A Coq-based Implementation of Tarski's Mereogeometry - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year :

A Coq-based Implementation of Tarski's Mereogeometry


During the last decade, the domain of Qualitative Spatial Reasoning, has known a renewal of interest for mereogeometry, a theory that has been initiated by Tarski. Mereogeometry relies on mereology, the Lesniewski's theory of parts and wholes that is further extended with geometrical primitives and appropriate definitions. However, most approaches (i) depart from the original Lesniewski's mereology which does not assume usual sets as a basis, (ii) restrict the logical power of mereology to a mere theory of part-whole relations and (iii) require the introduction of a connection relation. Moreover, the seminal paper of Tarki shows up unclear foundations and we argue that mereogeometry as it is introduced by Tarski, can be more suited to extend the whole theory of Lesniewski. For that purpose, we investigate a type-theoretical representation of space more closely related with the original ideas of Lesniewski and expressed with the Coq language. We show that (i) it can be given a more clear foundation, (ii) it can be based on three axioms instead of four and (iii) it can serve as a basis for spatial reasoning with full compliance with Lesniewski's systems.
presentICOSIT15.pdf (578.02 Ko) Télécharger le fichier
Format : Presentation
Origin : Files produced by the author(s)

Dates and versions

hal-01238709 , version 1 (08-12-2015)



Richard Dapoigny, Patrick Barlatier. A Coq-based Implementation of Tarski's Mereogeometry. COSIT'2015 - 12th International Conference on Spatial Information Theory, Oct 2015, Santa Fe, United States. pp.108-129, ⟨10.1007/978-3-319-23374-1_6⟩. ⟨hal-01238709⟩
65 View
151 Download



Gmail Facebook Twitter LinkedIn More