A decision procedure using discrete geometry

A Decision Procedure for Geometry in Coq

We present in this paper the development of a decision procedure for affine plane geometry in the Coq proof assistant. Among the existing decision methods, we have chosen to implement one based on the area method developed by Chou, Gao and Zhang, which provides short and “readable” proofs for geometry theorems. The idea of the method is to express the goal to be proved using three geometric qua...

Using Resolution as Decision Procedure

This cumulative habilitation thesis is based on five papers related to resolution decision procedures. Resolution is a well-known technique for first-order theorem proving. It is complete, but it does not terminate in general, when there exists no proof. In many cases, resolution can be modified in such a way that it becomes a decision procedure for certain subclasses of first-order logic. We h...

HABILITATIONSSCHRIFT Using Resolution as Decision Procedure

1 Introduction Logic made a major step in 1879, when Gottlob Frege published his 'Begriffss-chrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens', see [26]. In this paper, which marks the start of modern logic, Frege introduced a formal language, (which he called Begriffsschrift), in which mathematical statements can be formally stated, and also formally proven. (witho...

Geometry II - Discrete Differential Geometry

Modeling of a multimodal image aggregation process using discrete geometry

In order to help clinicians with the diagnosis of neurodegenerative diseases, we provide a synthetic functional information located in relation with anatomical structures. The final image is processed by multimodal data fusion between SPECT and MR images. We propose a new method for the management of such multiresolution data, in which a geometrical model allows an accurate correspondence of vo...