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Journal articles on the topic 'Automated theorem proving'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

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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2

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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3

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

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4

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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5

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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6

Pastre, Dominique. "Automated theorem proving in mathematics." Annals of Mathematics and Artificial Intelligence 8, no. 3-4 (1993): 425–47. http://dx.doi.org/10.1007/bf01530801.

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7

WOLF, ANDREAS, and REINHOLD LETZ. "STRATEGY PARALLELISM IN AUTOMATED THEOREM PROVING." International Journal of Pattern Recognition and Artificial Intelligence 13, no. 02 (1999): 219–45. http://dx.doi.org/10.1142/s0218001499000136.

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Automated theorem provers use search strategies. Unfortunately, there is no unique strategy which is uniformly successful on all problems. This motivates us to apply different strategies in parallel, in a competitive manner. In this paper, we discuss properties, problems, and perspectives of strategy parallelism in theorem proving. We develop basic concepts like the complementarity and the overlap value of strategy sets. Some of the problems such as initial strategy selection and run-time strategy exchange are discussed in more detail. The paper also contains the description of an implementati

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8

Elias, Joran. "Automated Geometric Theorem Proving: Wu's Method." Mathematics Enthusiast 3, no. 1 (2006): 3–50. http://dx.doi.org/10.54870/1551-3440.1034.

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9

Windsteiger, Wolfgang. "Automated Theorem Proving in the Classroom." Electronic Proceedings in Theoretical Computer Science 352 (December 30, 2021): 54–63. http://dx.doi.org/10.4204/eptcs.352.6.

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10

Peikert, R. "Automated theorem proving: the resolution method." ACM SIGSAM Bulletin 21, no. 3 (1987): 61–68. http://dx.doi.org/10.1145/29309.29319.

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11

Kinyon, Michael. "Proof simplification and automated theorem proving." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377, no. 2140 (2019): 20180034. http://dx.doi.org/10.1098/rsta.2018.0034.

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The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper, I describe a technique for simplifying automated proofs. Hopefully, this discussion will stimulate interest in the larger, still open, question of what reasonable measures of proof simplicity might be. This article is part of the theme issue ‘The notion of ‘simple proof’ - Hilbert's 24th problem’.

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12

Beavers, Gordon. "Automated theorem proving for ?ukasiewicz logics." Studia Logica 52, no. 2 (1993): 183–95. http://dx.doi.org/10.1007/bf01058388.

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13

Bonacina, Maria Paola, and Moa Johansson. "On Interpolation in Automated Theorem Proving." Journal of Automated Reasoning 54, no. 1 (2014): 69–97. http://dx.doi.org/10.1007/s10817-014-9314-0.

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14

Flower, Jean, and Gem Stapleton. "Automated Theorem Proving with Spider Diagrams." Electronic Notes in Theoretical Computer Science 91 (February 2004): 246–63. http://dx.doi.org/10.1016/j.entcs.2003.12.016.

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15

Ndungi, Rebeccah, and Shofwatul Uyun. "A Review of Automated Reasoning and Its Applications in the 21st Century." Indonesian Journal of Computer Science 12, no. 2 (2023): 483–91. http://dx.doi.org/10.33022/ijcs.v12i2.3175.

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This article takes a look at the progress and advancement of automated reasoning and its applications in the 21st century. Reasoning refers to the method of reaching logical conclusions. The construction of computing systems that automate this process over some knowledge bases is the focus of automatic reasoning. Automated Reasoning is frequently regarded as a subfield of machine learning. It is also studied in theoretical computer science and philosophy. Some of the applications of automated reasoning include but not limited to Tableau-style systems, Automatic Theorem Proving, Superposition a

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16

Murray, Neil V., and Erik Rosenthal. "Theory links: Applications to automated theorem proving." Journal of Symbolic Computation 4, no. 2 (1987): 173–90. http://dx.doi.org/10.1016/s0747-7171(87)80064-0.

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17

Sutcliffe, Geoff, and Christian Suttner. "Evaluating general purpose automated theorem proving systems." Artificial Intelligence 131, no. 1-2 (2001): 39–54. http://dx.doi.org/10.1016/s0004-3702(01)00113-8.

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18

Aguilera, Gabriel, Inma P. de Guzmán, and Manuel Ojeda. "Increasing the efficiency of automated theorem proving." Journal of Applied Non-Classical Logics 5, no. 1 (1995): 9–29. http://dx.doi.org/10.1080/11663081.1995.10510841.

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19

Stapleton, Gem, Judith Masthoff, Jean Flower, Andrew Fish, and Jane Southern. "Automated Theorem Proving in Euler Diagram Systems." Journal of Automated Reasoning 39, no. 4 (2007): 431–70. http://dx.doi.org/10.1007/s10817-007-9069-y.

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20

Botana, Francisco, Markus Hohenwarter, Predrag Janičić, et al. "Automated Theorem Proving in GeoGebra: Current Achievements." Journal of Automated Reasoning 55, no. 1 (2015): 39–59. http://dx.doi.org/10.1007/s10817-015-9326-4.

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21

BOUHOULA, ADEL. "Automated Theorem Proving by Test Set Induction." Journal of Symbolic Computation 23, no. 1 (1997): 47–77. http://dx.doi.org/10.1006/jsco.1996.0076.

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22

Sutcliffe, Geoff, and Martin Desharnais. "The CADE-28 Automated Theorem Proving System Competition – CASC-28." AI Communications 34, no. 4 (2022): 259–76. http://dx.doi.org/10.3233/aic-210235.

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The CADE ATP System Competition (CASC) is the annual evaluation of fully automatic, classical logic Automated Theorem Proving (ATP) systems. CASC-28 was the twenty-sixth competition in the CASC series. Twenty-two ATP systems competed in the various competition divisions. This paper presents an outline of the competition design and a commentated summary of the results.

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23

Sutcliffe, Geoff, and Josef Urban. "The CADE-25 Automated Theorem Proving system competition – CASC-25." AI Communications 29, no. 3 (2016): 423–33. https://doi.org/10.3233/AIC-150691.

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The CADE ATP System Competition (CASC) is an annual evaluation of fully automatic, classical logic Automated Theorem Proving (ATP) systems. CASC-25 was the twentieth competition in the CASC series. Twenty-seven ATP systems and system variants competed in the various competition divisions. An outline of the competition design, and a commentated summary of the results, are presented.

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24

Sutcliffe, Geoff. "The 10th IJCAR automated theorem proving system competition – CASC-J10." AI Communications 34, no. 2 (2021): 163–77. http://dx.doi.org/10.3233/aic-201566.

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The CADE ATP System Competition (CASC) is the annual evaluation of fully automatic, classical logic Automated Theorem Proving (ATP) systems. CASC-J10 was the twenty-fifth competition in the CASC series. Twenty-four ATP systems and system variants competed in the various competition divisions. This paper presents an outline of the competition design, and a commentated summary of the results.

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25

HOMMERSOM, ARJEN, PETER J. F. LUCAS, and PATRICK VAN BOMMEL. "Checking the quality of clinical guidelines using automated reasoning tools." Theory and Practice of Logic Programming 8, no. 5-6 (2008): 611–41. http://dx.doi.org/10.1017/s1471068408003451.

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AbstractRequirements about the quality of clinical guidelines can be represented by schemata borrowed from the theory of abductive diagnosis, using temporal logic to model the time-oriented aspects expressed in a guideline. Previously, we have shown that these requirements can be verified using interactive theorem proving techniques. In this paper, we investigate how this approach can be mapped to the facilities of a resolution-based theorem prover,otterand a complementary program that searches for finite models of first-order statements,mace-2. It is shown that the reasoning required for chec

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26

Franke, Andreas, Stephan Hess, Christoph Jung, Michael Kohlhase, and Volker Sorge. "Agent-Oriented Integration of Distributed Mathematical Services." JUCS - Journal of Universal Computer Science 5, no. (3) (1999): 156–87. https://doi.org/10.3217/jucs-005-03-0156.

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Real-world applications of automated theorem proving require modern software environments that enable modularisation, networked inter-operability, robustness, and scalability. These requirements are met by the Agent-Oriented Programming paradigm of Distributed Artificial Intelligence. We argue that a reasonable framework for automated theorem proving in the large regards typical mathematical services as autonomous agents that provide internal functionality to the outside and that, in turn, are able to access a variety of existing external services. This article describes the MathWeb architectu

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27

Jan, Jakubuv, and Kaliszyk Cezary. "Relaxed Weighted Path Order in Theorem Proving." Mathematics in Computer Science 14, no. 3 (2020): 657——670. https://doi.org/10.1007/s11786-020-00474-0.

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We propose an extension of the automated theorem prover E by the weighted path order- ing (WPO). Weighted path ordering is theoretically stronger than all the orderings used in E Prover, however its parametrization is more involved than those normally used in automated reasoning. In particular, it depends on a term algebra. We integrate the ordering in E Prover and perform an eval- uation on the standard theorem proving benchmarks. The ordering is complementary to the ones used in E prover so far. Furthermore, first-time presented here, we propose a relaxed variant of the weighted path order a

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28

Phillips, J. D., and David Stanovský. "Automated theorem proving in quasigroup and loop theory." AI Communications 23, no. 2-3 (2010): 267–83. http://dx.doi.org/10.3233/aic-2010-0460.

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29

Coelho, Helder, and Luis Moniz Pereira. "Automated reasoning in geometry theorem proving with Prolog." Journal of Automated Reasoning 2, no. 4 (1986): 329–90. http://dx.doi.org/10.1007/bf00248249.

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30

Li, Hongbo. "Automated Theorem Proving Practice with Null Geometric Algebra." Journal of Systems Science and Complexity 32, no. 1 (2019): 95–123. http://dx.doi.org/10.1007/s11424-019-8354-2.

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31

Hsiang, Jieh, Hélène Kirchner, Pierre Lescanne, and Michaël Rusinowitch. "The term rewriting approach to automated theorem proving." Journal of Logic Programming 14, no. 1-2 (1992): 71–99. http://dx.doi.org/10.1016/0743-1066(92)90047-7.

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32

Yang, Lu. "Recent advances in automated theorem proving on inequalities." Journal of Computer Science and Technology 14, no. 5 (1999): 434–46. http://dx.doi.org/10.1007/bf02948785.

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33

Hongbo, Li, and Cheng Minteh. "Ordering in automated theorem proving of differential geometry." Acta Mathematicae Applicatae Sinica 14, no. 4 (1998): 358–62. http://dx.doi.org/10.1007/bf02683818.

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34

Zhao, Zhaokeng, Jun Dai, and Wendan Chen. "Automated theorem proving in temporal logic: T-resolution." Journal of Computer Science and Technology 9, no. 1 (1994): 53–62. http://dx.doi.org/10.1007/bf02939486.

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35

Atayan, V. V., and M. K. Morokhovets. "Combining formal derivation search procedures and natural theorem proving techniques in an automated theorem proving system." Cybernetics and Systems Analysis 32, no. 3 (1996): 442–65. http://dx.doi.org/10.1007/bf02366511.

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36

Guo, Dakai, and Wensheng Yu. "A Comprehensive Formalization of Propositional Logic in Coq: Deduction Systems, Meta-Theorems, and Automation Tactics." Mathematics 11, no. 11 (2023): 2504. http://dx.doi.org/10.3390/math11112504.

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The increasing significance of theorem proving-based formalization in mathematics and computer science highlights the necessity for formalizing foundational mathematical theories. In this work, we employ the Coq interactive theorem prover to methodically formalize the language, semantics, and syntax of propositional logic, a fundamental aspect of mathematical reasoning and proof construction. We construct four Hilbert-style axiom systems and a natural deduction system for propositional logic, and establish their equivalences through meticulous proofs. Moreover, we provide formal proofs for ess

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37

Baghdasaryan, Ashot, and Hovhannes Bolibekyan. "On Recurrent Neural Network Based Theorem Prover For First Order Minimal Logic." JUCS - Journal of Universal Computer Science 27, no. (11) (2021): 1193–202. https://doi.org/10.3897/jucs.76563.

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There are three main problems for theorem proving with a standard cut-free system for the first order minimal logic. The first problem is the possibility of looping. Secondly, it might generate proofs which are permutations of each other. Finally, during the proof some choice should be made to decide which rules to apply and where to use them. New systems with history mechanisms were introduced for solving the looping problems of automated theorem provers in the first order minimal logic. In order to solve the rule selection problem, recurrent neural networks are deployed and they are used to

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38

Benzmüller, Christoph, David Fuenmayor, and Bertram Lomfeld. "Modelling Value-Oriented Legal Reasoning in LogiKEy." Logics 2, no. 1 (2024): 31–78. http://dx.doi.org/10.3390/logics2010003.

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The logico-pluralist LogiKEy knowledge engineering methodology and framework is applied to the modelling of a theory of legal balancing, in which legal knowledge (cases and laws) is encoded by utilising context-dependent value preferences. The theory obtained is then used to formalise, automatically evaluate, and reconstruct illustrative property law cases (involving the appropriation of wild animals) within the Isabelle/HOL proof assistant system, illustrating how LogiKEy can harness interactive and automated theorem-proving technology to provide a testbed for the development and formal verif

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39

Sutcliffe, Geoff. "The CADE ATP System Competition — CASC." AI Magazine 37, no. 2 (2016): 99–101. http://dx.doi.org/10.1609/aimag.v37i2.2620.

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The CADE ATP System Competition (CASC) is an annual evaluation of fully automatic automated theorem proving (ATP) systems for classical logic — the world championship for such systems. CASC provides a public evaluation of the relative capabilities of ATP systems, and aims stimulate ATP research towards the development of more powerful ATP systems. Over the years CASC has been a catalyst for impressive improvements in ATP.

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40

Kovács, Zoltán, Tomas Recio, Luis F. Tabera, and M. Pilar Vélez. "Dealing with Degeneracies in Automated Theorem Proving in Geometry." Mathematics 9, no. 16 (2021): 1964. http://dx.doi.org/10.3390/math9161964.

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We report, through different examples, the current development in GeoGebra, a widespread Dynamic Geometry software, of geometric automated reasoning tools by means of computational algebraic geometry algorithms. Then we introduce and analyze the case of the degeneracy conditions that so often arise in the automated deduction in geometry context, proposing two different ways for dealing with them. One is working with the saturation of the hypotheses ideal with respect to the ring of geometrically independent variables, as a way to globally handle the statement over all non-degenerate components

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41

Kabat and Wojcik. "Automated Synthesis of Combinational Logic Using Theorem-Proving Techniques." IEEE Transactions on Computers C-34, no. 7 (1985): 610–32. http://dx.doi.org/10.1109/tc.1985.1676600.

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42

Wos, Larry, and William McCune. "Automated theorem proving and logic programming: a natural symbiosis." Journal of Logic Programming 11, no. 1 (1991): 1–53. http://dx.doi.org/10.1016/0743-1066(91)90008-d.

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43

Sofronie-Stokkermans, Viorica. "Automated theorem proving by resolution in non-classical logics." Annals of Mathematics and Artificial Intelligence 49, no. 1-4 (2007): 221–52. http://dx.doi.org/10.1007/s10472-007-9051-8.

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44

Baier, Christel. "Verification Column." ACM SIGLOG News 10, no. 4 (2023): 24. http://dx.doi.org/10.1145/3636362.3636366.

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Automated theorem proving can be seen as a logic-based approach for generating mathematical proofs mechanically. Important applications are hardware and software verification, general-purpose proof assistants and proof checking. Most state-of-the-art theorem provers rely on proof calculi for higher-order logic that incorporate superposition techniques or satisfiability modulo theories. The article by Bentkamp, Blanchette, Nummelin, Tourret and Waldmann provides an overview of the recently developed λ-superposition approach. It takes inspirations of classical superposition for first-order logic

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45

Baghdasaryan, Ashot, and Hovhannes Bolibekyan. "On Recurrent Neural Network Based Theorem Prover For First Order Minimal Logic." JUCS - Journal of Universal Computer Science 27, no. 11 (2021): 1193–202. http://dx.doi.org/10.3897/jucs.76563.

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Abstract:

There are three main problems for theorem proving with a standard cut-free system for the first order minimal logic. The first problem is the possibility of looping. Secondly, it might generate proofs which are permutations of each other. Finally, during the proof some choice should be made to decide which rules to apply and where to use them. New systems with history mechanisms were introduced for solving the looping problems of automated theorem provers in the first order minimal logic. In order to solve the rule selection problem, recurrent neural networks are deployed and they are used to

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46

Steen, Alexander. "Higher-order theorem proving and its applications." it - Information Technology 61, no. 4 (2019): 187–91. http://dx.doi.org/10.1515/itit-2019-0001.

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Abstract Automated theorem proving systems validate or refute whether a conjecture is a logical consequence of a given set of assumptions. Higher-order provers have been successfully applied in academic and industrial applications, such as planning, software and hardware verification, or knowledge-based systems. Recent studies moreover suggest that automation of higher-order logic, in particular, yields effective means for reasoning within expressive non-classical logics, enabling a whole new range of applications, including computer-assisted formal analysis of arguments in metaphysics. My wor

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47

Stolzenburg, Frieder. "Loop-Detection in Hyper-Tableaux by Powerful Model Generation." JUCS - Journal of Universal Computer Science 5, no. (3) (1999): 135–55. https://doi.org/10.3217/jucs-005-03-0135.

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Automated reasoning systems often suffer from redundancy: similar parts of derivations are repeated again and again. This leads us to the problem of loop-detection, which clearly is undecidable in general. Nevertheless, we tackle this problem by extending the hyper-tableau calculus as proposed in [Baumgartner, 1998] by generalized terms with exponents, that can be computed by means of computer algebra systems. Although the proposed loop-detection rule is incomplete, the overall calculus remains complete, because loop-detection is only used as an additional, optional mechanism. In summary, this

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48

Słowik, Agnieszka, Chaitanya Mangla, Mateja Jamnik, Sean B. Holden, and Lawrence C. Paulson. "Bayesian Optimisation for Premise Selection in Automated Theorem Proving (Student Abstract)." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 10 (2020): 13919–20. http://dx.doi.org/10.1609/aaai.v34i10.7232.

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Modern theorem provers utilise a wide array of heuristics to control the search space explosion, thereby requiring optimisation of a large set of parameters. An exhaustive search in this multi-dimensional parameter space is intractable in most cases, yet the performance of the provers is highly dependent on the parameter assignment. In this work, we introduce a principled probabilistic framework for heuristic optimisation in theorem provers. We present results using a heuristic for premise selection and the Archive of Formal Proofs (AFP) as a case study.

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49

Sutcliffe, Geoff. "The 6th IJCAR automated theorem proving system competition – CASC-J6." AI Communications 26, no. 2 (2013): 211–23. http://dx.doi.org/10.3233/aic-130550.

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50

Sutcliffe, Geoff. "The CADE-24 automated theorem proving system competition – CASC-24." AI Communications 27, no. 4 (2014): 405–16. http://dx.doi.org/10.3233/aic-140606.

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