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Logical properties of foundational mereogeometrical relations in bio-ontologies

机译：生物本体中基本几何关系的逻辑性质

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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.rnA 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.rnA 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.rnAll 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.
机译：本文的一个目的是通过提供关系的逻辑属性的公理规范，例如part_of，located_in，connected_to，neighborto-to，attach_to等，来提高OBO关系本体的逻辑和本体严谨性。目前仅松散地指定所有这些关系在OBO.rn中的第二个目标是通过包括定性大小关系的公理化表征来提高关系本体的表达能力，这些定性大小关系的大小大致相同，而大小可忽略不计，这些关系对于以与其几何特性的正常变化兼容的方式比较解剖实体非常重要。此外，定性大小关系对于区分不同尺度的解剖实体很重要。不幸的是，由于这些关系的上下文相关性质和固有的模糊性，很难正式对待这些关系。本文提出了一种形式化的形式，以促进将上下文无关和模糊的本体方面与上下文无关且易受模糊性的方面分开。第三个目标是明确考虑所有上下文的特定时间特性。关系并提供形式化信息，可以用作规范解剖结构和实例化解剖结构形式化表示的基础。所有关系及其特性均以人体滑膜关节为例进行非正式说明。在形式层面，公理理论是使用Isabelle开发的，Isabelle是用于实施逻辑形式主义的计算系统。所有证明都经过计算机验证，并且可以使用该理论的计算表示。

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