MEREOLOGY on DISTRIBUTIVE SET THEORY
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Mereology_on_DST_structurev1.v is a Coq library created by R. Dapoigny and P. Barlatier whose main objective is to provide a consistent structure of Mereology. For that purpose, the developed structure relies on the Distributive Set Theory (DST) expressed in Dependent Type Theory 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 structure based on definitions in order to get rid of axioms and to allow for incremental modelling of applications. Furthermore, the base theory has also been proved in Isabelle/HOL for full automation.
- Coq (> v8.9)
- Click here to download Mereology_on_DST_structure (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_DST_structurev1.v” in order to use it.