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Proceedings of ADG 2016 Julien Narboux, Pascal Schreck, Ileana Streinu Proceedings of ADG 2016 Julien Narboux, Pascal Schreck, Ileana Streinu To cite this version: Julien Narboux, Pascal Schreck, Ileana Streinu. Proceedings of ADG 2016: Eleventh International Workshop on Automated Deduction in Geometry. Jun 2016, Strasbourg, France. pp.224, 2016. hal- 01334334 HAL Id: hal-01334334 https://hal.inria.fr/hal-01334334 Submitted on 20 Jun 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Julien Narboux Pascal Schreck Ileana Streinu (Eds.) 2016 ADGEleventh International Workshop on Automated Deduction in Geometry University of Strasbourg, France, June 27-29, 2016 Julien Narboux Pascal Schreck Ileana Streinu (Eds.) Automated Deduction in Geometry 11th International Workshop, ADG 2016 Strasbourg, France, June 27-29, 2016 Preface This volume contains the 14 papers and 3 invited talks presented at ADG 2016: Eleventh International Work- shop on Automated Deduction in Geometry held on June 26-28, 2016 in Strasbourg, France. ADG is a forum facilitating the exchange of ideas, presentation of new research results and demonstrations of software tools lying at the intersection of geometry and automated deduction. The selected papers, reviewed by an international Program Committee, cover diverse topics ranging from polynomial algebra, invariant and coordinate-free methods, synthetic and logic approaches, techniques for automated geometric reasoning from dis- crete mathematics, symbolic and numeric methods for geometric computation, geometric algorithms, geometric constraint solving, experimental studies with automated theorem provers, applications to mechanics, origami and geometric modeling. The previous ten workshops were held in Coimbra 2014, Edinburgh 2012, Munich 2010, Shangha¨ı2008, Ponteve- dra 2006, Gainesville 2004, Linz 2002, Zurich 2000, Bei- jing 1998, and Toulouse 1996. The conference was organized by the Computer Graph- ics and Geometry Group of ICube Laboratory (CNRS / Universit´ede Strasbourg). We would like to thank the invited speakers and au- thors for their contributions. We are very grateful to the program committee members and referees for their exper- tise which ensures the high scientific standard of ADG. We also warmly thank all the local organizers for con- tributing to the practical organisation so that the meet- ing can be held smoothly. We thank the IGG team and the ICube laboratory for helping us by sponsoring this conference. Support from EasyChair is also gratefully ac- knowledged. June 13, 2016 Julien Narboux Strasbourg Pascal Schreck Ileana Streinu Program Committee Michael Beeson San Jose State University Francisco Botana University of Vigo John Bowers James Madison University Xiaoyu Chen Beihang University Xiao-Shan Gao Academia Sinica Tetsuo Ida University of Tsukuba Filip Mari´c University of Belgrade Pascal Mathis University of Strasbourg Julien Narboux University of Strasbourg Pavel Pech University of South Bohemia Pedro Quaresma University of Coimbra Tomas Recio Universidad de Cantabria Pascal Schreck University of Strasbourg Meera Sitharam University of Florida Ileana Streinu Smith College Dongming Wang Beihang University and CNRS Bican Xia Peking University Additional Reviewers Fadoua Ghourabi Wenping Wang Menghan Wang Jeremy Youngquist Organizers Pierre Boutry Pascal Mathis David Braun Julien Narboux Gabriel Braun Pascal Schreck Nicolas Magaud Dan Song Table of Contents Invited Speakers Geometrisation of Geometry ................... 1 Predrag Janiˇci´c Solving With Or Without Equations ............ 15 Dominique Michelucci Dependence of Axioms for Weak Geometries Proved Syntactically .......................... 21 Victor Pambuccian Contributed Papers Implementing Automatic Discovery in GeoGebra . 23 Miguel A. Ab´anades,Francisco Botana, Zolt´an Kov´acs,Tom´asRecio and Csilla S´olyom-Gecse Geodesic Star Unfolding ...................... 32 Md. Ashraful Alam and Ileana Streinu Geometric Deformations of Sodalite Frameworks . 44 Ciprian Borcea and Ileana Streinu Computing the Straight Skeleton of a Simple Polygon from its Motorcycle Graph in Deterministic O(n.logn) Time ................. 54 John C. Bowers An Equivalence Proof Between Rank Theory and Incidence Projective Geometry ............. 62 David Braun, Nicolas Magaud and Pascal Schreck From Hilbert to Tarski ........................ 78 Gabriel Braun, Pierre Boutry and Julien Nar- boux Massic points, B´ezierCurves and Conics: a Survey 97 Lionel Garnier and Jean-Paul B´ecar A New Formalization of Origami in Geometric Algebra ..................................... 117 Tetsuo Ida, Jacques Fleuriot and Fadoua Ghourabi Automatic Rewrites of Input Expressions in Complex Algebraic Geometry Provers ........... 137 Zolt´anKov´acs,Tom´asRecio and Csilla S´olyom- Gecse Two ways of using Rabinowitsch trick for imposing non-degeneracy conditions ............ 144 Manuel Ladra, Pilar P´aez-Guill´anand Tom´as Recio Portfolio Methods in Theorem Proving for Elementary Geometry ........................ 152 Vesna Marinkovi´c,Mladen Nikoli´c,Zolt´anKov´acs and Predrag Janiˇci´c On a Certain Class of Cubic Surfaces Related to the Simson–Wallace Theorem .................. 162 Pavel Pech Automated Generation of Keywords from Images for Geometric Information Search ........ 172 Dan Song and Xiaoyu Chen Formalization of a Surface Subdivision Allowing a Region with Holes without Coordinates ........ 190 Kazuko Takahashi, Sosuke Moriguchi and Mizuki Goto Geometrisation of Geometry? Predrag Janiˇci´c1 Faculty of Mathematics, University of Belgrade, Serbia Abstract. Coherent logic (CL) is a fragment of first-order logic suitable for automation of proving process and also for formalization of various mathematical theories, including geometry. This paper gives an overview of several developments based on CL with geometry as the domain: au- tomated theorem provers for CL, CL-based formalizations of geometry, CL-based proof representation, links between CL and geometry construc- tion problems, links between CL and geometrical illustrations, etc. 1 Introduction Automated deduction in geometry has been around for more than sixty years now and it still attracts a lot of attention for several reasons: it requires paradigmatic reasoning that is very difficult to automate, progress in automated reasoning in geometry often leads to ideas that influence other fields, there are practical appli- cations in areas such as robotics, ... and, of course, it is very beautiful. Over the decades, there were several ingenious insights into geometrical reasoning and also links to algebra that led to new methods capable of solving many hard geometry problems [9,10,22]. Still, after all that years and methods, there are no computer programs capable of routinely solving all geometry problems explored in high- school Euclidean geometry. Like in other related domains, there are important issues and challenges concerning scope and efficiency, but in geometry it is also readability of solutions that matters. While algebraic theorem provers for geom- etry proved that they can efficiently solve a wide scope of geometry problems, they cannot provide readable, understandable solutions in terms of synthetic geometry. The same holds for resolution-based approaches. Some semi-synthetic approaches (such as the area method or the full-angle method) provide proofs that can be concise and intuitive, but not always (often their outputs involve enormously large expressions). In this paper, coherent logic, denoted by CL, is discussed. A number of theories and theorems can be formulated directly and simply in CL, for in- stance group theory, ring theory, category theory, the theory of fields, lattice theory, a range of geometries, etc. Several authors independently point to CL or similar fragments of first order logic as suitable for expressing (sometimes – also automating) portions of standard mathematics, for instance, Ganesalingam and Gowers in the context of automated generation of readable proofs [18], Tarski in the context of his geometry [37], Avigad et.al. in the context of a ? Partly supported by the grant 174021 of the Ministry of Science of Serbia. 2 Predrag Janiˇci´c new diagram-based axiomatic foundations of geometry [1], etc. In contrast to resolution-based theorem proving, in CL the conjecture being proved is kept un- changed and proved without using refutation, Skolemization and clausal form. Thanks to this, CL can serve as a vehicle for producing, at least in some cases and to some extent, human-readable synthetic geometry proofs (in the style of forward reasoning) [4] with ”structure of ordinary mathematical arguments bet- ter retained“ [16]. Moreover, since it allows (limited) existential quantification, it allows building theorem provers with the scope that goes beyond universally quantified fragment, typical for most available proving methods in geometry. CL proofs can also be easily translated into input language of different proof assistants and in a natural language form. 2 Coherent and Geometric Logic A formula of first-order logic is said to be coherent if it has the following form: A (x)
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