Result: Higher-order intuitionistic formalization and proofs in Hilbert's elementary geometry
Title:
Higher-order intuitionistic formalization and proofs in Hilbert's elementary geometry
Source:
ADG 2000 : automated deduction in geometry (Zurich, 25-27 September 2000, revised papers)Lecture notes in computer science. :306-323
Publisher Information:
Berlin: Springer, 2001.
Publication Year:
2001
Physical Description:
print, 23 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Fonctions de plusieurs variables complexes et espaces analytiques, Several complex variables and analytic spaces, Sciences appliquees, Applied sciences, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Intelligence artificielle, Artificial intelligence, Reconnaissance des formes. Traitement numérique des images. Géométrie algorithmique, Pattern recognition. Digital image processing. Computational geometry, Axiomatique, Axiomatic, Axiomático, Espace Hilbert, Hilbert space, Espacio Hilbert, Géométrie algorithmique, Computational geometry, Geometría computacional, Géométrie algébrique, Algebraic geometry, Geometría algebraica, Modèle géométrique, Geometrical model, Modelo geométrico, Type donnée, Data type, Tipo dato, Calcul construction inductive, Inductive construction calculus, Calculo construcción inductivo, Logique ordre supérieur, High order logic
Document Type:
Conference
Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection (UMR CNRS 7005), Université Louis-Pasteur de Strasbourg, Pôle API, boulevard S. Brant, 67400 Illkirch, France
ISSN:
0302-9743
Rights:
Copyright 2002 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems
Mathematics
Mathematics
Accession Number:
edscal.14047691
Database:
PASCAL Archive
Further Information
We propose the basis of a higher-order logical framework to axiomatize and build proofs in Hilbert's elementary geometry in which intuitionistic aspects are emphasized. More precisely, we use the Calculus of inductive constructions and the system Coq to specify geometric concepts and to study and interactively handle proofs for the first two groups of Hilbert's axiomatics. It is the first step to a formalization well adapted to the definition of primitive operations that are used in many different geometric algorithms.