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Electronic Proceedings in Theoretical Computer Science最新文献

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Open Source Prover in the Attic 阁楼上的开放源代码验证器
Electronic Proceedings in Theoretical Computer Science Pub Date : 2024-01-20 DOI: 10.4204/eptcs.398.9
Zoltán Kovács, Alexander Vujic
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引用次数: 0
Automated Completion of Statements and Proofs in Synthetic Geometry: an Approach based on Constraint Solving 自动完成合成几何中的语句和证明：基于约束求解的方法
Electronic Proceedings in Theoretical Computer Science Pub Date : 2024-01-20 DOI: 10.4204/EPTCS.398.6
Salwa Tabet Gonzalez, Predrag Janivci'c, Julien Narboux
{"title":"Automated Completion of Statements and Proofs in Synthetic Geometry: an Approach based on Constraint Solving","authors":"Salwa Tabet Gonzalez, Predrag Janivci'c, Julien Narboux","doi":"10.4204/EPTCS.398.6","DOIUrl":"https://doi.org/10.4204/EPTCS.398.6","url":null,"abstract":"Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn a conjecture with missing assumptions and with an under-specified goal into a proper theorem. Also, the proposed framework can help in completing a proof sketch into a human-readable and machine-checkable proof. Our approach is focused on synthetic geometry, and uses coherent logic and constraint solving. The proposed approach is uniform for all three kinds of tasks, flexible and, to our knowledge, unique such approach.","PeriodicalId":30085,"journal":{"name":"Electronic Proceedings in Theoretical Computer Science","volume":"27 13","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139610690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Using GXWeb for Theorem Proving and Mathematical Modelling 使用 GXWeb 进行定理证明和数学建模
Electronic Proceedings in Theoretical Computer Science Pub Date : 2024-01-20 DOI: 10.4204/EPTCS.398.7
Philip Todd, Danny Aley
{"title":"Using GXWeb for Theorem Proving and Mathematical Modelling","authors":"Philip Todd, Danny Aley","doi":"10.4204/EPTCS.398.7","DOIUrl":"https://doi.org/10.4204/EPTCS.398.7","url":null,"abstract":"GXWeb is the free browser based version of the symbolic geometry software Geometry Expressions. We demonstrate its use in an educational setting with examples from theorem proving, mathematical modelling and loci and envelopes.","PeriodicalId":30085,"journal":{"name":"Electronic Proceedings in Theoretical Computer Science","volume":"80 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139611052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solving with GeoGebra Discovery an Austrian Mathematics Olympiad problem: Lessons Learned 用 GeoGebra Discovery 解决奥地利数学奥林匹克问题：经验教训
Electronic Proceedings in Theoretical Computer Science Pub Date : 2024-01-20 DOI: 10.4204/EPTCS.398.13
Bel'en Arino-Morera, Zolt'an Kov'acs, Tom'as Recio, Piedad Tolmos
{"title":"Solving with GeoGebra Discovery an Austrian Mathematics Olympiad problem: Lessons Learned","authors":"Bel'en Arino-Morera, Zolt'an Kov'acs, Tom'as Recio, Piedad Tolmos","doi":"10.4204/EPTCS.398.13","DOIUrl":"https://doi.org/10.4204/EPTCS.398.13","url":null,"abstract":"We address, through the automated reasoning tools in GeoGebra Discovery, a problem from a regional phase of the Austrian Mathematics Olympiad 2023. Trying to solve this problem gives rise to four different kind of feedback: the almost instantaneous, automated solution of the proposed problem; the measure of its complexity, according to some recent proposals; the automated discovery of a generalization of the given assertion, showing that the same statement is true over more general polygons than those mentioned in the problem; and the difficulties associated to the analysis of the surprising and involved high number of degenerate cases that appear when using the LocusEquation command in this problem. In our communication we will describe and reflect on these diverse issues, enhancing its exemplar role for showing some of the advantages, problems, and current fields of development of GeoGebra Discovery.","PeriodicalId":30085,"journal":{"name":"Electronic Proceedings in Theoretical Computer Science","volume":"57 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139611407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Towards an Independent Version of Tarski's System of Geometry 塔尔斯基几何体系的独立版本
Electronic Proceedings in Theoretical Computer Science Pub Date : 2024-01-20 DOI: 10.4204/EPTCS.398.11
Pierre Boutry, St'ephane Kastenbaum, Cl'ement Saintier
{"title":"Towards an Independent Version of Tarski's System of Geometry","authors":"Pierre Boutry, St'ephane Kastenbaum, Cl'ement Saintier","doi":"10.4204/EPTCS.398.11","DOIUrl":"https://doi.org/10.4204/EPTCS.398.11","url":null,"abstract":"In 1926-1927, Tarski designed a set of axioms for Euclidean geometry which reached its final form in a manuscript by Schwabh\"auser, Szmielew and Tarski in 1983. The differences amount to simplifications obtained by Tarski and Gupta. Gupta presented an independent version of Tarski's system of geometry, thus establishing that his version could not be further simplified without modifying the axioms. To obtain the independence of one of his axioms, namely Pasch's axiom, he proved the independence of one of its consequences: the previously eliminated symmetry of betweenness. However, an independence model for the non-degenerate part of Pasch's axiom was provided by Szczerba for another version of Tarski's system of geometry in which the symmetry of betweenness holds. This independence proof cannot be directly used for Gupta's version as the statements of the parallel postulate differ. In this paper, we present our progress towards obtaining an independent version of a variant of Gupta's system. Compared to Gupta's version, we split Pasch's axiom into this previously eliminated axiom and its non-degenerate part and change the statement of the parallel postulate. We verified the independence properties by mechanizing counter-models using the Coq proof-assistant.","PeriodicalId":30085,"journal":{"name":"Electronic Proceedings in Theoretical Computer Science","volume":"53 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139611544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Locus Story of a Rocking Camel in a Medical Center in the City of Freistadt 弗赖施塔特市医疗中心摇摆骆驼的 Locus 故事
Electronic Proceedings in Theoretical Computer Science Pub Date : 2024-01-20 DOI: 10.4204/EPTCS.398.16
Anna Kaferbock, Zolt'an Kov'acs
{"title":"The Locus Story of a Rocking Camel in a Medical Center in the City of Freistadt","authors":"Anna Kaferbock, Zolt'an Kov'acs","doi":"10.4204/EPTCS.398.16","DOIUrl":"https://doi.org/10.4204/EPTCS.398.16","url":null,"abstract":"We give an example of automated geometry reasoning for an imaginary classroom project by using the free software package GeoGebra Discovery. The project is motivated by a publicly available toy, a rocking camel, installed at a medical center in Upper Austria. We explain how the process of a false conjecture, experimenting, modeling, a precise mathematical setup, and then a proof by automated reasoning could help extend mathematical knowledge at secondary school level and above.","PeriodicalId":30085,"journal":{"name":"Electronic Proceedings in Theoretical Computer Science","volume":"74 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139611285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Improving Angular Speed Uniformity by Piecewise Radical Reparameterization 通过分片根式重参数化改善角速度均匀性
Electronic Proceedings in Theoretical Computer Science Pub Date : 2024-01-20 DOI: 10.4204/EPTCS.398.19
Hoon Hong, Dongming Wang, Jing Yang
{"title":"Improving Angular Speed Uniformity by Piecewise Radical Reparameterization","authors":"Hoon Hong, Dongming Wang, Jing Yang","doi":"10.4204/EPTCS.398.19","DOIUrl":"https://doi.org/10.4204/EPTCS.398.19","url":null,"abstract":"For a rational parameterization of a curve, it is desirable that its angular speed is as uniform as possible. Hence, given a rational parameterization, one wants to find re-parameterization with better uniformity. One natural way is to use piecewise rational reparameterization. However, it turns out that the piecewise rational reparameterization does not help when the angular speed of the given rational parameterization is zero at some points on the curve. In this paper, we show how to overcome the challenge by using piecewise radical reparameterization.","PeriodicalId":30085,"journal":{"name":"Electronic Proceedings in Theoretical Computer Science","volume":"57 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139611406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Using Java Geometry Expert as Guide in the Preparations for Math Contests 用 Java 几何专家指导数学竞赛准备工作
Electronic Proceedings in Theoretical Computer Science Pub Date : 2024-01-20 DOI: 10.4204/eptcs.398.15
Ines Ganglmayr, Zoltán Kovács
{"title":"Using Java Geometry Expert as Guide in the Preparations for Math Contests","authors":"Ines Ganglmayr, Zoltán Kovács","doi":"10.4204/eptcs.398.15","DOIUrl":"https://doi.org/10.4204/eptcs.398.15","url":null,"abstract":"","PeriodicalId":30085,"journal":{"name":"Electronic Proceedings in Theoretical Computer Science","volume":"13 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139523692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Towards Automatic Transformations of Coq Proof Scripts 实现 Coq 证明脚本的自动转换
Electronic Proceedings in Theoretical Computer Science Pub Date : 2024-01-20 DOI: 10.4204/EPTCS.398.4
Nicolas Magaud
{"title":"Towards Automatic Transformations of Coq Proof Scripts","authors":"Nicolas Magaud","doi":"10.4204/EPTCS.398.4","DOIUrl":"https://doi.org/10.4204/EPTCS.398.4","url":null,"abstract":"Proof assistants like Coq are increasingly popular to help mathematicians carry out proofs of the results they conjecture. However, formal proofs remain highly technical and are especially difficult to reuse. In this paper, we present a framework to carry out a posteriori script transformations. These transformations are meant to be applied as an automated post-processing step, once the proof has been completed. As an example, we present a transformation which takes an arbitrary large proof script and produces an equivalent single-line proof script, which can be executed by Coq in one single step. Other applications, such as fully expanding a proof script (for debugging purposes), removing all named hypotheses, etc. could be developed within this framework. We apply our tool to various Coq proof scripts, including some from the GeoCoq library.","PeriodicalId":30085,"journal":{"name":"Electronic Proceedings in Theoretical Computer Science","volume":"7 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139524191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Towards Automated Readable Proofs of Ruler and Compass Constructions 实现尺规和罗盘构造的自动可读证明
Electronic Proceedings in Theoretical Computer Science Pub Date : 2024-01-20 DOI: 10.4204/EPTCS.398.5
Vesna Marinković, Tijana vSukilovi'c, Filip Marić
{"title":"Towards Automated Readable Proofs of Ruler and Compass Constructions","authors":"Vesna Marinković, Tijana vSukilovi'c, Filip Marić","doi":"10.4204/EPTCS.398.5","DOIUrl":"https://doi.org/10.4204/EPTCS.398.5","url":null,"abstract":"Although there are several systems that successfully generate construction steps for ruler and compass construction problems, none of them provides readable synthetic correctness proofs for generated constructions. In the present work, we demonstrate how our triangle construction solver ArgoTriCS can cooperate with automated theorem provers for first order logic and coherent logic so that it generates construction correctness proofs, that are both human-readable and formal (can be checked by interactive theorem provers such as Coq or Isabelle/HOL). These proofs currently rely on many high-level lemmas and our goal is to have them all formally shown from the basic axioms of geometry.","PeriodicalId":30085,"journal":{"name":"Electronic Proceedings in Theoretical Computer Science","volume":"53 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139611706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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