MEREOLOGY with DISTRIBUTIVE SET THEORY
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Mereology_on_Onto_sets_v2.vo is a Coq library created by R. Dapoigny and P. Barlatier whose main objective is to provide a consistent structure for Mereology. For that purpose, the developed structure relies on the Monadic Second Order (MSO) translation of the basic part of Lesniewski’s Ontology and based on characteristic functions to construct appropriate sets. Using Clay’s single axiom for partial order, we prove that this axiom is equivalent to the single axiom of mereology and then that the latter has a boolean model without zero. We have extended the MSO structure based on definitions in order to get rid of axioms and to allow for an incremental modelling of applications. The library is available in two files. The file Mereology_on_Onto_sets_v3.vo is the library file to be included in the header in order to use its content. The file Mereology_on_Onto_sets_v3_src.v contains the source code. Notice that since these files implement automation, they require the additional software CoqHammer v1.3.
- Coq (> v8.12)
- Click here to download the library Mereology_on_Onto_sets_v3 (7z file).
- Unzip the file content (e.g. with 7-zip) in your local directory.
- Start Coq.
- Open a new file and incorporate the external file “Mereology_on_Onto_sets_v3” in order to use it.
- Click here to download source code (7z file).