usual notion of the real numbers as a line. This experiment gives an apparent refutation of the Axiom of Choice and the Continuum Hypothesis; however, it also leads to an equally apparent paradox. I conclude that such paradoxes are inevitable as the formalization of mathematics takes us further from our initial intuitions.
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41

Toninho, Bernardo Parente Coutinho Fernandes. "A Logic and tool for local reasoning about security protocols." Master's thesis, FCT - UNL, 2009. http://hdl.handle.net/10362/2307.

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Trabalho apresentado no âmbito do Mestrado em Engenharia Informática, como requisito parcial para obtenção do grau de Mestre em Engenharia Informática
This thesis tackles the problem of developing a formal logic and associated model-checking techniques to verify security properties, and its integration in the Spatial Logic Model Checker(SLMC) tool. In the areas of distributed system design and analysis, there exists a substantial amount of work related to the verification of correctness properties of systems, in which the work aimed at the verification of security properties mostly relies on precise yet informal methods of reasoning. This work follows a line of research that applies formal methodologies to the verification of security properties in distributed systems, using formal tools originally developed for the study of concurrent and distributed systems in general. Over the years, several authors have proposed spatial logics for local and compositional reasoning about algebraic models of distributed systems known as process calculi. In this work, we present a simplification of a process calculus known as the Applied - calculus, introduced by Abadi and Fournet, designed for the study of security protocols. We then develop a spatial logic for this calculus, extended with knowledge modalities, aimed at reasoning about security protocols using the concept of local knowledge of processes. Furthermore, we conclude that the extensions are sound and complete regarding their intended semantics and that they preserve decidability, under reasonable assumptions. We also present a model-checking algorithm and the proof of its completeness for a large class of processes. Finally, we present an OCaml implementation of the algorithm, integrated in the Spatial Logic Model Checker tool, developed by Hugo Vieira and Luis Caires, thus producing the first tool for security protocol analysis that employs spatial logics.
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42

趙炳權 and Ping-kuen Peter Chiu. "Primitive interval labelled net model for logic simulation." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1991. http://hub.hku.hk/bib/B31232541.

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43

Akishev, Galym. "Monadic bounded algebras : a thesis submitted to the Victoria University of Wellington in fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics /." ResearchArchive@Victoria e-Thesis, 2009. http://hdl.handle.net/10063/915.

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French, Timothy Noel. "Bisimulation quantifiers for modal logics." University of Western Australia. School of Computer Science and Software Engineering, 2006. http://theses.library.uwa.edu.au/adt-WU2007.0013.

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Modal logics have found applications in many diferent contexts. For example, epistemic modal logics can be used to reason about security protocols, temporal modal logics can be used to reason about the correctness of distributed systems and propositional dynamic logic can reason about the correctness of programs. However, pure modal logic is expressively weak and cannot represent many interesting secondorder properties that are expressible, for example, in the μ-calculus. Here we investigate the extension of modal logics with propositional quantification modulo bisimulation (bisimulation quantification). We extend existing work on bisimulation quantified modal logic by considering the variety of logics that result by restricting the structures over which they are interpreted. We show this can be a natural extension of modal logic preserving the intuitions of both modal logic and propositional quantification. However, we also find cases where such intuitions are not preserved. We examine cases where the axioms of pure modal logic and propositional quantification are preserved and where bisimulation quantifiers preserve the decidability of modal logic. We translate a number of recent decidability results for monadic second-order logics into the context of bisimulation quantified modal logics, and show how these results can be used to generate a number of interesting bisimulation quantified modal logics.
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Abraham, Tara Helen. "Microscopic cybernetics, mathematical logic, automata theory, and the formalization of biological phenomena, 1936-1970." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ53763.pdf.

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46

Horng, Wen-Bing. "Using Extended Logic Programs to Formalize Commonsense Reasoning." Thesis, University of North Texas, 1992. https://digital.library.unt.edu/ark:/67531/metadc278054/.

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In this dissertation, we investigate how commonsense reasoning can be formalized by using extended logic programs. In this investigation, we first use extended logic programs to formalize inheritance hierarchies with exceptions by adopting McCarthy's simple abnormality formalism to express uncertain knowledge. In our representation, not only credulous reasoning can be performed but also the ambiguity-blocking inheritance and the ambiguity-propagating inheritance in skeptical reasoning are simulated. In response to the anomalous extension problem, we explore and discover that the intuition underlying commonsense reasoning is a kind of forward reasoning. The unidirectional nature of this reasoning is applied by many reformulations of the Yale shooting problem to exclude the undesired conclusion. We then identify defeasible conclusions in our representation based on the syntax of extended logic programs. A similar idea is also applied to other formalizations of commonsense reasoning to achieve such a purpose.
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47

Brey, Amina. "Multiple representations and cognitive load: words, arrows, and colours when solving algebraic problems." Thesis, Nelson Mandela Metropolitan University, 2013. http://hdl.handle.net/10948/d1020392.

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This study investigates the possible effects that access to selected multiple representations (words, arrows and colours) have in terms of cognitive load and learner achievement when presented with algebraic problems at grade nine level. The presentation of multiple representations (the intervention) was intended to decrease extraneous cognitive load, manage the intrinsic cognitive load (algebraic problems) and optimise germane cognition (schema acquisition and automation). An explanatory sequential mixed-method design was employed with six hundred and seventy three learners in four secondary schools. Quantitative data were generated via pre-, intervention and post-tests/questionnaires, while qualitative data were obtained from open-ended questions in the pre-, intervention, and post-tests/questionnaires, eight learner focus group interviews (n = 32), and four semi-structured, open-ended teacher interviews. Statistically and practically significant improvement in mean test scores from the pre- to intervention test scores in all schools was noted. No statistically and practically significant improvement was noted in further post-tests except for post-test 2 which employed more challenging problems (statistically significant decrease with a small practical effect). Learners expressed their preference for arrows, followed by colours and then words as effective representations. Teacher generated qualitative data suggests that they realise the importance of using multiple representations as an instructional strategy and implicitly understand the notion of cognitive load. The findings, when considered in the light of literature on cognitive load, suggest that a reduction in extraneous cognitive load by using a more effective instructional design (multiple representations) frees working memory capacity which can then be devoted to the intrinsic cognitive load (algebraic problems) and thereby increase germane cognition (schema acquisition and automation).
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D'Silva, Vijay Victor. "Logical abstract interpretation." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:3648e579-01dc-4054-8290-31626d53b003.

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Logical deduction and abstraction from detail are fundamental, yet distinct aspects of reasoning about programs. This dissertation shows that the combination of logic and abstract interpretation enables a unified and simple treatment of several theoretical and practical topics which encompass the model theory of temporal logics, the analysis of satisfiability solvers, and the construction of Craig interpolants. In each case, the combination of logic and abstract interpretation leads to more general results, simpler proofs, and a unification of ideas from seemingly disparate fields. The first contribution of this dissertation is a framework for combining temporal logics and abstraction. Chapter 3 introduces trace algebras, a new lattice-based semantics for linear and branching time logics. A new representation theorem shows that trace algebras precisely capture the standard trace-based semantics of temporal logics. We prove additional representation theorems to show how structures that have been independently discovered in static program analysis, model checking, and algebraic modal logic, can be derived from trace algebras by abstract interpretation. The second contribution of this dissertation is a framework for proving when two lattice-based algebras satisfy the same logical properties. Chapter 5 introduces functions called subsumption and bisubsumption and shows that these functions characterise logical equivalence of two algebras. We also characterise subsumption and bisubsumption using fixed points and finitary logics. We prove a representation theorem and apply it to derive the transition system analogues of subsumption and bisubsumption. These analogues strictly generalise the well studied notions of simulation and bisimulation. Our fixed point characterisations also provide a technique to construct property preserving abstractions. The third contribution of this dissertation is abstract satisfaction, an abstract interpretation framework for the design and analysis of satisfiability procedures. We show that formula satisfiability has several different fixed point characterisations, and that satisfiability procedures can be understood as abstract interpreters. Our main result is that the propagation routine in modern sat solvers is a greatest fixed point computation involving abstract transformers, and that clause learning is an abstract transformer for a form of negation. The final contribution of this dissertation is an abstract interpretation based analysis of algorithms for constructing Craig interpolants. We identify and analyse a lattice of interpolant constructions. Our main result is that existing algorithms are two of three optimal abstractions of this lattice. A second new result we derive in this framework is that the lattice of interpolation algorithms can be ordered by logical strength, so that there is a strongest and a weakest possible construction.
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Davies, James Edgar. "Changes of Setting and the History of Mathematics: A New Study of Frege." Thesis, University of Canterbury. Mathematics & Statistics, 2010. http://hdl.handle.net/10092/4330.

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This thesis addresses an issue in the philosophy of Mathematics which is little discussed, and indeed little recognised. This issue is the phenomenon of a ‘change of setting’. Changes of setting are events which involve a change in a scientific framework which is fruitful for answering questions which were, under an old framework, intractable. The formulation of the new setting usually involves a conceptual re-orientation to the subject matter. In the natural sciences, such re-orientations are arguably unremarkable, inasmuch as it is possible that within the former setting for one’s thinking one was merely in error, and under the new orientation one is merely getting closer to the truth of the matter. However, when the subject matter is pure mathematics, a problem arises in that mathematical truth is (in appearance) timelessly immutable. The conceptions that had been settled upon previously seem not the sort of thing that could be vitiated. Yet within a change of setting that is just what seems to happen. Changes of setting, in particular in their effects on the truth of individual propositions, pose a problem for how to understand mathematical truth. Thus this thesis aims to give a philosophical analysis of the phenomenon of changes of setting, in the spirit of the investigations performed in Wilson (1992) and Manders (1987) and (1989). It does so in three stages, each of which occupies a chapter of the thesis: 1. An analysis of the relationship between mathematical truth and settingchanges, in terms of how the former must be viewed to allow for the latter. This results in a conception of truth in the mathematical sciences which gives a large role to the notion that a mathematical setting must ‘explain itself’ in terms of the problems it is intended to address. 2. In light of (1), I begin an analysis of the change of setting engendered in mathematical logic by Gottlob Frege. In particular, this chapter will address the question of whether Frege’s innovation constitutes a change of setting, by asking the question of whether he is seeking to answer questions which were present in the frameworks which preceded his innovations. I argue that the answer is yes, in that he is addressing the Kantian question of whether alternative systems of arithmetic are possible. This question arises because it had been shown earlier in the 19th century that Kant’s conclusion, that Euclid’s is the only possible description of space, was incorrect. 3. I conclude with an in-depth look at a specific aspect of the logical system constructed in Frege’s Grundgesetze der Arithmetik. The purpose of this chapter is to find evidence for the conclusions of chapter two in Frege’s technical work (as opposed to the philosophical). This is necessitated by chapter one’s conclusions regarding the epistemic interdependence of formal systems and informal views of those frameworks. The overall goal is to give a contemporary account of the possibility of setting-changes; it will turn out that an epistemic grasp of a mathematical system requires that one understand it within a broader, somewhat historical context.
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50

Hamrin, Göran. "Effective Domains and Admissible Domain Representations." Doctoral thesis, Uppsala University, Department of Mathematics, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-5883.

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This thesis consists of four papers in domain theory and a summary. The first two papers deal with the problem of defining effectivity for continuous cpos. The third and fourth paper present the new notion of an admissible domain representation, where a domain representation D of a space X is λ-admissible if, in principle, all other λ-based domain representations E of X can be reduced to X via a continuous function from E to D.

In Paper I we define a cartesian closed category of effective bifinite domains. We also investigate the method of inducing effectivity onto continuous cpos via projection pairs, resulting in a cartesian closed category of projections of effective bifinite domains.

In Paper II we introduce the notion of an almost algebraic basis for a continuous cpo, showing that there is a natural cartesian closed category of effective consistently complete continuous cpos with almost algebraic bases. We also generalise the notion of a complete set, used in Paper I to define the bifinite domains, and investigate what closure results that can be obtained.

In Paper III we consider admissible domain representations of topological spaces. We present a characterisation theorem of exactly when a topological space has a λ-admissible and κ-based domain representation. We also show that there is a natural cartesian closed category of countably based and countably admissible domain representations.

In Paper IV we consider admissible domain representations of convergence spaces, where a convergence space is a set X together with a convergence relation between nets on X and elements of X. We study in particular the new notion of weak κ-convergence spaces, which roughly means that the convergence relation satisfies a generalisation of the Kuratowski limit space axioms to cardinality κ. We show that the category of weak κ-convergence spaces is cartesian closed. We also show that the category of weak κ-convergence spaces that have a dense, λ-admissible, κ-continuous and α-based consistently complete domain representation is cartesian closed when α ≤ λ ≥ κ. As natural corollaries we obtain corresponding results for the associated category of weak convergence spaces.

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