Logical properties of foundational mereogeometrical relations in bio-ontologies
One aim of this paper is to improve the logical and ontological rigor of the OBO relation ontology by providing axiomatic specifications for logical properties of relations such as part_of, located_in, connected_to, adjacent_to, attached_to, etc. All of these relations are currently only loosely specified in OBO. A second aim is to improve the expressive power of the relation ontology by including axiomatic characterizations of qualitative size relations such as (roughly-the-) same-size-as, negligible-in-size-with-respect-to, same-scale, etc. These relations are important for comparing anatomical entities in a way that is compatible with the normal variations of their geometric properties. Moreover, qualitative size relations are important for distinguishing anatomical entities at different scales. Unfortunately, the formal treatment of these relations is difficult due to their context-dependent nature and their inherent vagueness. This paper presents a formalization that facilitates the separation of ontological aspects that are context-independent and non-vague from aspects that are context-dependent and subject to vagueness. A third aim is to explicitly take into account the specific temporal properties of all of the relations and to provide a formalization that can be used as a basis for the formal representation of canonical anatomy as well as of instantiated anatomy. All the relations and their properties are illustrated informally using a human synovial joint as a running example. At the formal level the axiomatic theory is developed using Isabelle, a computational system for implementing logical formalisms. All proofs are computer-verified and the computational representation of the theory is accessible on http://www.ifomis.org/bfo/fol.
obo vagueness formal ontology mereology mereotopology mereogeometry qualitative representation and reasoning context