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Dissertations / Theses on the topic 'Theorem proving'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

Ballarin, Clemens Michael. "Computer algebra and theorem proving." Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624429.

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2

Ji, Kailiang. "Model checking and theorem proving." Sorbonne Paris Cité, 2015. http://www.theses.fr/2015USPCC250.

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Le model checking est une technique de vérification automatique de propriétés de correction de systèmes finis. Normalement, les outils de model checking ont deux caractéristiques remarquables : ils sont automatisés et ils produisent un contre-exemple si le système ne satisfait pas la propriété. La Déduction Modulo est une reformulation de la logique des prédicats où certains axiomes---possiblement tous---sont remplacés par des règles de réécriture. Le but de cette dissertation est de donner un encodage de propriétés temporelles exprimées en CTL en des formules du premier ordre, en exprimant l'

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3

Kakkad, Aman. "Machine Learning for Automated Theorem Proving." Scholarly Repository, 2009. http://scholarlyrepository.miami.edu/oa_theses/223.

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Developing logic in machines has always been an area of concern for scientists. Automated Theorem Proving is a field that has implemented the concept of logical consequence to a certain level. However, if the number of available axioms is very large then the probability of getting a proof for a conjecture in a reasonable time limit can be very small. This is where the ability to learn from previously proved theorems comes into play. If we see in our own lives, whenever a new situation S(NEW) is encountered we try to recollect all old scenarios S(OLD) in our neural system similar to the new one

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4

Folkler, Andreas. "Automated Theorem Proving : Resolution vs. Tableaux." Thesis, Blekinge Tekniska Högskola, Institutionen för programvaruteknik och datavetenskap, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-5531.

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The purpose of this master thesis was to investigate which of the two methods, resolution and tableaux, that is the most appropriate for automated theorem proving. This was done by implementing an automated theorem prover, comparing and documenting implementation problems, and measuring proving efficiency. In this thesis, I conclude that the resolution method might be more suitable for an automated theorem prover than tableaux, in the aspect of ease of implementation. Regarding the efficiency, the test results indicate that resolution is the better choice.<br>Syftet med detta magisterarbete va

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5

Amjad, Hasan. "Combining model checking and theorem proving." Thesis, University of Cambridge, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.616074.

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6

Bridge, J. P. "Machine learning and automated theorem proving." Thesis, University of Cambridge, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.596901.

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Computer programs to find formal proofs of theorems were originally designed as tools for mathematicians, but modern applications are much more diverse. In particular they are used in formal methods to verify software and hardware designs to prevent errors being introduced into systems. Despite this, the high level of human expertise required in their use means that theorem proving tools are not widely used by non-specialists. The work described in this dissertation addresses one aspect of this problem, that of heuristic selection. In theory theorem provers should be automatic; in practice the

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7

Hou, Tie. "Interactive theorem proving and program extraction." Thesis, Swansea University, 2014. https://cronfa.swan.ac.uk/Record/cronfa42845.

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8

Syme, Donald Robert. "Declarative theorem proving for operational semantics." Thesis, University of Cambridge, 1999. https://www.repository.cam.ac.uk/handle/1810/252967.

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This dissertation is concerned with techniques for formally checking properties of systems that are described by operational semantics. We describe innovations and tools for tackling this problem, and a large case study in the application of these tools. The innovations centre on the notion of "declarative theorem proving", and in particular techniques for declarative proof description. We define what we mean by this, assess its costs and benefits, and describe the impact of this approach with respect to four fundamental areas of theorem prover design: specification, proof description, automat

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9

Harrison, John Robert. "Theorem proving with the real numbers." Thesis, University of Cambridge, 1996. https://www.repository.cam.ac.uk/handle/1810/265488.

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This thesis discusses the use of the real numbers in theorem proving. Typically, theorem provers only support a few 'discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification of floating point hardware and hybrid systems. It also allows the formalization of many more branches of classical mathematics, which is particularly relevant for attempts to inject more rigour into computer algebra systems. Our work is conducted in a version of the HOL theorem prover. We describe the ri

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10

Donato, Pablo. "Deep Inference for Graphical Theorem Proving." Electronic Thesis or Diss., Institut polytechnique de Paris, 2024. http://www.theses.fr/2024IPPAX015.

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Les assistants de preuve sont des logiciels permettant de vérifier rigoureusement des raisonnements mathématiques. Ils peuvent être généraux (comme Coq, Lean, Isabelle...) ou plus spécialisés (comme EasyCrypt). Ils permettent un niveau de précision qui certifie qu'aucune erreur ne peut se produire, mais restent difficiles d'utilisation. Nous proposons un nouveau paradigme de construction de preuves formelles par actions effectuées dans une interface graphique, afin de permettre une utilisation plus confortable et plus intuitive. Intitulé Proof-by-Action, notre paradigme s'appuie sur des princi

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11

Haufe, Sebastian. "Automated Theorem Proving for General Game Playing." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-89998.

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While automated game playing systems like Deep Blue perform excellent within their domain, handling a different game or even a slight change of rules is impossible without intervention of the programmer. Considered a great challenge for Artificial Intelligence, General Game Playing is concerned with the development of techniques that enable computer programs to play arbitrary, possibly unknown n-player games given nothing but the game rules in a tailor-made description language. A key to success in this endeavour is the ability to reliably extract hidden game-specific features from a given gam

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12

Kim, Choon Kyu 1963. "Parallel semantic tree theorem proving with resolutions." Thesis, McGill University, 2004. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=85076.

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Semantic trees have often been used as theoretical tools for showing the unsatisfiability of clauses in first-order predicate logic. Their practicality has been overshadowed, however, by other strategies though considerable effort has been made to improve semantic tree theorem provers over the last decade.<br>In this thesis, we propose building a parallel system through the integration of semantic trees with resolution-refutation. The proposal comes from the observations that the appropriate strategy for one class of theorems is often very different from that for another class and many

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13

Sadri, Fariba. "A theorem-proving approach to database integrity." Thesis, Imperial College London, 1988. http://hdl.handle.net/10044/1/47238.

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14

Ne, Win Toh 1979. "Theorem-proving distributed algorithms with dynamic analysis." Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/29702.

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Thesis (M.Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2003.<br>Includes bibliographical references (p. 185-194).<br>Theorem provers are notoriously hard to use because of the amount of human interaction they require, but they are important tools that can verify infinite state distributed systems. We present a method to make theorem-proving safety properties of distributed algorithms more productive by reducing human intervention. We model the algorithms as I/O automata, render the automata executable, and analyze the test executions with

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15

Martin, Andrew Philip. "Machine-assisted theorem-proving for software engineering." Thesis, University of Oxford, 1994. http://ora.ox.ac.uk/objects/uuid:728d3cee-1dfe-4186-a49f-52b33cbc6551.

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16

Gill, David Michael. "Automatic theorem proving programs and group presentations." Thesis, University of St Andrews, 1995. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.268121.

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17

Zacchiroli, Stefano <1979&gt. "User interaction widgets for interactive theorem proving." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2007. http://amsdottorato.unibo.it/616/1/Tesi_Zacchiroli.pdf.

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Matita (that means pencil in Italian) is a new interactive theorem prover under development at the University of Bologna. When compared with state-of-the-art proof assistants, Matita presents both traditional and innovative aspects. The underlying calculus of the system, namely the Calculus of (Co)Inductive Constructions (CIC for short), is well-known and is used as the basis of another mainstream proof assistant—Coq—with which Matita is to some extent compatible. In the same spirit of several other systems, proof authoring is conducted by the user as a goal directed proof search, using

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18

Zacchiroli, Stefano <1979&gt. "User interaction widgets for interactive theorem proving." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2007. http://amsdottorato.unibo.it/616/.

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Matita (that means pencil in Italian) is a new interactive theorem prover under development at the University of Bologna. When compared with state-of-the-art proof assistants, Matita presents both traditional and innovative aspects. The underlying calculus of the system, namely the Calculus of (Co)Inductive Constructions (CIC for short), is well-known and is used as the basis of another mainstream proof assistant—Coq—with which Matita is to some extent compatible. In the same spirit of several other systems, proof authoring is conducted by the user as a goal directed proof search, using

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19

Prince, Rawle C. S. "Aspects of the theory of containers within automated theorem proving." Thesis, University of Nottingham, 2011. http://eprints.nottingham.ac.uk/11793/.

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This thesis explores applications of the theory of containers within automated theorem proving. Container theory provides a foundational analysis of data types as containers, specified by a type $S$ of shapes and a function P assigning to each shape its set of positions for data.More importantly, a representation theorem guarantees that polymorphic functions between container data types are given by container morphisms, which are characterised by mappings between shapes and positions. Container theory is interesting, in this context, for the following reasons. A mechanism for representing and

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20

Hunter, Christopher. "Agent-based proof support for interactive theorem proving /." [St. Lucia, Qld.], 2005. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe19390.pdf.

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21

Lapierre, Patrice. "Willow : extending Herby's semantic tree theorem-proving heuristics." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape7/PQDD_0022/MQ50812.pdf.

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22

Matthews, S. "Metalevel and reflexive extension in mechanical theorem proving." Thesis, University of Edinburgh, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.657448.

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In spite of many years of research into mechanical assistance for mathematics it is still much more difficult to construct a proof on a machine than on paper. Of course this is partly because, unlike a proof on paper, a machine checked proof must be formal in the strictest sense of that word, but it is also because usually the ways of going about building proofs on a machine are limited compared to what a mathematician is used to. This thesis looks at some possible extensions to the range of tools available on a machine that might lend a user more flexibility in proving theorems, complementing

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23

SCHROEDER, BRUNO. "A GRAPH BASED THEOREM PROVING PLATFORM WITH STRATEGIES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2008. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=29093@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>PROGRAMA DE EXCELENCIA ACADEMICA<br>Demonstrações em lógica podem tornar-se muito grandes e complexas. Para resolver problemas, e para estudar lógica, é comum valer-se de assistentes de demonstração. Um assistente de demonstração geral deve integrar ferramentas que ajudem a especificar as lógicas, as equações, os conjuntos de regras, e as estratégias de busca (semi) automática de demonstrações. A comunidade usuária de Provadores Automáticos de Teoremas conhece algumas ferrament

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24

Suen, Edward Shaw-Lee Carleton University Dissertation Computer Science. "Tableau-based theorem proving for representation and reasoning." Ottawa, 1987.

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25

Blanco, Martínez Roberto. "Applications of Foundational Proof Certificates in theorem proving." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLX111/document.

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La confiance formelle en une propriété abstraite provient de l'existence d'une preuve de sa correction, qu'il s'agisse d'un théorème mathématique ou d'une qualité du comportement d'un logiciel ou processeur. Il existe de nombreuses définitions différentes de ce qu'est une preuve, selon par exemple qu'elle est écrite soit par des humains soit par des machines, mais ces définitions sont toutes concernées par le problème d'établir qu'un document représente en fait une preuve correcte. Le cadre des Certificats de Preuve Fondamentaux (Foundational Proof Certificates, FPC) est une approche proposée

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26

Urbas, Matej. "Mechanising heterogeneous reasoning in theorem provers." Thesis, University of Cambridge, 2014. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.708290.

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27

Gottliebsen, Hanne. "Automated theorem proving for mathematics : real analysis in PVS." Thesis, University of St Andrews, 2002. http://hdl.handle.net/10023/15046.

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Computer Algebra Systems (CASs), such as Maple and Mathematica, are now widely used in both industry and education. In many areas of mathematics they perform well. However, many well-established methods in mathematics, such as definite integration via the fundamental theorem of calculus, rely on analytic side conditions which CASs in general do not support. This thesis presents our work with automatic, formal mathematics using the theorem prover PVS. Based on an existing real analysis library for PVS, we have implemented transcendental functions such as exp, cos, sin, tan and their inverses, a

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28

Hesketh, Jane Thurmann. "Using middle-out reasoning to guide inductive theorem proving." Thesis, University of Edinburgh, 1992. http://hdl.handle.net/1842/19842.

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Techniques derived from proof theory for logic alone have been insufficient as a basis for efficient, elegant automatic theorem proving. They concentrate on syntax, neglecting both strategy for particular domains and classes of problem, and guidance from modelling human mathematicians. A novel technique suggested by Bundy, developing ideas from Ernst & Newell, is to reason 'middle-out'. Often, the overall structure of a proof may be known, but its details must be fleshed out according to the individual theorem. Conventional research might use heuristic guidance to backtrack over all possibilit

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29

Mário, Oliveira Rodrigues Cleyton. "Component assembly and theorem proving in constraint handling rules." Universidade Federal de Pernambuco, 2009. https://repositorio.ufpe.br/handle/123456789/1821.

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Made available in DSpace on 2014-06-12T15:52:36Z (GMT). No. of bitstreams: 1 license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2009<br>Devido á grande demanda por softwares cada vez mais robustos, complexos e flexíveis, e, sobretudo, pelo curtíssimo tempo de entrega exigido, a engenharia de software tem procurado novos meios de desenvolvimento que supram satisfatoriamente essas demandas. Uma forma de galgar esses novos patamares de produtividade provém do uso de uma metodologia baseada em agentes que se comunicam e com isso, ao invés dos prog

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30

Araragi, Tadashi. "Applications of automated theorem proving methods to multi-agent systems." 京都大学 (Kyoto University), 2006. http://hdl.handle.net/2433/143884.

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31

Winterstein, Daniel. "Using diagrammatic reasoning for theorem proving in a continuous domain." Thesis, University of Edinburgh, 2005. http://hdl.handle.net/1842/642.

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This project looks at using diagrammatic reasoning to prove mathematical theorems. The work is motivated by a need for theorem provers whose reasoning is readily intelligible to human beings. It should also have practical applications in mathematics teaching. We focus on the continuous domain of analysis - a geometric subject, but one which is taught using a dry algebraic formalism which many students find hard. The geometric nature of the domain makes it suitable for a diagram-based approach. However it is a difficult domain, and there are several problems, including handling alternating quan

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32

Heaton, John Edward. "Goal driven theorem proving using conceptual graphs and Peirce logic." Thesis, Loughborough University, 1994. https://dspace.lboro.ac.uk/2134/7706.

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The thesis describes a rational reconstruction of Sowa's theory of Conceptual Graphs. The reconstruction produces a theory with a firmer logical foundation than was previously the case and which is suitable for computation whilst retaining the expressiveness of the original theory. Also, several areas of incompleteness are addressed. These mainly concern the scope of operations on conceptual graphs of different types but include extensions for logics of higher orders than first order. An important innovation is the placing of negation onto a sound representational basis. A comparison of theore

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33

Petschulat, Cap. "Transparency in formal proof." [Boise, Idaho] : Boise State University, 2009. http://scholarworks.boisestate.edu/td/54/.

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34

Ghazizadeh, Behrad. "Hyperresolution for resolution logics." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/MQ39193.pdf.

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35

Shanahan, Murray Patrick. "Exploiting dependencies in search and inference mechanisms." Thesis, University of Cambridge, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.252643.

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36

Okoli, Ifeyinwa. "A novel term rewriting strategy for certain hierarchical AC-algebraic systems." Thesis, Loughborough University, 1989. https://dspace.lboro.ac.uk/2134/10641.

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37

Boulton, Richard John. "Efficiency in a fully-expansive theorem prover." Thesis, University of Cambridge, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319465.

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38

Almulla, Mohammed Ali. "Analysis of the use of semantic trees in automated theorem proving." Thesis, McGill University, 1994. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=28662.

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Semantic trees have served as a theoretical tool for confirming the unsatisfiability of clauses in first-order predicate logic, but it has seemed impractical to use them in practice. In this thesis we experimentally investigated the practicality of generating semantic trees for proofs of unsatisfiability. We considered two ways of generating semantic trees. First, we looked at semantic trees generated using the canonical enumeration of atoms from the Herbrand base of the given clauses. Then, we considered semantic trees generated by selectively choosing the atoms from the Herbrand base using a

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39

Lim, Hongping. "Translating timed I/O automata specifications for theorem proving in PVs." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/36803.

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Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.<br>Includes bibliographical references (leaves 68-70).<br>The timed input/output automaton modeling framework is a mathematical framework for specification and analysis of systems that involve discrete and continuous evolution. In order to employ an interactive theorem prover in deducing properties of a timed input/output automaton, its state-transition based description has to be translated to the language of the theorem prover. This thesis describes a tool for translating from

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40

Roberts, Brian Glenn. "Modular Detection of Feature Interactions Through Theorem Proving: A Case Study." Link to electronic thesis, 2003. http://www.wpi.edu/Pubs/ETD/Available/etd-0821103-122029.

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Thesis (M.S.)--Worcester Polytechnic Institute.<br>Keywords: theorem proving; modular verification; software verification; feature-oriented programming; feature interaction. Includes bibliographical references (p. 131-136).

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41

Johnson, Robert David. "Parallel analytic tableaux systems." Thesis, Queen Mary, University of London, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.362777.

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42

Duncan, Hazel. "The use of data-mining for the automatic formation of tactics." Thesis, University of Edinburgh, 2007. http://hdl.handle.net/1842/1768.

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As functions which further the state of a proof in automated theorem proving, tactics are an important development in automated deduction. This thesis describes a method to tackle the problem of tactic formation. Tactics must currently be developed by hand, which can be a complicated and time-consuming process. A method is presented for the automatic production of useful tactics. The method presented works on the principle that commonly occurring patterns within proof corpora may have some significance and could therefore be exploited to provide novel tactics. These tactics are discovered usin

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43

Lerner, Sorin. "Automatically proving the correctness of program analyses and transformations /." Thesis, Connect to this title online; UW restricted, 2006. http://hdl.handle.net/1773/7001.

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Montano-Rivas, Omar. "Scheme-based theorem discovery and concept invention." Thesis, University of Edinburgh, 2012. http://hdl.handle.net/1842/6269.

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In this thesis we describe an approach to automatically invent/explore new mathematical theories, with the goal of producing results comparable to those produced by humans, as represented, for example, in the libraries of the Isabelle proof assistant. Our approach is based on ‘schemes’, which are formulae in higher-order logic. We show that it is possible to automate the instantiation process of schemes to generate conjectures and definitions. We also show how the new definitions and the lemmata discovered during the exploration of a theory can be used, not only to help with the proof obligati

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45

Schmidt-Samoa, Tobias. "Flexible heuristic control for combining automation and user-interaction in inductive theorem proving." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980519268.

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Mackling, Thomas. "Contributions to automated theorem proving and formal methods with applications to control systems." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0018/NQ44506.pdf.

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47

Meng, Jia. "The integration of higher order interactive proof with first order automatic theorem proving." Thesis, University of Cambridge, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.615216.

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48

Frank, Mario. "TEMPLAR : efficient determination of relevant axioms in big formula sets for theorem proving." Master's thesis, Universität Potsdam, 2013. http://opus.kobv.de/ubp/volltexte/2014/7211/.

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This document presents a formula selection system for classical first order theorem proving based on the relevance of formulae for the proof of a conjecture. It is based on unifiability of predicates and is also able to use a linguistic approach for the selection. The scope of the technique is the reduction of the set of formulae and the increase of the amount of provable conjectures in a given time. Since the technique generates a subset of the formula set, it can be used as a preprocessor for automated theorem proving. The document contains the conception, implementation and evaluation of bo

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49

DeCloss, Daniel P. "An analysis of Specware and its usefulness in the verification of high assurance systems." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2006. http://library.nps.navy.mil/uhtbin/hyperion/06Jun%5FDeCloss.pdf.

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Thesis (M.S. in Computer Science)--Naval Postgraduate School, June 2006.<br>Thesis Advisor(s): Timothy Levin and Cynthia Irvine. "June 2006." Includes bibliographical references (p. 87-89). Also available in print.

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Sabharwal, Ashish. "Algorithmic applications of propositional proof complexity /." Thesis, Connect to this title online; UW restricted, 2005. http://hdl.handle.net/1773/6938.

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