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Some observations on the logical foundations of inductive theorem proving [PDF]
Logical Methods in Computer Science, 2018 In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a goal. Based on
Stefan Hetzl, Tin Lok Wong
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Proof simplification and automated theorem proving. [PDF]
Philos Trans A Math Phys Eng Sci, 2019 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
Kinyon M.
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Rewriting and Well-Definedness within a Proof System [PDF]
Electronic Proceedings in Theoretical Computer Science, 2010 Term rewriting has a significant presence in various areas, not least in automated theorem proving where it is used as a proof technique. Many theorem provers employ specialised proof tactics for rewriting.
Issam Maamria, Michael Butler
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Automatic Generation of Proof Tactics for Finite-Valued Logics [PDF]
Electronic Proceedings in Theoretical Computer Science, 2010 A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage.
João Marcos
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Another look at automated theorem-proving
Journal of Mathematical Cryptology, 2007 I examine the use of automated theorem-proving for reductionist security arguments in cryptography and discuss three papers that purport to show the potential of computer-assisted proof-writing and proof-checking.
Koblitz Neal
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Automated theorem proving in elementary geometry
Le Matematiche, 1988 A survey of the main procedures for automatic theorem proving in geometry is presented.
Alfredo Ferro, Giovanni Gallo
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On Recurrent Neural Network Based Theorem Prover For First Order Minimal Logic [PDF]
Journal of Universal Computer Science, 2021 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
Ashot Baghdasaryan, Hovhannes Bolibekyan
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Dealing with Degeneracies in Automated Theorem Proving in Geometry
Mathematics, 2021 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.
Zoltán Kovács +3 more
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Clause Set Cycles and Induction [PDF]
Logical Methods in Computer Science, 2020 In this article we relate a family of methods for automated inductive theorem proving based on cycle detection in saturation-based provers to well-known theories of induction.
Stefan Hetzl, Jannik Vierling
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Learning-Assisted Automated Reasoning with Flyspeck [PDF]
, 2014 The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machine-learning premise selection methods trained on the proofs, producing an AI system capable of answering a wide ...
Kaliszyk, Cezary, Urban, Josef
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