Rozprawy doktorskie: „Mathematical and symbolic”

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Redelinghuys, Gideon. "Symbolic string execution". Thesis, Stellenbosch : Stellenbosch University, 2012. http://hdl.handle.net/10019.1/20335.

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Thesis (MSc)--Stellenbosch University, 2012.
ENGLISH ABSTRACT: Symbolic execution is a well-established technique for automated test generation and for nding errors in complex code. Most of the focus has however been on programs that manipulate integers, booleans, and even, references in object-oriented programs. Recently researchers have started looking at programs that do lots of string processing, motivated, in part, by the popularity of the web and the risk that errors in web servers may lead to security violations. Attempts to extend symbolic execution to the domain of strings are mainly divided into one of two camps: automata-based approaches and approaches based on bitvector analysis. Here we investigate these two approaches in a uni ed setting, namely the symbolic execution framework of Java PathFinder. We describe the implementations of both approaches and then do an evaluation to show under what circumstances each approach performs well (or not so well). We also illustrate the usefulness of the symbolic execution of strings by nding errors in real-world examples.
AFRIKAANSE OPSOMMING: Simboliese uitvoering is 'n bekende tegniek vir automatiese genereering van toetse en om foute te vind in ingewikkelde bronkode. Die fokus sover was grotendeels op programme wat gebruik maak van heelgetalle, boolse waardes en selfs verwysings in objek geörienteerde programme. Navorsers het onlangs begin kyk na programme wat baie gebruik maak van string prosessering, deelteliks gemotiveerd deur die populariteit van die web en die gepaardgaande risiko's daarvan. Vorige implementasies van simboliese string uitvoering word binne twee kampe verdeel: die automata gebaseerde benadering en bitvektoor gebaseerde benadering. Binne hierdie tesis word die twee benaderings onder een dak gebring, naamliks Java PathFinder. Die implentasie van beide benaderings word bespreek en ge-evalueer om die omstandighede uit te wys waarbinne elk beter sou vaar. Die nut van simboliese string uitvoering word geïllustreer deur dit toe te pas in foutiewe regte wêreld voorbeelde.

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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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Uwimbabazi, Aline. "Extended probabilistic symbolic execution". Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/85804.

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Thesis (MSc)--Stellenbosch University, 2013.
ENGLISH ABSTRACT: Probabilistic symbolic execution is a new approach that extends the normal symbolic execution with probability calculations. This approach combines symbolic execution and model counting to estimate the number of input values that would satisfy a given path condition, and thus is able to calculate the execution probability of a path. The focus has been on programs that manipulate primitive types such as linear integer arithmetic in object-oriented programming languages such as Java. In this thesis, we extend probabilistic symbolic execution to handle data structures, thus allowing support for reference types. Two techniques are proposed to calculate the probability of an execution when the programs have structures as inputs: an approximate approach that assumes probabilities for certain choices stay fixed during the execution and an accurate technique based on counting valid structures. We evaluate these approaches on an example of a Binary Search Tree and compare it to the classic approach which only take symbolic values as input.
AFRIKAANSE OPSOMMING: Probabilistiese simboliese uitvoering is ’n nuwe benadering wat die normale simboliese uitvoering uitbrei deur waarksynlikheidsberekeninge by te voeg. Hierdie benadering kombineer simboliese uitvoering en modeltellings om die aantal invoerwaardes wat ’n gegewe padvoorwaarde sal bevredig, te beraam en is dus in staat om die uitvoeringswaarskynlikheid van ’n pad te bereken. Tot dus vêr was die fokus op programme wat primitiewe datatipes manipuleer, byvoorbeeld lineêre heelgetalrekenkunde in objek-geörienteerde tale soos Java. In hierdie tesis brei ons probabilistiese simboliese uitvoering uit om datastrukture, en dus verwysingstipes, te dek. Twee tegnieke word voorgestel om die uitvoeringswaarskynlikheid van ’n program met datastrukture as invoer te bereken. Eerstens is daar die benaderingstegniek wat aanneem dat waarskynlikhede vir sekere keuses onveranderd sal bly tydens die uitvoering van die program. Tweedens is daar die akkurate tegniek wat gebaseer is op die telling van geldige datastrukture. Ons evalueer hierdie benaderings op ’n voorbeeld van ’n binêre soekboom en vergelyk dit met die klassieke tegniek wat slegs simboliese waardes as invoer neem.

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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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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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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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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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Lindberg, Maja. "The innate ability to cope with mathematics : A comparative fMRI study of children's and adults' neural activity during non-symbolic mathematical tasks". Thesis, Linköpings universitet, Institutionen för datavetenskap, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-158199.

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Humans as well as animals are born with a number sense, an innate ability to make approximations (Dehaene, 1997). However, low numeracy is an issue today and have a larger impact on the individuals lives than poor reading abilities (Parsons & Bynner, 2006). To be able to understand the cause of developmental dyscalculia the fully functional brain coping with numbers must be further investigated. The aim of this study is hence to examine how the number sense develop during maturation. Seven children and seven adults (all healthy) have participated in this neuro imaging study. The participants were required to perform a non-symbolic mathematic task and a control task both outside and within the scanner. The results indicate a transition of active areas in the brain during maturation. In the children prefrontal areas were recruited, and for the adults the activation was primarily found in the parietal cortex. These findings, despite low statistical power indicates a shift of neural activity from a more cognitive demanding task into an automated task. Further studies will have to replicate the experiment to validate the findings of this study.

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Wheeler, Russell Clark. "Using symbolic dynamical systems: A search for knot invariants". CSUSB ScholarWorks, 1998. https://scholarworks.lib.csusb.edu/etd-project/3033.

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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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Steffy, Daniel E. "Topics in exact precision mathematical programming". Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/39639.

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The focus of this dissertation is the advancement of theory and computation related to exact precision mathematical programming. Optimization software based on floating-point arithmetic can return suboptimal or incorrect resulting because of round-off errors or the use of numerical tolerances. Exact or correct results are necessary for some applications. Implementing software entirely in rational arithmetic can be prohibitively slow. A viable alternative is the use of hybrid methods that use fast numerical computation to obtain approximate results that are then verified or corrected with safe or exact computation. We study fast methods for sparse exact rational linear algebra, which arises as a bottleneck when solving linear programming problems exactly. Output sensitive methods for exact linear algebra are studied. Finally, a new method for computing valid linear programming bounds is introduced and proven effective as a subroutine for solving mixed-integer linear programming problems exactly. Extensive computational results are presented for each topic.

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Xu, Dan. "Superstatistics and symbolic dynamics of share price returns on different time scales". Thesis, Queen Mary, University of London, 2017. http://qmro.qmul.ac.uk/xmlui/handle/123456789/24873.

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Share price returns on different time scales can be well modeled by a superstatistical dynamics. We provide an investigation which type of superstatistics is most suitable to properly describe share price dynamics on various time scales. It is shown that while chi-square-superstatistics works well on a time scale of days, on a much smaller time scale of minutes the price changes are better described by lognormal superstatistics. The system dynamics thus exhibits a transition from lognormal to chi-square-superstatistics as a function of time scale. We discuss a more general model interpolating between both statistics which fits the observed data very well. We also present results on correlation functions of the extracted superstatistical volatility parameter, which exhibits exponential decay for returns on large time scales, whereas for returns on small time scales there are long-range correlations and power-law decays. We also apply the symbolic dynamics technique from dynamical system theory to analyse the coarse-grained evolution of share price returns. A nontrivial spectrum of Renyi entropies is found. We study how the spectrum depends on the time scale of returns, the sector of stocks considered, as well as the number of symbols used for the symbolic description. Overall our analysis confirms that in the symbol space transition probabilities of observed share price returns depend on the entire history of previous symbols, thus emphasizing the need for a model of share price evolution based on non-Markovian stochastic processes. Our method allows for quantitative comparisons of entirely different complex systems, for example the statistics of coarse-grained share price returns using 4 symbols can be compared with that of other complex systems.

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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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湯志輝 i 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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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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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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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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Smart, Angela. "Undergraduate Students’ Connections Between the Embodied, Symbolic, and Formal Mathematical Worlds of Limits and Derivatives: A Qualitative Study Using Tall’s Three Worlds of Mathematics". Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/24247.

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Calculus at the university level is taken by thousands of undergraduate students each year. However, a significant number of students struggle with the subject, resulting in poor problem solving, low achievement, and high failure rates in the calculus courses overall (e.g., Kaput, 1994; Szydlik, 2000; Tall, 1985; Tall & Ramos, 2004; White & Mitchelmore, 1996). This is cause for concern as the lack of success in university calculus creates further barriers for students who require the course for their programs of study. This study examines this issue from the perspective of Tall’s Three Worlds of Mathematics (Tall, 2004a, 2004b, 2008), a theory of mathematics and mathematical cognitive development. A fundamental argument of Tall’s theory suggests that connecting between the different mathematical worlds, named the Embodied-Conceptual, Symbolic-Proceptual, and Formal-Axiomatic worlds, is essential for full cognitive development and understanding of mathematical concepts. Working from this perspective, this research examined, through the use of calculus task questions and semi-structured interviews, how fifteen undergraduate calculus students made connections between the different mathematical worlds for the calculus topics of limits and derivatives. The analysis of the findings suggests that how the students make connections can be described by eight different Response Categories. The study also found that how the participants made connections between mathematical worlds might be influenced by the type of questions that are asked and their experience in calculus courses. I infer that these Response Categories have significance for this study and offer potential for further study and educational practice. I conclude by identifying areas of further research in regards to calculus achievement, the Response Categories, and other findings such as a more detailed study of the influence of experience.

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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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Bester, Willem Hendrik Karel. "Bug-finding and test case generation for java programs by symbolic execution". Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/85832.

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Thesis (MSc)--Stellenbosch University, 2013.
ENGLISH ABSTRACT: In this dissertation we present a software tool, Artemis, that symbolically executes Java virtual machine bytecode to find bugs and automatically generate test cases to trigger the bugs found. Symbolic execution is a technique of static software analysis that entails analysing code over symbolic inputs—essentially, classes of inputs—where each class is formulated as constraints over some input domain. The analysis then proceeds in a path-sensitive way adding the constraints resulting from a symbolic choice at a program branch to a path condition, and branching non-deterministically over the path condition. When a possible error state is reached, the path condition can be solved, and if soluble, value assignments retrieved to be used to generate explicit test cases in a unit testing framework. This last step enhances confidence that bugs are real, because testing is forced through normal language semantics, which could prevent certain states from being reached. We illustrate and evaluate Artemis on a number of examples with known errors, as well as on a large, complex code base. A preliminary version of this work was successfully presented at the SAICSIT conference held on 1–3 October 2012, in Centurion, South Africa.
AFRIKAANSE OPSOMMING: In die dissertasie bied ons ’n stuk sagtewaregereedskap, Artemis, aan wat biskode van die Java virtuele masjien simbolies uitvoer om foute op te spoor en toetsgevalle outomaties voort te bring om die foute te ontketen. Simboliese uitvoering is ’n tegniek van statiese sagteware-analise wat behels dat kode oor simboliese toevoere—in wese, klasse van toevoer—geanaliseer word, waar elke klas geformuleer word as beperkinge oor ’n domein. Die analise volg dan ’n pad-sensitiewe benadering deur die domeinbeperkinge, wat volg uit ’n simboliese keuse by ’n programvertakking, tot ’n padvoorwaarde by te voeg en dan nie-deterministies vertakkings oor die padvoorwaarde te volg. Wanneer ’n moontlike fouttoestand bereik word, kan die padvoorwaarde opgelos word, en indien dit oplaasbaar is, kan waardetoekennings verkry word om eksplisiete toetsgevalle in ’n eenheidstoetsingsraamwerk te formuleer. Die laaste stap verhoog vertroue dat die foute gevind werklik is, want toetsing word deur die normale semantiek van die taal geforseer, wat sekere toestande onbereikbaar maak. Ons illustreer en evalueer Artemis met ’n aantal voorbeelde waar die foute bekend is, asook op ’n groot, komplekse versameling kode. ’n Voorlopige weergawe van die´ werk is suksesvol by die SAICSIT-konferensie, wat van 1 tot 3 Oktober 2012 in Centurion, Suid-Afrika, gehou is, aangebied.

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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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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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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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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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Ott, Natalie [Verfasser], i Roland [Akademischer Betreuer] Brünken. "From dual coding to multiple coding : Effects of multiple symbolic representations for mathematical understanding / Natalie Ott ; Betreuer: Roland Brünken". Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2017. http://d-nb.info/1152094300/34.

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Ott, Natalie Verfasser], i Roland [Akademischer Betreuer] [Brünken. "From dual coding to multiple coding : Effects of multiple symbolic representations for mathematical understanding / Natalie Ott ; Betreuer: Roland Brünken". Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:291-scidok-ds-268806.

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Rajagopalan, Jayendar. "Symbolic and connectionist machine learning techniques for short-term electric load forecasting". Thesis, This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-08222009-040506/.

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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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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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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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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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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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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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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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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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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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37

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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38

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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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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40

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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41

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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42

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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43

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
Made available in DSpace on 2018-08-10T04:02:35Z (GMT). No. of bitstreams: 1 BatistaNeto_AlbertoLeopoldo_M.pdf: 764702 bytes, checksum: 38e943aef1a6e4a5f892916208eca7a5 (MD5) Previous issue date: 2007
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
Mestre em Filosofia

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44

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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45

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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46

Fransson, Linnea. "Skolans underskattade språk : En studie om användningen av det matematiska symbolspråket i den gymnasiala undervisningen". Thesis, Linnéuniversitetet, Institutionen för matematikdidaktik (MD), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-27410.

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Symboler har alltid varit en viktig del av matematik, därför är det inte konstigt att kunskaperom symbolspråket behövs för att uppnå en full förståelse av ämnet. Den här studiensyftar därför på att utreda användningen av det symboliska språket i den svenska gymnasialaundervisningen ur ett språkvetenskapligt perspektiv. Empirin till det här arbetetbestår av 52 elevlösningar till ett test i matematik samt transkribering av en parintervju.Det insamlade materialet har analyserats utifrån teorier om den metalingvistiska medvetenhetensamt symbolernas semiotiska och epistemologiska funktioner. Det matematiskasymbolspråkets roll i styrdokumenten har också belysts i det här arbetet. Från elevernasfel i testet var det möjligt att åskådliggöra vikten av den metalingvistiska medvetenhetenoch den semiotiska medlingen i algebrainlärningen. Slutligen blev det även tydligt att detmatematiska symbolspråket behöver en mer explicit roll i den svenska matematikundervisningen.
Symbols have always been an important part of mathematics, which is why learning thesymbolic language is necessary in order to acquire a full understanding of the subject.This study aims to investigate the use of the symbolic language in the Swedish uppersecondary school from a linguistic perspective. The data for this study consists of samplesfrom 52 student solutions from a mathematical test, together with one transcribed groupinterview, where two students participated. The analysis is based on theories about themetalinguistic awareness and symbols’ semiotic and epistemological functions. The roleof the mathematical symbolic language described in the steering documents has also beenconsidered in the study. From the mistakes made in the test, it was possible to visualisethe importance of the metalinguistic awareness and the semiotic mediation in algebralearning. In the end, it also became clear that the mathematical symbolic language needsa more explicit role in the Swedish mathematics education.

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Lawley, Michael John, i 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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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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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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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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