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Dissertations / Theses on the topic 'Automated theorem proving'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

Goble, Tiffany Danielle. "Automate Reasoning: Computer Assisted Proofs in Set Theory Using Godel's Algorithm for Class Formation." Thesis, Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/4767.

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Automated reasoning, and in particular automated theorem proving, has become a very important research field within the world of mathematics. Besides being used to verify proofs of theorems, it has also been used to discover proofs of theorems which were previously open problems. In this thesis, an automated reasoning assistant based on Godel's class theory is used to deduce several theorems.

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9

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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10

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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11

Hoder, Krystof. "Practical aspects of automated first-order reasoning." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/practical-aspects-of-automated-firstorder-reasoning(1331ec1f-802c-4aeb-9265-1248d8db2a8e).html.

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Our work focuses on bringing the first-order reasoning closer to practicalapplications, particularly in software and hardware verification. The aim is to develop techniques that make first-order reasoners more scalablefor large problems and suitable for the applications. In pursuit of this goal the work focuses in three main directions. First, wedevelop an algorithm for an efficient pre-selection of axioms. This algorithmis already being widely used by the community and enables off-the-shelf theoremprovers to work with problems having millions of axioms that would otherwisebe overwhelming for

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12

De, Waal David Andre. "Analysis and transformation of proof procedures." Thesis, University of Bristol, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.240493.

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13

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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14

Johansson, Moa. "Automated discovery of inductive lemmas." Thesis, University of Edinburgh, 2009. http://hdl.handle.net/1842/9807.

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The discovery of unknown lemmas, case-splits and other so called eureka steps are challenging problems for automated theorem proving and have generally been assumed to require user intervention. This thesis is mainly concerned with the automated discovery of inductive lemmas. We have explored two approaches based on failure recovery and theory formation, with the aim of improving automation of firstand higher-order inductive proofs in the IsaPlanner system. We have implemented a lemma speculation critic which attempts to find a missing lemma using information from a failed proof-attempt. Howev

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15

Rode, Benjamin Paul. "Making sense of common sense : learning, fallibilism, and automated reasoning /." Full text (PDF) from UMI/Dissertation Abstracts International, 2000. http://wwwlib.umi.com/cr/utexas/fullcit?p3004366.

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16

Ridge, Thomas. "Enhancing the expressivity and automation of an interactive theorem prover in order to verify multicast protocols." Thesis, University of Edinburgh, 2006. http://hdl.handle.net/1842/1461.

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This thesis was motivated by a case study involving the formalisation of arguments that simplify the verification of tree-oriented multicast protocols. As well as covering the case study itself, it discusses our solution to problems we encountered concerning expressivity and automation. The expressivity problems related to the need for theory interpretation. We found the existing Locale and axiomatic type class mechanisms provided by the Isabelle theorem prover we were using to be inadequate. This led us to develop a new prototype implementation of theory interpretation. To support this implem

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17

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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18

Platzer, André [Verfasser], and Ernst-Rüdiger [Akademischer Betreuer] Olderog. "Differential dynamic logics - automated theorem proving for hybrid systems / André Platzer. Betreuer: Ernst-Rüdiger Olderog." Oldenburg : IBIT - Universitätsbibliothek, 2012. http://d-nb.info/1029141800/34.

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19

Meikle, Laura Isabel. "Intuition in formal proof : a novel framework for combining mathematical tools." Thesis, University of Edinburgh, 2014. http://hdl.handle.net/1842/9663.

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This doctoral thesis addresses one major difficulty in formal proof: removing obstructions to intuition which hamper the proof endeavour. We investigate this in the context of formally verifying geometric algorithms using the theorem prover Isabelle, by first proving the Graham’s Scan algorithm for finding convex hulls, then using the challenges we encountered as motivations for the design of a general, modular framework for combining mathematical tools. We introduce our integration framework — the Prover’s Palette, describing in detail the guiding principles from software engineering and the

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20

Goble, Tiffany Danielle. "Automate Reasoning computer assisted proofs in set theory using Gödel's algorithm for class formation /." Available online, Georgia Institute of Technology, 2004:, 2004. http://etd.gatech.edu/theses/available/etd-07252004-165909/unrestricted/Goble%5FTiffany%5FD%5F200412%5FMaster.pdf.

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Thesis (M.S.)--Mathematics, Georgia Institute of Technology, 2005.<br>Belinfante, Johan, Committee Chair ; Green, William, Committee Member ; Manolios, Panagiotis, Committee Member. Includes bibliographical references.

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21

Raggi, Daniel. "Searching the space of representations : reasoning through transformations for mathematical problem solving." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/22936.

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The role of representation in reasoning has been long and widely regarded as crucial. It has remained one of the fundamental considerations in the design of information-processing systems and, in particular, for computer systems that reason. However, the process of change and choice of representation has struggled to achieve a status as a task for the systems themselves. Instead, it has mostly remained a responsibility for the human designers and programmers. Many mathematical problems have the characteristic of being easy to solve only after a unique choice of representation has been made. In

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22

Haufe, Sebastian [Verfasser], Michael [Akademischer Betreuer] Thielscher, and Torsten [Akademischer Betreuer] Schaub. "Automated Theorem Proving for General Game Playing / Sebastian Haufe. Gutachter: Michael Thielscher ; Torsten Schaub. Betreuer: Michael Thielscher." Dresden : Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://d-nb.info/1067732276/34.

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23

Boehm, Peter. "Incremental modelling for verified communication architectures." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:ec6c9e06-7395-4af4-b961-b2ed837fda89.

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Modern computer systems are advancing from multi-core to many-core designs and System-on-chips (SoC) are becoming increasingly complex while integrating a great variety of components, thus constituting complex distributed systems. Such architectures rely on extremely complex communication protocols to exchange data with required performance. Arguing formally about the correctness of communication is an acknowledged verification challenge. This thesis presents a generic framework that formalises the idea of incremental modelling and step-wise verification to tackle this challenge: to control th

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24

Lundberg, Didrik. "Provably Sound and Secure Automatic Proving and Generation of Verification Conditions." Thesis, KTH, Teoretisk datalogi, TCS, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-239441.

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Formal verification of programs can be done with the aid of an interactive theorem prover. The program to be verified is represented in an intermediate language representation inside the interactive theorem prover, after which statements and their proofs can be constructed. This is a process that can be automated to a high degree. This thesis presents a proof procedure to efficiently generate a theorem stating the weakest precondition for a program to terminate successfully in a state upon which a certain postcondition is placed. Specifically, the Poly/ML implementation of the SML metalanguage

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25

Tan, Jiaqi. "Prescriptive Safety-Checks through Automated Proofs for Control-Flow Integrity." Research Showcase @ CMU, 2016. http://repository.cmu.edu/dissertations/715.

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Embedded software today is pervasive: they can be found everywhere, from coffee makers and medical devices, to cars and aircraft. Embedded software today is also open and connected to the Internet, exposing them to external attacks that can cause its Control-Flow Integrity (CFI) to be violated. Control-Flow Integrity is an important safety property of software, which ensures that the behavior of the software is not inadvertently changed. The violation of CFI in software can cause unintended behaviors, and can even lead to catastrophic incidents in safety-critical systems. This dissertation dev

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26

Wallen, Lincoln A. "Automated proof search in non-classical logics : efficient matrix proof methods for modal and intuitionistic logics." Thesis, University of Edinburgh, 1987. http://hdl.handle.net/1842/6600.

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In this thesis we develop efficient methods for automated proof search within an important class of mathematical logics. The logics considered are the varying, cumulative and constant domain versions of the first-order modal logics K, K4, D, D4, T, S4 and S5, and first-order intuitionistic logic. The use of these non-classical logics is commonplace within Computing Science and Artificial Intelligence in applications in which efficient machine assisted proof search is essential. Traditional techniques for the design of efficient proof methods for classical logic prove to be of limited use in th

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27

Arnold, Holger. "A linearized DPLL calculus with learning." Universität Potsdam, 2007. http://opus.kobv.de/ubp/volltexte/2007/1542/.

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This paper describes the proof calculus LD for clausal propositional logic, which is a linearized form of the well-known DPLL calculus extended by clause learning. It is motivated by the demand to model how current SAT solvers built on clause learning are working, while abstracting from decision heuristics and implementation details. The calculus is proved sound and terminating. Further, it is shown that both the original DPLL calculus and the conflict-directed backtracking calculus with clause learning, as it is implemented in many current SAT solvers, are complete and proof-confluent inst

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Arnold, Holger. "A linearized DPLL calculus with clause learning (2nd, revised version)." Universität Potsdam, 2009. http://opus.kobv.de/ubp/volltexte/2009/2908/.

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Many formal descriptions of DPLL-based SAT algorithms either do not include all essential proof techniques applied by modern SAT solvers or are bound to particular heuristics or data structures. This makes it difficult to analyze proof-theoretic properties or the search complexity of these algorithms. In this paper we try to improve this situation by developing a nondeterministic proof calculus that models the functioning of SAT algorithms based on the DPLL calculus with clause learning. This calculus is independent of implementation details yet precise enough to enable a formal analysis of

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29

Shminke, Boris. "Applications de l'IA à l'étude des structures algébriques finies et à la démonstration automatique de théorèmes." Electronic Thesis or Diss., Université Côte d'Azur, 2023. http://www.theses.fr/2023COAZ4058.

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Cette thèse contribue à une recherche de modèles finis et à la démonstration automatisée de théorèmes, en se concentrant principalement, mais sans s'y limiter, sur les méthodes d'intelligence artificielle. Dans la première partie, nous résolvons une question de recherche ouverte à partir de l'algèbre abstraite en utilisant une recherche automatisée de modèles finis massivement parallèles, en utilisant l'assistant de preuve Isabelle. À savoir, nous établissons l'indépendance de certaines lois de distributivité abstraites dans les binaires résiduels dans le cas général. En tant que sous-produit

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30

Jacquel, Mélanie. "Automatisation des preuves pour la vérification des règles de l'Atelier B." Phd thesis, Conservatoire national des arts et metiers - CNAM, 2013. http://tel.archives-ouvertes.fr/tel-00840484.

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Cette thèse porte sur la vérification des règles ajoutées de l'Atelier B en utilisant une plate-forme appelée BCARe qui repose sur un plongement de la théorie sous-jacente à la méthode B (théorie de B) dans l'assistant à la preuve Coq. En particulier, nous proposons trois approches pour prouver la validité d'une règle, ce qui revient à prouver une formule exprimée dans la théorie de B. Ces trois approches ont été évaluées sur les règles de la base de règles de SIEMENS IC-MOL. La première approche dite autarcique est développée avec le langage de tactiques de Coq Ltac. Elle repose sur une premi

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31

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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Jacquel, Mélanie. "Automatisation des preuves pour la vérification des règles de l'Atelier B." Electronic Thesis or Diss., Paris, CNAM, 2013. http://www.theses.fr/2013CNAM0860.

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Cette thèse porte sur la vérification des règles ajoutées de l'Atelier B en utilisant une plate-forme appelée BCARe qui repose sur un plongement de la théorie sous-jacente à la méthode B (théorie de B) dans l'assistant à la preuve Coq. En particulier, nous proposons trois approches pour prouver la validité d'une règle, ce qui revient à prouver une formule exprimée dans la théorie de B. Ces trois approches ont été évaluées sur les règles de la base de règles de SIEMENS IC-MOL. La première approche dite autarcique est développée avec le langage de tactiques de Coq Ltac. Elle repose sur une premi

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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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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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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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Savchenko, Sergei. "Resolution based techniques for automated proving of theorems in Tarskian-Euclidian geometry." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0035/MQ64447.pdf.

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Savchenko, Sergei. "Resolution based techniques for automated proving of theorems in Tarskian-Euclidian geometry." Thesis, McGill University, 1999. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=30742.

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The discipline of automated theorem proving encompasses techniques which allow us to find a justification of a logical statement expressing an assertion in some domain of knowledge. Beside obvious importance for mathematics, many of the tasks traditionally associated with human intellect can be solved through application of these techniques. Methods based on Robinson's resolution form one of the cornerstones of automated theorem proving. The efficiency of these methods, however, is less than admissible for many interesting domains of mathematics. By studying the underlining axioms of the domai

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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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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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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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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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Bensaid, Hicham. "Utilisation des schématisations de termes en déduction automatique." Phd thesis, Université de Grenoble, 2011. http://tel.archives-ouvertes.fr/tel-00618531.

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Les schématisations de termes permettent de représenter des ensembles infinis de termes ayant une structure similaire de manière finie et compacte. Dans ce travail, nous étudions certains aspects liés à l'utilisation des schématisations de termes en déduction automatique, plus particulièrement dans les méthodes de démonstration de théorèmes du premier ordre par saturation. Après une brève étude comparée des formalismes de schématisation existants, nous nous concentrons plus particulièrement sur les termes avec exposants entiers (ou I-termes). Dans un premier temps, nous proposons une nouvelle

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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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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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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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Poernomo, Iman Hafiz 1976. "Variations on a theme of Curry and Howard : the Curry-Howard isomorphism and the proofs-as-programs paradigm adapted to imperative and structured program synthesis." Monash University, School of Computer Science and Software Engineering, 2003. http://arrow.monash.edu.au/hdl/1959.1/9405.

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48

Raimi, Richard Saul. "Environment modeling and efficient state reachability checking /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.

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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 ide

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Fuchs, Alexander Tinelli C. "Evolving model evolution." [Iowa City, Iowa] : University of Iowa, 2009. http://ir.uiowa.edu/etd/361.

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