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Artykuły w czasopismach na temat „Theorem proving”

Autor: Grafiati

Data publikacji: 4 czerwca 2021

Data aktualizacji: 25 lipca 2025

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1

Gan, Wenbin, Xinguo Yu, Ting Zhang, and Mingshu Wang. "Automatically Proving Plane Geometry Theorems Stated by Text and Diagram." International Journal of Pattern Recognition and Artificial Intelligence 33, no. 07 (2019): 1940003. http://dx.doi.org/10.1142/s0218001419400032.

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This paper presents an algorithm for proving plane geometry theorems stated by text and diagram in a complementary way. The problem of proving plane geometry theorems involves two challenging subtasks, being theorem understanding and theorem proving. This paper proposes to consider theorem understanding as a problem of extracting relations from text and diagram. A syntax–semantics (S2) model method is proposed to extract the geometric relations from theorem text, and a diagram mining method is proposed to extract geometry relations from diagram. Then, a procedure is developed to obtain a set o

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2

Stojanović-Đurđević, Sana, Andrija Urošević, and Filip Marić. "Improving mathematical proving skills through interactive theorem proving." Journal of Educational Studies in Mathematics and Computer Science 1, no. 2 (2024): 37–49. https://doi.org/10.5937/jesmac2402037s.

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Understanding and constructing proofs of mathematical theorems is a fundamental component of mastering mathematics and developing the logical apparatus. In addition, the theorems in mathematical textbooks are often only understandable through their proofs. However, students sometimes lack the precision needed to write detailed proofs and the understanding of basic proving concepts. In this paper, we propose the use of interactive theorem provers by math teachers with the goal of improving students' mathematical proving skills and understanding of logical rules. This approach utilizes feedback

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3

Crouse, Maxwell, Ibrahim Abdelaziz, Bassem Makni, et al. "A Deep Reinforcement Learning Approach to First-Order Logic Theorem Proving." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 7 (2021): 6279–87. http://dx.doi.org/10.1609/aaai.v35i7.16780.

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Automated theorem provers have traditionally relied on manually tuned heuristics to guide how they perform proof search. Deep reinforcement learning has been proposed as a way to obviate the need for such heuristics, however, its deployment in automated theorem proving remains a challenge. In this paper we introduce TRAIL, a system that applies deep reinforcement learning to saturation-based theorem proving. TRAIL leverages (a) a novel neural representation of the state of a theorem prover and (b) a novel characterization of the inference selection process in terms of an attention-based action

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4

Xiao, Da, Yue Fei Zhu, Sheng Li Liu, Dong Xia Wang, and You Qiang Luo. "Digital Hardware Design Formal Verification Based on HOL System." Applied Mechanics and Materials 716-717 (December 2014): 1382–86. http://dx.doi.org/10.4028/www.scientific.net/amm.716-717.1382.

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This article selects HOL theorem proving systems for hardware Trojan detection and gives the symbol and meaning of theorem proving systems, and then introduces the symbol table, item and the meaning of HOL theorem proving systems. In order to solve the theorem proving the application of the system in hardware Trojan detection requirements, this article analyses basic hardware Trojan detection methods which applies for theorem proving systems and introduces the implementation methods and process of theorem proving about hardware Trojan detection.

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5

Lu, Jian, and Qi Wan. "Lagrange's Mean Value Theorem and Taylor's Theorem and Their Applications." Journal of Education and Culture Studies 8, no. 3 (2024): p42. http://dx.doi.org/10.22158/jecs.v8n3p42.

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Lagrange's mean value theorem and Taylor's theorem are two important and widely used formulas in calculus courses. In this paper, we introduce the method for proving Lagrange's mean value theorem and Taylor's theorem using Rolle's theorem, and the application of these two theorems in estimating the value of integrals, determining the concavity and convexity of functions, and solving the limits of functions.

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6

Yadav, Aanand Kumar. "An Axiomatic Approach to Prove the Converse of Bayes’ Theorem in Probability." Orchid Academia Siraha 3, no. 1 (2024): 79–94. https://doi.org/10.3126/oas.v3i1.78106.

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The converse of Bayes' theorem, have been proved using axiomatic approach to probability. This approach to probability utilizes the relations and theorems of set theory. Simply presentation of the converse of Bayes' theorem has been possible due to the correspondence theorem in set theory. This theorem is seen to be more applicable in the proof of Bayes' theorem and its converse. So at first, the correspondence theorem of set theory with its proof has been presented here and then has been applied to prove the Bayes' theorem and its converse. Some important applications of correspondence theore

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7

Perron, Steven. "Examining Fragments of the Quantified Propositional Calculus." Journal of Symbolic Logic 73, no. 3 (2008): 1051–80. http://dx.doi.org/10.2178/jsl/1230396765.

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AbstractWhen restricted to proving formulas, the quantified propositional proof system is closely related to the theorems of Buss's theory . Namely, has polynomial-size proofs of the translations of theorems of , and proves that is sound. However, little is known about when proving more complex formulas. In this paper, we prove a witnessing theorem for similar in style to the KPT witnessing theorem for . This witnessing theorem is then used to show that proves is sound with respect to formulas. Note that unless the polynomial-time hierarchy collapses is the weakest theory in the S2 hierarchy f

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8

Bahodirovich, Hojiyev Dilmurodjon, Muhammadjonov Akbarshoh Akramjon Og`Li Og`Li, Muzaffarova Dilshoda Botirjon Qizi, Ibrohimjonov Islombek Ilhomjon O`G`Li, and Ahmadjonova Musharrafxon Dilmurod Qizi. "About One Theorem Of 2x2 Jordan Blocks Matrix." American Journal of Applied sciences 03, no. 06 (2021): 28–33. http://dx.doi.org/10.37547/tajas/volume03issue06-05.

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In this paper, we have studied one theorem on 2x2 Jordan blocks matrix. There are 4 important statements which is used for proving other theorems such as in the differensial equations. In proving these statements, we have used mathematic induction, norm of matrix, Taylor series of

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9

Jupri, Al, Siti Fatimah, and Dian Usdiyana. "Dampak Perkuliahan Geometri Pada Penalaran Deduktif Mahasiswa: Kasus Pembelajaran Teorema Ceva." AKSIOMA : Jurnal Matematika dan Pendidikan Matematika 11, no. 1 (2020): 93–104. http://dx.doi.org/10.26877/aks.v11i1.6011.

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Geometry is one of branches of mathematics that can develop deductive thinking ability for anyone, including students of prospective mathematics teachers, who learning it. This deductive thinking ability is needed by prospective mathematics teachers for their future careers as mathematics educators. This research therefore aims to investigate the influence of the learning process of a geometry course toward deductive reasoning ability of students of prospective mathematics teachers. To do so, this qualitative research was carried out through an observation of the learning process and assessmen

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10

Wang, Dongming. "A Method for Proving Theorems in Differential Geometry and Mechanics." JUCS - Journal of Universal Computer Science 1, no. (9) (1995): 658–73. https://doi.org/10.3217/jucs-001-09-0658.

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A zero decomposition algorithm is presented and used to devise a method for proving theorems automatically in differential geometry and mechanics. The method has been implemented and its practical efficiency is demonstrated by several non-trivial examples including Bertrand s theorem, Schell s theorem and Kepler-Newton s laws.

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11

KANSO, KARIM, and ANTON SETZER. "A light-weight integration of automated and interactive theorem proving." Mathematical Structures in Computer Science 26, no. 1 (2014): 129–53. http://dx.doi.org/10.1017/s0960129514000140.

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In this paper, aimed at dependently typed programmers, we present a novel connection between automated and interactive theorem proving paradigms. The novelty is that the connection offers a better trade-off between usability, efficiency and soundness when compared to existing techniques. This technique allows for a powerful interactive proof framework that facilitates efficient verification of finite domain theorems and guided construction of the proof of infinite domain theorems. Such situations typically occur with industrial verification. As a case study, an embedding of SAT and CTL model c

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12

Stickel, M. E. "Resolution Theorem Proving." Annual Review of Computer Science 3, no. 1 (1988): 285–316. http://dx.doi.org/10.1146/annurev.cs.03.060188.001441.

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13

Gogate, Vibhav, and Pedro Domingos. "Probabilistic theorem proving." Communications of the ACM 59, no. 7 (2016): 107–15. http://dx.doi.org/10.1145/2936726.

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14

Klein, Gerwin, and Ruben Gamboa. "Interactive Theorem Proving." Journal of Automated Reasoning 56, no. 3 (2016): 201–3. http://dx.doi.org/10.1007/s10817-016-9363-7.

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15

Plaisted, David A. "Automated theorem proving." Wiley Interdisciplinary Reviews: Cognitive Science 5, no. 2 (2014): 115–28. http://dx.doi.org/10.1002/wcs.1269.

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16

Lin, Shenghan. "Unveiling Lagrange’s Theorem and its Applications in Proving other Theorems." Highlights in Science, Engineering and Technology 128 (February 25, 2025): 64–68. https://doi.org/10.54097/ewsds596.

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The group theory is an essential subject in Mathematics and Physics, and the target of this paper is to prove a famous theorem in group theory, so-called Lagrange’s Theorem. By using some really basic definitions of group, the exsistance of this theorem is essential for abstract algebra. In this paper, the author will focus on how to prove Lagrange’s Theorem step by step from the base of group theorey, mainly by using the nature of cosets and how does each coset in the same subgroup behaves to get the final result. Ultimately, the author will demonstrate that the order of the group is divisibl

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17

Zhao, Wenxian. "Study on Cauchy Theorem as a Special Case of Sylow Theorem." Highlights in Science, Engineering and Technology 128 (February 25, 2025): 91–96. https://doi.org/10.54097/7046we49.

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The Cauchy Group Theorem and the Sylow Theorem are foundations of the finite group theory. The Cauchy Group Theorem focuses on the existence of prime order elements in a finite group, whereas Sylow Theorems provide a more complete framework for the analysis of the structure and number of subgroups. A formal proof of the two theorems is given in this paper. The Cauchy Group Theorem is proved by proving the existence of an order element in a finite group , here is a prime divisor of , and is the order of group . The Sylow Theorem is proved by existence, conjugacy and amount of Sylow -subgroups.

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18

López-Renteria, Jorge-Antonio, Baltazar Aguirre-Hernández, and Fernando Verduzco. "The Boundary Crossing Theorem and the Maximal Stability Interval." Mathematical Problems in Engineering 2011 (2011): 1–13. http://dx.doi.org/10.1155/2011/123403.

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The boundary crossing theorem and the zero exclusion principle are very useful tools in the study of the stability of family of polynomials. Although both of these theorem seem intuitively obvious, they can be used for proving important results. In this paper, we give generalizations of these two theorems and we apply such generalizations for finding the maximal stability interval.

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19

Chen, Baoying. "The Related Extension and Application of the Ši'lnikov Theorem." Journal of Applied Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/287123.

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The traditional Ši'lnikov theorems provide analytic criteria for proving the existence of chaos in high-dimensional autonomous systems. We have established one extended version of the Ši'lnikov homoclinic theorem and have given a set of sufficient conditions under which the system generates chaos in the sense of Smale horseshoes. In this paper, the extension questions of the Ši'lnikov homoclinic theorem and its applications are still discussed. We establish another extended version of the Ši'lnikov homoclinic theorem. In addition, we construct a new three-dimensional chaotic system which meets

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20

Hsiang, Jieh, and Michaël Rusinowitch. "Proving refutational completeness of theorem-proving strategies." Journal of the ACM 38, no. 3 (1991): 558–86. http://dx.doi.org/10.1145/116825.116833.

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21

Coghetto, Roland. "Pascal’s Theorem in Real Projective Plane." Formalized Mathematics 25, no. 2 (2017): 107–19. http://dx.doi.org/10.1515/forma-2017-0011.

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Summary In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem)1. Pappus’ theorem is a special case of a degenerate conic of two lines. For proving Pascal’s theorem, we use the techniques developed in the section “Projective Proofs of Pappus’ Theorem” in the chapter “Pappus’ Theorem: Nine proofs and three variations” [11]. We also follow some ideas from Harrison’s work. With HOL Light, he has the proof of Pascal’s theorem2. For a lemma, we use PROVER93 and OTT2

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22

Voronkov, A. A., and A. I. Degtyarev. "Automatic theorem proving. I." Cybernetics 22, no. 3 (1986): 290–97. http://dx.doi.org/10.1007/bf01069967.

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23

Bertrand, P. "Simply proving Pythagoras's theorem." Teaching Mathematics and its Applications 15, no. 1 (1996): 10–11. http://dx.doi.org/10.1093/teamat/15.1.10.

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24

Nossum, Rolf. "Automated theorem proving methods." BIT 25, no. 1 (1985): 51–64. http://dx.doi.org/10.1007/bf01934987.

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25

Cooper, D. "Overview of Theorem Proving." ACM SIGSOFT Software Engineering Notes 10, no. 4 (1985): 53–54. http://dx.doi.org/10.1145/1012497.1012517.

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26

RUSSELL, STEPHEN, and TRACI WHEELER UNISYS. "On Automated Theorem Proving." Annals of the New York Academy of Sciences 661, no. 1 Frontiers of (1992): 160–73. http://dx.doi.org/10.1111/j.1749-6632.1992.tb26040.x.

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Voronkov, A. A., and A. I. Degtyarev. "Automatic theorem proving. II." Cybernetics 23, no. 4 (1988): 547–56. http://dx.doi.org/10.1007/bf01078915.

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28

Policriti, Alberto, and Jacob T. Schwartz. "T-Theorem Proving I." Journal of Symbolic Computation 20, no. 3 (1995): 315–42. http://dx.doi.org/10.1006/jsco.1995.1053.

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Alsaadi, Ateq, Bijender Singh, Vizender Singh, and Izhar Uddin. "Meir–Keeler Type Contraction in Orthogonal M-Metric Spaces." Symmetry 14, no. 9 (2022): 1856. http://dx.doi.org/10.3390/sym14091856.

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In this article, we prove fixed point results for a Meir–Keeler type contraction due to orthogonal M-metric spaces. The results of the paper improve and extend some recent developments in fixed point theory. The extension is assured by the concluding remarks and followed by the main theorem. Finally, an application of the main theorem is established in proving theorems for some integral equations and integral-type contractive conditions.

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30

Wan, Hai, Anping He, Zhiyang You, and Xibin Zhao. "Formal Proof of a Machine Closed Theorem in Coq." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/892832.

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The paper presents a formal proof of a machine closed theorem of TLA+in the theorem proving system Coq. A shallow embedding scheme is employed for the proof which is independent of concrete syntax. Fundamental concepts need to state that the machine closed theorems are addressed in the proof platform. A useful proof pattern of constructing a trace with desired properties is devised. A number of Coq reusable libraries are established.

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Al-Hawasy, Jamil A. Ali, and Lamyaa H. Ali. "Constraints Optimal Control Governing by Triple Nonlinear Hyperbolic Boundary Value Problem." Journal of Applied Mathematics 2020 (April 10, 2020): 1–14. http://dx.doi.org/10.1155/2020/8021635.

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The focus of this work lies on proving the existence theorem of a unique state vector solution (Stvs) of the triple nonlinear hyperbolic boundary value problem (TNHBVP) when the classical continuous control vector (CCCVE) is fixed by using the Galerkin method (Galm), proving the existence theorem of a unique constraints classical continuous optimal control vector (CCCOCVE) with vector state constraints (equality EQVC and inequality INEQVC). Also, it consists of studying for the existence and uniqueness adjoint vector solution (Advs) of the triple adjoint vector equations (TAEqs) associated wit

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32

Jureczko, Joanna. "Strong sequences and partition relations." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 16, no. 1 (2017): 51–59. http://dx.doi.org/10.1515/aupcsm-2017-0004.

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AbstractThe first result in partition relations topic belongs to Ramsey (1930). Since that this topic has been still explored. Probably the most famous partition theorem is Erdös-Rado theorem (1956). On the other hand in 60’s of the last century Efimov introduced strong sequences method, which was used for proving some famous theorems in dyadic spaces. The aim of this paper is to generalize theorem on strong sequences and to show that it is equivalent to generalized version of well-known Erdös-Rado theorem. It will be also shown that this equivalence holds for singulars. Some applications and

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Thakur, Ramkrishna, and S. K. Samanta. "A Study on Some Fundamental Properties of Continuity and Differentiability of Functions of Soft Real Numbers." Advances in Fuzzy Systems 2018 (2018): 1–8. http://dx.doi.org/10.1155/2018/6429572.

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We introduce a new type of functions from a soft set to a soft set and study their properties under soft real number setting. Firstly, we investigate some properties of soft real sets. Considering the partial order relation of soft real numbers, we introduce concept of soft intervals. Boundedness of soft real sets is defined, and the celebrated theorems like nested intervals theorem and Bolzano-Weierstrass theorem are extended in this setting. Next, we introduce the concepts of limit, continuity, and differentiability of functions of soft sets. It has been possible for us to study some fundame

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Dawson, C. Bryan. "L-correspondences: the inclusionLp(μ,X)⊂Lq(ν,Y)". International Journal of Mathematics and Mathematical Sciences 19, № 4 (1996): 723–26. http://dx.doi.org/10.1155/s0161171296000993.

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In order to study inclusions of the typeLp(μ,X)⊂Lq(ν,Y), we introduce the notion of anL-correspondence. After proving some basic theorems, we give characterizations of some types ofL-correspondences and offer a conjecture that is similar to an equimeasurability theorem.

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Dalinger, Victor Alekseevich. "Revisiting a Proof of the Sine Theorem." Development of education, no. 1 (7) (March 13, 2020): 16–18. http://dx.doi.org/10.31483/r-74764.

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The author of the article outlines, that in school geometry course, the sine theorem and the cosine theorem are well known. In this course, they are proved by the authors of the textbook in a way different from the one that is presented in the article. The article considers the author's method of proving the sine theorem unknown in the literature sources and based on the vector-coordinate method; two more theorems are also proved, one of which concerns the calculation of the inscribed angle in the circle, and the other concerns the calculation of viewing angles of the chord of the circle; one

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36

Wu, Shuchen. "Proof and Application of the Mean Value Theorem." Highlights in Science, Engineering and Technology 72 (December 15, 2023): 565–71. http://dx.doi.org/10.54097/nw2nd028.

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In calculus, mean value theorem (MVT) connects a function's derivative and its rate of change over a certain interval. This paper delves into the mathematical intricacies of the MVT and its multifaceted applications. Through rigorous proofs and illustrative examples, this study establishes the MVT's fundamental role in calculus and its relevance in understanding the behavior of functions. The paper extends its exploration to encompass related theorems, including extreme value theorem, which connects function’s continuity and extrema, Intermediate Value Theorem, which states that the function v

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Hamdani, Deni, Ketut Sarjana, Ratna Yulis Tyaningsih, Ulfa Lu’luilmaknun, and J. Junaidi. "Exploration of Student Thinking Process in Proving Mathematical Statements." Prisma Sains : Jurnal Pengkajian Ilmu dan Pembelajaran Matematika dan IPA IKIP Mataram 8, no. 2 (2020): 150. http://dx.doi.org/10.33394/j-ps.v8i2.3081.

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A mathematical statement is not a theorem until it has been carefully derived from previously proven axioms, definitions and theorems. The proof of a theorem is a logical argument that is given deductively and is often interpreted as a justification for statements as well as a fundamental part of the mathematical thinking process. Studying the proof can help decide if and why our answers are logical, develop the habit of arguing, and make investigating an integral part of any problem solving. However, not a few students have difficulty learning it. So it is necessary to explore the student's t

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Cao, Daming, Lin Zhou, and Vincent Y. F. Tan. "A Strong Converse Theorem for Hypothesis Testing Against Independence over a Two-Hop Network." Entropy 21, no. 12 (2019): 1171. http://dx.doi.org/10.3390/e21121171.

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By proving a strong converse theorem, we strengthen the weak converse result by Salehkalaibar, Wigger and Wang (2017) concerning hypothesis testing against independence over a two-hop network with communication constraints. Our proof follows by combining two recently-proposed techniques for proving strong converse theorems, namely the strong converse technique via reverse hypercontractivity by Liu, van Handel, and Verdú (2017) and the strong converse technique by Tyagi and Watanabe (2018), in which the authors used a change-of-measure technique and replaced hard Markov constraints with soft in

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Humphreys, A. James, and Stephen G. Simpson. "Separation and Weak König's Lemma." Journal of Symbolic Logic 64, no. 1 (1999): 268–78. http://dx.doi.org/10.2307/2586763.

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AbstractWe continue the work of [14, 3, 1, 19, 16, 4, 12, 11, 20] investigating the strength of set existence axioms needed for separable Banach space theory. We show that the separation theorem for open convex sets is equivalent to WKL0 over RCA0. We show that the separation theorem for separably closed convex sets is equivalent to ACA0 over RCA0. Our strategy for proving these geometrical Hahn–Banach theorems is to reduce to the finite-dimensional case by means of a compactness argument.

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40

Hovhannisyan, Gro. "On Oscillations of Solutions of Third-Order Dynamic Equation." Abstract and Applied Analysis 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/715981.

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We are proving the new oscillation theorems for the solutions of third-order linear nonautonomous differential equation with complex coefficients. In the case of real coefficients we derive the oscillation criterion that is invariant with respect to the adjoint transformation. Our main tool is a new version of Levinson's asymptotic theorem.

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Lin, Ming-Shr, and Chih-Sheng Chuang. "Adaptive Douglas–Rachford Algorithms for Biconvex Optimization Problem in the Finite Dimensional Real Hilbert Spaces." Mathematics 12, no. 23 (2024): 3785. https://doi.org/10.3390/math12233785.

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In this paper, we delve into the realm of biconvex optimization problems, introducing an adaptive Douglas–Rachford algorithm and presenting related convergence theorems in the setting of finite-dimensional real Hilbert spaces. It is worth noting that our approach to proving the convergence theorem differs significantly from those in the literature.

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Kolobyanina, A. E., E. V. Nozdrinova, and O. V. Pochinka. "Classification of rough transformations of a circle from a modern point of view." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 20, no. 4 (2018): 408–18. http://dx.doi.org/10.15507/2079-6900.20.201804.408-418.

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In this paper the authors use modern methods and approaches to present a solution to the problem of the topological classification of circle’s rough transformations in canonical formulation. In the modern theory of dynamical systems such problems are understood as the complete topological classification: finding topological invariants, proving the completeness of the set of invariants found and constructing a standard representative from a given set of topological invariants. Namely, in the first theorem of this paper the type of periodic data of circle’s rough transformations is established.

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Lemor Jr., Luiz Carlos, Simone André da Costa Cavalheiro, and Luciana Foss. "Proof Tactics for Theorem Proving Graph Grammars through Rodin." Revista de Informática Teórica e Aplicada 22, no. 1 (2015): 190. http://dx.doi.org/10.22456/2175-2745.50383.

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Graph grammar is a formal language suitable for the specification of distributed and concurrent systems. Theorem proving is a technique that allows the verification of systems with huge (and infinite) state space. One of the disadvantages of theorem proving graph grammars (and theorem proving in general) is the specific mathematical knowledge required from the user for concluding the proofs. Previous works have proposed proof strategies to help the developer in the verification process when adopting such approach, firstly establishing proof tactics for some properties and after proposing a vis

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Loring, Terry A. "From Matrix to Operator Inequalities." Canadian Mathematical Bulletin 55, no. 2 (2012): 339–50. http://dx.doi.org/10.4153/cmb-2011-063-8.

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AbstractWe generalize Löwner's method for proving that matrix monotone functions are operator monotone. The relation x ≤ y on bounded operators is our model for a definition of C*-relations being residually finite dimensional.Our main result is a meta-theorem about theorems involving relations on bounded operators. If we can show there are residually finite dimensional relations involved and verify a technical condition, then such a theorem will follow from its restriction to matrices.Applications are shown regarding norms of exponentials, the norms of commutators, and “positive” noncommutativ

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Leslie-Hurd, Joe, and G. McC Haworth. "Computer Theorem Proving and HoTT." ICGA Journal 36, no. 2 (2013): 100–103. http://dx.doi.org/10.3233/icg-2013-36204.

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Jones, C. B. "Theorem proving and software engineering." Software Engineering Journal 3, no. 1 (1988): 2. http://dx.doi.org/10.1049/sej.1988.0001.

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Chen, Chiyan, and Hongwei Xi. "Combining programming with theorem proving." ACM SIGPLAN Notices 40, no. 9 (2005): 66–77. http://dx.doi.org/10.1145/1090189.1086375.

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Murthy, S., and K. Sekharam. "Software Reliability through Theorem Proving." Defence Science Journal 59, no. 3 (2009): 314–17. http://dx.doi.org/10.14429/dsj.59.1527.

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Finger, M. "Towards structurally-free theorem proving." Logic Journal of IGPL 6, no. 3 (1998): 425–49. http://dx.doi.org/10.1093/jigpal/6.3.425.

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Fleuriot, J. "Theorem proving in infinitesimal geometry." Logic Journal of IGPL 9, no. 3 (2001): 447–74. http://dx.doi.org/10.1093/jigpal/9.3.447.

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