Tesis: "Logic (symbolic and mathematical)"

1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

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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12

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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13

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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14

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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15

Weydert, Emil. "How to approximate the naive comprehension scheme inside of classical logic". Bonn : [s.n.], 1989. http://catalog.hathitrust.org/api/volumes/oclc/19990751.html.

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16

Lavers, Peter Stanley. "Generating intensional logics : the application of paraconsistent logics to investigate certain areas of the boundaries of mathematics /". Title page, table of contents and summary only, 1985. http://web4.library.adelaide.edu.au/theses/09ARM/09arml399.pdf.

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17

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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18

Wagner, Gerd. "Vivid logic : knowledge-based reasoning with two kinds of negation /". Berlin [u.a.] : Springer, 1994. http://www.loc.gov/catdir/enhancements/fy0815/93046747-d.html.

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19

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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20

湯志輝 y Chi-fai Tong. "On checking the temporal consistency of data". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1993. http://hub.hku.hk/bib/B31211914.

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21

Tong, Chi-fai. "On checking the temporal consistency of data /". [Hong Kong : University of Hong Kong], 1993. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13570353.

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22

Sharma, Richa. "Semi-automated approach to support logical formalism for requirements analysis and validation". Thesis, IIT Delhi, 2016. http://localhost:8080/xmlui/handle/12345678/7227.

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23

Hassani, Sarah Dossey John A. "Calculus students' knowledge of the composition of functions and the chain rule". Normal, Ill. Illinois State University, 1998. http://wwwlib.umi.com/cr/ilstu/fullcit?p9835906.

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Thesis (D.A.)--Illinois State University, 1998.
Title from title page screen, viewed July 3, 2006. Dissertation Committee: John A. Dossey (chair), Roger Day, Michael Marsali, Michael Plantholt. Includes bibliographical references (leaves 196-202) and abstract. Also available in print.

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24

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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25

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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26

Pemmaraju, Sriram V. "Modal logics of provability". Thesis, Virginia Tech, 1989. http://hdl.handle.net/10919/44652.

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Gödel proved his Incompleteness theorems for any theory 'strong' enough to represent recursive functions. In the process he showed that the provability predicate can be represented in such theories. Modal logics of provability are modal logics which attempt to express the concept of 'provability' and 'consistency' using the modal operators '[]' and '<>' respectively. This is achieved by forcing '[]' to behave like the provability predicate. GL is a modal logic which has been shown to be complete and sound with respect to arithmetic theories (theories which can represent all recursive functions), hence results about concepts such as 'consistency,' 'provability' and 'decidability' in arithmetic theories can be stated and proved in GL. It has also been proved that GL is complete with respect to the class of finite, transitive, reversely well-founded models. This essentially means that the set of theorems of GL is recursive and hence there exists an effective procedure to determine whether a given wff is a theorem of GL or not. We investigate a weaker version of GL called GH and show that GH is not complete with respect to arithmetic theories. We show this by first showing that GH is a proper subset of GL and then showing that the theorems missing from GH are properties of the provability predicate. We finally, show that GH is not complete with respect to the class of transitive, reversely well-founded models and hence not sound and complete with respect to any frame.

Master of Science

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27

Loomis, Eric John. "Meaning, generality, and rules : language and logic in the later Wittgenstein /". Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.

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28

Gat, Erann. "Reasoning about knowledge using extensional logics". Thesis, Virginia Polytechnic Institute and State University, 1987. http://hdl.handle.net/10919/90971.

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When representing statements about knowledge in an extensional logic, it occasionally happens that undesired conclusions arise. Such extraneous conclusions are often the result of substitution of equals for equals or existential instantiation within intensional operators such as Know. In the past, efforts at solving this problem have centered on modifications to the logic. In this thesis, I propose a solution that leaves the logic intact and changes the representation of the statements instead. The solution presented here has four main points: 1) Only propositions can be known. 2) Relations rather than functions should be used to describe objects. 3) Temporal reasoning is often necessary to represent many real world problems. 4) In cases where more than one label can apply to the same object, an agent's knowledge about labels must be explicitly represented. When these guidelines are followed, statements about knowledge can be represented in standard first-order predicate logic in such a way that extraneous conclusions cannot be drawn. Standard first-order theorem provers (like Prolog) can then be used to solve problems which involve reasoning about knowledge
M.S.

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29

Munoz, Ricardo A. (Ricardo Alberto). "Using Normal Deduction Graphs in Common Sense Reasoning". Thesis, University of North Texas, 1992. https://digital.library.unt.edu/ark:/67531/metadc277922/.

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This investigation proposes a powerful formalization of common sense knowledge based on function-free normal deduction graphs (NDGs) which form a powerful tool for deriving Horn and non-Horn clauses without functions. Such formalization allows common sense reasoning since it has the ability to handle not only negative but also incomplete information.

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30

Almeida, Edgar Luis Bezerra de 1976. "Lógicas abstratas e o primeiro teorema de Lindström". [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/282036.

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Orientador: Itala Maria Loffredo D'Ottaviano
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas
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Resumo: Esta Dissertação apresenta uma definição de lógica abstrata e caracteriza alguns sistemas lógicos bastante conhecidos na literatura como casos particulares desta. Em especial, mostramos que a lógica de primeira ordem, lógica de segunda ordem, lógica com o operador Q1 de Mostowski e a lógica infinitária L!1! são casos particulares de lógicas abstratas. Mais que isso, mostramos que tais lógicas são regulares. Na análise de cada uma das lógicas acima citadas, mostramos o comportamento das mesmas com relação às propriedades de Löwenheim-Skolem e compacidade enumerável, resultados estes centrais à teoria de modelos. Nossa análise permite-nos constatar que, dentre os quatro casos apresentados, o único que goza de ambas as propriedades é a lógica de primeira ordem; as demais falham em uma, na outra ou em ambas as propriedades. Mostramos que isso não é mera coincidência, mas sim um resultado profundo, que estabelece fronteiras bem delimitadas à lógica de primeira ordem, conhecido como primeiro teorema de Lindström: se uma lógica é regular, ao menos tão expressiva quanto à lógica de primeira ordem e satisfaz ambas as propriedades citadas, então esta é equivalente a lógica de primeira ordem. Realizamos uma prova cuidadosa do teorema, em que cada ideia e cada estratégia de prova é estabelecida criteriosamente. Com seu trabalho, Lindström inaugurou um novo e profícuo campo de estudo, a teoria abstrata de modelos que estabelece, com relação a diversas combinações de propriedades de sistemas lógicos, uma estratificação entre lógicas. Apresentamos um outro exemplo de tal estratificação através de uma versão modal do teorema de Lindström, versão esta que caracteriza a lógica modal básica como maximal quanto a bissimilaridade e compacidade. Encerramos esta Dissertação com algumas considerações acerca da influência do primeiro teorema de Lindström
Abstract: This thesis presents the definition of abstract logic and features some quite logical systems presented in the literature as particular cases of this. In particular, we show that first-order logic, second-order logic, the logic with Mostowski's operator Q1 and the infinitary logic L!1! are specific systems of abstract logic. Moreover, we show that such logics are regular. In the analysis of each above mentioned logical systems we analyses his performance with regard to the properties of compactness and Löwenheim-Skolem, results that have important role in model theory. Our analysis allows us to conclude that among the four cases, the only one who enjoys both properties is the first-order logic, and all others fail in one, other or both properties. We show that this is not mere coincidence, but rather a deep, well-defined boundaries establishing the first-order logic, known as first Lindström's theorem: a regular logic that is at least as expressive as first-order logic and satisfies both properties mentioned, then this is equivalent to first-order logic. We conducted a thorough proof of the theorem, in which each idea and each proof strategy is carefully established. With his work Lindström inaugurated a new and fruitful field of study, the abstract model theory, which establishes with respect to different combinations of properties of logical systems, stratification between logical. Here is another example of such stratification through one of the theorem of modal version Lindström, which characterizes this version of the logic basic modal such as maximal bissimimulation and compactness. We conclude the thesis with some considerations about the influence of the Lindström's theorem
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Filosofia
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31

Legge, Gaynor W. "A Mechanism for Facilitating Temporal Reasoning in Discrete Event Simulation". Thesis, University of North Texas, 1992. https://digital.library.unt.edu/ark:/67531/metadc278352/.

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This research establishes the feasibility and potential utility of a software mechanism which employs artificial intelligence techniques to enhance the capabilities of standard discrete event simulators. As background, current methods of integrating artificial intelligence with simulation and relevant research are briefly reviewed.

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32

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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33

Schwartzkopff, Robert. "The numbers of the marketplace : commitment to numbers in natural language". Thesis, University of Oxford, 2015. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.711821.

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34

Secco, Érica Fernanda Aparecida [UNESP]. "Teoria de conjuntos fuzzy e aplicações". Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/94362.

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Neste traboalho são apresentados alguns conceitos básicos da Teoria de Conjuntos Fuzzy como: operações comu conjunto fuzzy, Princípio de Extensão de Zadeh, números fuzzy e noçoes de lógica fuzzy. As relações são apresentadas com o objetivo de tratarmos de sistemas baseados em regras fuzzy e algumas aplicações
In this paper are presented some basic concepts of Fuzzy Sets Theory: operation with fuzzy sets, Zadeh extension principle, fuzzy numbers and fuzzy logic. The fuzzy relations are presented for the purpose of treating systems based on fuzzy rules and some application

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35

Lannin, John K. Langrall Cynthia Willey. "Developing middle school students' understanding of recursive and explicit reasoning". Normal, Ill. Illinois State University, 2001. http://wwwlib.umi.com/cr/ilstu/fullcit?p3006621.

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Thesis (Ph. D.)--Illinois State University, 2001.
Title from title page screen, viewed April 25, 2006. Dissertation Committee: Cynthia W. Langrall (Chair), Graham A. Jones, Tami S. Martin, Patricia H. Klass. Includes bibliographical references (leaves 138-146) and abstract. Also available in print.

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36

Batista, Neto Alberto Leopoldo. "Representação e combinação de logicas : questões conceituais". [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/278894.

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Orientador: Marcelo Esteban Coniglio
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas
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Resumo: Visando a atingir um esclarecimento sobre os conceitos fundamentais envolvidos no estudo das combinações entre lógicas, empreendemos uma alise do problema da representação geral de sistemas lógicos (com ênfase no conceito central de conseqüência lógica), juntamente com o do estabelecimento de uma noção apropriada de tradução ou morfismo entre os sistemas definidos de um determinado modo, com base em que podemos fundamentar algumas técnicas de combinação, especialmente a fibrilação algébrica. Tais técnicas são definidas e apresentadas em suas propriedades mais relevantes, sendo encontrados, no caso particular da fibrilação, problemas tais como o colapso e o anti-colapso. Para estes, a solução parece residir na escolha de formas adequadas de representar lógicas em geral e de traduzir lógicas umas nas outras. Uma apresentação modelo-teorética mostra-se apropriada para algumas representações de lógicas em geral (como, por exemplo, sistemas de Hilbert), embora não o seja para outras (como sistemas de conseqüências múltiplas). No entanto, duas das mais promissoras tentativas de solucionar, em particular, o problema do anti-colapso da fibrilação algébrica as meta-traduções e os transfers elementares podem ser definidas dentro desse arcabouço. Os transfers incluindo os transfers elementares - foram definidos em [17] - e aqui apresentamos uma representação das meta-traduções como tipo específico de transfer
Abstract: In order to accomplish an elucidation of the fundamental concepts involved in the study of the combinations between logics, we undertake an analysis of the problem of the general representation of logical systems (with an emphasis on the central concept of logical consequence) together with that of the establishment of an appropriate notion of translation or morphism between the logical systems defined in a certain fashion, on which basis we can ground some of the combination techniques, specially that of algebraic fibring. Such techniques are defined and presented in their most relevant features, and we find, in the particular case of fibring, problems such as collapsing and anticollapsing. The solution for these seem to rest on the choice of adequate forms of representing logics in general and translating logics into others. A modeltheoretic presentation shows itself appropriate for some representations of logics in general (such as Hilbert calculi), although they are not for some others (such as multipleconclusion systems). Notwithstanding, two of the most promising attempts to solve, in particular, the problem of the anticollapsing of algebraic fibring metatranslations and elementary transfers , are definable within that framework. Transfers including elementary transfers have been defined in [17] and we here present a representation of metatranslations as an specific kind of transfers
Mestrado
Logica
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37

Tabada, Winston M. "An analysis and implementation of linear derivation strategies". Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 1991. https://ro.ecu.edu.au/theses/1125.

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This study examines the efficacy of six linear derivation strategies: (i) s-linear resolution, (ii) the ME procedure; (iii) t-linear resolution, (iv) SL -resolution, (v) the GC procedure, and (vi) SLM. The analysis is focused on the different restrictions and operations employed in each derivation strategy. The selection function, restrictive ancestor resolution, compulsory ancestor resolution on literals having atoms which are or become identical, compulsory merging operations, reuse of truncated literals, spreading of FALSE literals, no-tautologies resection, no two non-B-literals having identical atoms restriction, and the use of semantic information to trim irrelevant derivations from the search tree are the major features found In these six derivation strategies. Detecting loops and minimizing irrelevant derivations are the identified weak points of SLM. Two variations of SLM are suggested to rectify these problems. The ME procedure, SL-resolution, the GC procedure, SLM and one of the suggested variations of SLM were implemented using the Arity/Prolog compiler to produce the ME -TP, SL-TP, GC-TP, SLM-TP and SLM5-TP theorem provers respectively. In addition to the original features of each derivation strategy, the following search strategies were included in the implementations : the modified consecutively bounded depth-first search unit preference strategy, set of support strategy, pure literal elimination, tautologous clause elimination, selection function based on the computed weight of a literal, and a match check. The extension operation used by each theorem prover was extended to include subsumed unit extension and paramodulation. The performance of each theorem prover was determined. Experimental results were obtained using twenty four selected problems. The performance was measured in terms of the memory use and the execution time. A comparison of results between the five theorem provers using the, ME-TP as the basis was done. The results show that none of the theorem provers, consistently perform better than the others. Two of the selected problems were not proved by SL-TP and one problem was not proved by SLM-TP due to memory problems. The ME-TP, GC-TP and SLM5-TP proved all the selected problems. In some problems, the ME-TP and GC-TP performed better than SLM5-TP. However, the ME-TP and GC-TP had difficulties in some problems in which SLM5-TP performed well.

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Konecny, Jan. "Isotone fuzzy Galois connections and their applications in formal concept analysis". Diss., Online access via UMI:, 2009.

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Thesis (Ph. D.)--State University of New York at Binghamton, Thomas J. Watson School of Engineering and Applied Science, Department of Systems Science and Industrial Engineering, 2009.
Includes bibliographical references.

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Bueno-Soler, Juliana 1976. "Multimodalidades anodicas e catodicas : a negação controlada em logicas multimodais e seu poder expressivo". [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/280387.

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Orientador: Itala Maria Loffredo D'Ottaviano
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas
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Resumo: O presente trabalho tem por objetivo investigar o papel da negação no âmbito das modalidades, de forma a poder esclarecer até que ponto a negação pode ser atenuada, controlada ou mesmo totalmente eliminada em favor da melhor expressabilidade lógica de certas teorias, asserções ou raciocínios que sofrem os efeitos da negação. Contudo, atenuar ou eliminar a negação tem um alto preço: métodos tradicionais em lógica podem deixar de ser válidos e certos resultados, como teoremas de completude para sistemas lógicos, podem ser derrogados. Do ponto de vista formal, a questão central que investigamos aqui e até que ponto tais métodos podem ser restabelecidos. Com tal finalidade, iniciamos nosso estudo a partir do que denominamos sistemas anódicos" (sem negação) e, a posteriori, introduzimos gradativamente o elemento catódico" (negações, com diversas gradações e diferentes características) nos sistemas modais por meio de combinações com certas lógicas paraconsistentes, as chamadas lógicas da inconsistência formal (LFIs). Todos os sistemas tratados são semanticamente caracterizados por semânticas de mundos possíveis; resultados de incompletude são também obtidos e discutidos. Obtemos ainda semânticas modais de traduções possíveis para diversos desses sistemas. Avançamos na direção das multimodalidades, investigando os assim chamados sistemas multimodais anódicos e catódicos. Finalmente, procuramos avaliar criticamente o alcance e o interesse dos resultados obtidos na direção da racionalidade sensível à negação.
Abstract: The present work aims to investigate the role of negations in the scope of modalities and in the reasoning expressed by modalities. The investigation starts from what we call anodic" systems (without any form of negation) and gradually reaches the cathodic" elements, where negations are introduced by means of combining modal logics with certain paraconsistent logics known as logics of formal inconsistency (LFIs). We obtain completeness results for all treated systems, and also show that certain incompleteness results can be obtained. The class of the investigated systems includes all normal modal logics that are extended by means of the schema Gk;l;m;n due to E. J. Lemmon and D. Scott combined with LFIs. We also tackle the question of obtaining modal possible-translations semantics for these systems. Analogous results are analyzed in the scope of multimodalities, where anodic as much as cathodic logics are studied. Finally, we advance a critical evaluation of the reach and scope of all the results obtained to what concerns expressibility of reasoning considered to be sensible to negation. We also critically assess the obtained results in contrast with problems of rationality that are sensible to negation.
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40

Lawley, Michael John y n/a. "Program Transformation for Proving Database Transaction Safety". Griffith University. School of Computing and Information Technology, 2000. http://www4.gu.edu.au:8080/adt-root/public/adt-QGU20070228.150125.

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In this thesis we propose the use of Dijkstra's concept of a predicate transformer [Dij75] for the determination of database transaction safety [SS89] and the generation of simple conditions to check that a transaction will not violate the integrity constraints in the case that it is not safe. The generation of this simple condition is something that can be done statically, thus providing a mechanism for generating safe transactions. Our approach treats a database as state, a database transaction as a program, and the database's integrity constraints as a postcondition in order to use a predicate transformer [Dij75] to generate a weakest precondition. We begin by introducing a set-oriented update language for relational databases for which a predicate transformer is then defined. Subsequently, we introduce a more powerful update language for deductive databases and define a new predicate transformer to deal with this language and the more powerful integrity constraints that can be expressed using recursive rules. Next we introduce a data model with object-oriented features including methods, inheritance and dynamic overriding. We then extend the predicate transformer to handle these new features. For each of the predicate transformers, we prove that they do indeed generate a weakest precondition for a transaction and the database integrity constraints. However, the weakest precondition generated by a predicate transformer still involves much redundant checking. For several general classes of integrity constraint, including referential integrity and functional dependencies, we prove that the weakest precondition can be substantially further simplified to avoid checking things we already know to be true under the assumption that the database currently satisfies its integrity con-straints. In addition, we propose the use of the predicate transformer in combination with meta-rules that capture the exact incremental change to the database of a particular transaction. This provides a more general approach to generating simple checks for enforcing transaction safety. We show that this approach is superior to known existing previous approaches to the problem of efficient integrity constraint checking and transaction safety for relational, deductive, and deductive object-oriented databases. Finally we demonstrate several further applications of the predicate transformer to the problems of schema constraints, dynamic integrity constraints, and determining the correctness of methods for view updates. We also show how to support transactions embedded in procedural languages such as C.

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41

Paddock, Jeff. "Informed by silence". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/MQ62412.pdf.

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Lawley, Michael John. "Program Transformation for Proving Database Transaction Safety". Thesis, Griffith University, 2000. http://hdl.handle.net/10072/365511.

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In this thesis we propose the use of Dijkstra's concept of a predicate transformer [Dij75] for the determination of database transaction safety [SS89] and the generation of simple conditions to check that a transaction will not violate the integrity constraints in the case that it is not safe. The generation of this simple condition is something that can be done statically, thus providing a mechanism for generating safe transactions. Our approach treats a database as state, a database transaction as a program, and the database's integrity constraints as a postcondition in order to use a predicate transformer [Dij75] to generate a weakest precondition. We begin by introducing a set-oriented update language for relational databases for which a predicate transformer is then defined. Subsequently, we introduce a more powerful update language for deductive databases and define a new predicate transformer to deal with this language and the more powerful integrity constraints that can be expressed using recursive rules. Next we introduce a data model with object-oriented features including methods, inheritance and dynamic overriding. We then extend the predicate transformer to handle these new features. For each of the predicate transformers, we prove that they do indeed generate a weakest precondition for a transaction and the database integrity constraints. However, the weakest precondition generated by a predicate transformer still involves much redundant checking. For several general classes of integrity constraint, including referential integrity and functional dependencies, we prove that the weakest precondition can be substantially further simplified to avoid checking things we already know to be true under the assumption that the database currently satisfies its integrity con-straints. In addition, we propose the use of the predicate transformer in combination with meta-rules that capture the exact incremental change to the database of a particular transaction. This provides a more general approach to generating simple checks for enforcing transaction safety. We show that this approach is superior to known existing previous approaches to the problem of efficient integrity constraint checking and transaction safety for relational, deductive, and deductive object-oriented databases. Finally we demonstrate several further applications of the predicate transformer to the problems of schema constraints, dynamic integrity constraints, and determining the correctness of methods for view updates. We also show how to support transactions embedded in procedural languages such as C.
Thesis (PhD Doctorate)
Doctor of Philosophy (PhD)
School of Computing and Information Technology
Faculty of Information and Communication Technology
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43

Brinkerhoff, Jennifer Alder. "Applying Toulmin's Argumentation Framework to Explanations in a Reform Oriented Mathematics Class". Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1960.pdf.

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Duff, Karen Malina. "What Are Some of the Common Traits in the Thought Processes of Undergraduate Students Capable of Creating Proof?" Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1856.pdf.

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Alves, Marcos Antonio 1975. "Lógica e Informação : uma análise da consequência lógica a partir de uma perspectiva quantitativa da informação". [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/280390.

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Orientador: Ítala Maria Loffredo D'Ottaviano
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas
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Resumo: Nosso objetivo nesta Tese é desenvolver uma definição da consequência lógica a partir de uma perspectiva quantitativa da informação. O trabalho pode ser dividido em duas partes. Na primeira, que consiste dos três capítulos iniciais, fazemos um estudo crítico de algumas das principais concepções usuais de consequência lógica. No primeiro capítulo expomos três das características centrais da consequência lógica, quais sejam, necessidade, formalidade e anterioridade. Apresentamos uma noção geral de consequência lógica, a partir da qual classificamos as diferentes noções de consequência lógica em clássicas e não-clássicas. Nos dois próximos capítulos tratamos da consequência lógica a partir das perspectivas sintática e semântica, analisando em que medida elas satisfazem as três características acima enunciadas. Na segunda parte, constituída dos três últimos capítulos, desenvolvemos a nossa proposta. No quarto capítulo expomos criticamente a concepção de informação a ser utilizada na Tese. No quinto capítulo construímos uma semântica probabilística para a lógica sentencial clássica, mostrando os seus principais resultados. A partir desta semântica, definimos, no sexto capítulo, a quantidade de informação em uma fórmula da lógica sentencial clássica e a consequência lógica probabilística. Feito isso, definimos a consequência lógica informacional, demonstrando os seus principais resultados
Abstract: Our goal in this work is to develop a definition of logical consequence from a quantitative perspective of information. The work can be divided into two parts. The first, consisting of three chapters, we make a critical study of some key concepts usual logical consequence. In the first chapter we expose three of the central features of logical consequence, namely, necessity, formality and apriority. We present a general notion of logical consequence, from which classify the different notions of logical consequence in classical and non-classical. In the next two chapters deal with the logical consequence from the syntactic and semantic perspectives, analyzing the extent to which they meet the three above features. In the second part, which consists of the last three chapters, we developed our proposal. In the fourth chapter critically expose the concept of information to be used in the thesis. In the fifth chapter we build a probabilistic semantics for classical sentential logic, showing its main results. From this semantics, we define, in the sixth chapter, the amount of information in a formula of classical sentence logic and probabilistic logical consequence. That done, we define the informational logical consequence, showing its main results
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46

Suguitani, Leandro Oliva 1976. "Sobre a lógica e a aritmética das relações". [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/280386.

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Orientador: Itala Maria Loffredo D'Ottaviano
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas
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Resumo: O resumo poderá ser visualizado no texto completo da tese digital
Abstract: The complete abstract is available with the full electronic document.
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47

Rodrigues, Tarcísio Genaro. "Sobre os fundamentos de programação lógica paraconsistente". [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/278897.

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Orientador: Marcelo Esteban Coniglio
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas
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Resumo: A Programação Lógica nasce da interação entre a Lógica e os fundamentos da Ciência da Computação: teorias de primeira ordem podem ser interpretadas como programas de computador. A Programação Lógica tem sido extensamente utilizada em ramos da Inteligência Artificial tais como Representação do Conhecimento e Raciocínio de Senso Comum. Esta aproximação deu origem a uma extensa pesquisa com a intenção de definir sistemas de Programação Lógica paraconsistentes, isto é, sistemas nos quais seja possível manipular informação contraditória. Porém, todas as abordagens existentes carecem de uma fundamentação lógica claramente definida, como a encontrada na programação lógica clássica. A questão básica é saber quais são as lógicas paraconsistentes subjacentes a estas abordagens. A presente dissertação tem como objetivo estabelecer uma fundamentação lógica e conceitual clara e sólida para o desenvolvimento de sistemas bem fundados de Programação Lógica Paraconsistente. Nesse sentido, este trabalho pode ser considerado como a primeira (e bem sucedida) etapa de um ambicioso programa de pesquisa. Uma das teses principais da presente dissertação é que as Lógicas da Inconsistência Formal (LFI's), que abrangem uma enorme família de lógicas paraconsistentes, proporcionam tal base lógica. Como primeiro passo rumo à definição de uma programação lógica genuinamente paraconsistente, demonstramos nesta dissertação uma versão simplificada do Teorema de Herbrand para uma LFI de primeira ordem. Tal teorema garante a existência, em princípio, de métodos de dedução automática para as lógicas (quantificadas) em que o teorema vale. Um pré-requisito fundamental para a definição da programação lógica é justamente a existência de métodos de dedução automática. Adicionalmente, para a demonstração do Teorema de Herbrand, são formuladas aqui duas LFI's quantificadas através de sequentes, e para uma delas demonstramos o teorema da eliminação do corte. Apresentamos também, como requisito indispensável para os resultados acima mencionados, uma nova prova de correção e completude para LFI's quantificadas na qual mostramos a necessidade de exigir o Lema da Substituição para a sua semântica
Abstract: Logic Programming arises from the interaction between Logic and the Foundations of Computer Science: first-order theories can be seen as computer programs. Logic Programming have been broadly used in some branches of Artificial Intelligence such as Knowledge Representation and Commonsense Reasoning. From this, a wide research activity has been developed in order to define paraconsistent Logic Programming systems, that is, systems in which it is possible to deal with contradictory information. However, no such existing approaches has a clear logical basis. The basic question is to know what are the paraconsistent logics underlying such approaches. The present dissertation aims to establish a clear and solid conceptual and logical basis for developing well-founded systems of Paraconsistent Logic Programming. In that sense, this text can be considered as the first (and successful) stage of an ambitious research programme. One of the main thesis of the present dissertation is that the Logics of Formal Inconsistency (LFI's), which encompasses a broad family of paraconsistent logics, provide such a logical basis. As a first step towards the definition of genuine paraconsistent logic programming we shown, in this dissertation, a simplified version of the Herbrand Theorem for a first-order LFI. Such theorem guarantees the existence, in principle, of automated deduction methods for the (quantified) logics in which the theorem holds, a fundamental prerequisite for the definition of logic programming over such logics. Additionally, in order to prove the Herbrand Theorem we introduce sequent calculi for two quantified LFI's, and cut-elimination is proved for one of the systems. We also present, as an indispensable requisite for the above mentioned results, a new proof of soundness and completeness for first-order LFI's in which we show the necessity of requiring the Substitution Lemma for the respective semantics
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Reis, Teofilo de Souza. "Conectivos flexíveis : uma abordagem categorial às semânticas de traduções possíveis". [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/278896.

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Orientador: Marcelo Esteban Coniglio
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas
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Resumo: Neste trabalho apresentamos um novo formalismo de decomposição de Lógicas, as Coberturas por Traduções Possíveis, ou simplesmente CTPs. As CTPs constituem uma versão formal das Semânticas de Traduções Possíveis, introduzidas por W. Carnielli em 1990. Mostramos como a adoção de um conceito mais geral de morfismo de assinaturas proposicionais (usando multifunções no lugar de funções) nos permite definir uma categoria Sig?, na qual os conectivos, ao serem traduzidos de uma assinatura para outra, gozam de grande flexibilidade. A partir de Sig?, contruímos a categoria Log? de lógicas tarskianas e morfismos (os quais são funções obtidas a partir de um morfismo de assinaturas, isto é, de uma multifunção). Estudamos algumas características de Sig? e Log?, afim de verificar que estas categorias podem de fato acomodar as construções que pretendemos apresentar. Mostramos como definir em Log? o conjunto de traduções possíveis de uma fórmula, e a partir disto definimos a noção de CTP para uma lógica L. Por fim, exibimos um exemplo concreto de utilização desta nova ferramenta, e discutimos brevemente as possíveis abordagens para uma continuação deste trabalho.
Abstract: We present a general study of a new formalism of decomposition of logics, the Possible- Translations Coverings (in short PTC 's) which constitute a formal version of Possible-Translations Semantics, introduced by W. Carnielli in 1990. We show how the adoption of a more general notion of propositional signatures morphism allows us to define a category Sig?, in which the connectives, when translated from a signature to another one, enjoy of great flexibility. Essentially, Sig? -morphisms will be multifunctions instead of functions. From Sig? we construct the category Log? of tarskian logics and morphisms between them (these .are functions obtained from signature morphisms, that is, from multifunctions) . We show how to define in Log? the set of possible translations of a given formula, and we define the notion of a PTC for a logic L. We analyze some properties of PTC 's and give concrete examples of the above mentioned constructions. We conclude with a discussion of the approaches to be used in a possible continuation of these investigations.
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Araújo, Anderson. "Uma abordagem modelo-teórica da computabilidade de Turing clássica". [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/281062.

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Orientador: Walter Alexandre Carnielli
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas
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Resumo: Esta tese propõe uma nova abordagem da computabilidade de Turing clássica, denominada abordagem modelo-teórica. De acordo com essa abordagem, estruturas e teorias são associadas às máquinas de Turing a fim de investigar as características de suas computações. Uma abordagem modelo-teórica da computabilidade de Turing através da lógica de primeira ordem é desenvolvida, e resultados de correspondência, correção, representação e completude entre máquinas, estruturas e teorias de Turing são demonstrados. Nessa direção, os resultados obtidos a respeito de propriedades tais como estabilidade, absoluticidade, universalidade e logicidade enfatizam as potencialidades da computabilidade modelo-teórica de primeira ordem. Demonstra-se que a lógica subjacente às teorias de Turing é uma lógica minimal intuicio-nista, sendo capaz, inclusive, de internalizar um operador de negação clássico. As técnicas formuladas nesta tese permitem, sobretudo, investigar a computabilidade de Turing em modelos não-padrão da aritmética. Nesse contexto, uma nova perspectiva acerca do fenômeno de Tennenbaum e uma avaliação crítica da abordagem de Dershowitz e Gurevich da tese de Church-Turing sào apresentadas. Como conseqüência, postula-se um princípio de interna-lidade aritmética na computabilidade, segundo o qual o próprio conceito de computação é relativo ao modelo aritmético em que as máquinas de Turing operam. Assim, a tese unifica as caracterizações modelo-aritméticas do problema P versus NP existentes na literatura, revelando, por fim, uma barreira modelo-aritmética para a possibilidade de solução desse problema central em complexidade computacional no que diz respeito a certos métodos. Em sua totalidade, a tese sustenta que características cruciais do conceito de computação podem ser vislumbradas a partir da dualidade entre finitude e infinitude presente na distinção entre números naturais padrão e não-padrão
Abstract: This PhD thesis proposes a new approach to classical Turing computability, called a model-theoretic approach. In that approach, structures and theories are associated to Turing machines in order to study the characteristics of their computations. A model-theoretic approach to Turing computability through first-order logic is developed, and first results about correspondence, soundness, representation and completeness among Turing machines, structures and theories are proved. In this line, the results about properties as stability, absoluteness, universality and logicality emphasize the importance of the model-theoretic standpoint. It is shown that the underlying logic of Turing theories is a minimal intuicionistic logic, being able to internalize a classical negation operator. The techniques obtained in the present dissertation permit us to examine the Turing computability over nonstandard models of arithmetic as well. In this context, a new perspective about Tennenbaum's phenomenon and a critical evaluation of Dershowitz and Gurevich's account on Church-Turing's thesis are given. As a consequence, an arithmetic internality principle is postulated, according to which the concept of computation itself is relative to the arithmetic model that Turing machines operate. In this way, the dissertation unifies the existing model-arithmetic characterizations of the P versus NP problem, leading, as a by-product, to a model-arithmetic barrier to the solvability of that central problem in computational complexity with respect to certain techniques. As a whole, the dissertation sustains that crucial characteristics of the concept of computation may be understood from the duality between finiteness and infiniteness inherent within the distinction between standard and nonstandard natural numbers
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Secco, Érica Fernanda Aparecida. "Teoria de conjuntos fuzzy e aplicações /". Rio Claro, 2013. http://hdl.handle.net/11449/94362.

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Orientador: Renata Zotin Gomes de Oliveira
Banca: Elaine Cristina Catapani Poletti
Banca: Wladimir Seixas
Resumo: Neste traboalho são apresentados alguns conceitos básicos da Teoria de Conjuntos Fuzzy como: operações comu conjunto fuzzy, Princípio de Extensão de Zadeh, números fuzzy e noçoes de lógica fuzzy. As relações são apresentadas com o objetivo de tratarmos de sistemas baseados em regras fuzzy e algumas aplicações
Abstract: In this paper are presented some basic concepts of Fuzzy Sets Theory: operation with fuzzy sets, Zadeh extension principle, fuzzy numbers and fuzzy logic. The fuzzy relations are presented for the purpose of treating systems based on fuzzy rules and some application
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