MATHEMATICAL AND COGNITIVE FOUNDATION FOR THE SYSTEMATIZATION OF ONTOLOGICAL RELATIONS
DOI:
https://doi.org/10.34185/1991-7848.itmm.2025.01.093Keywords:
Ontology, taxonomy, relations, image schemas, knowledge formalization, semantics, relation algebra.Abstract
This paper analyzes the methods and approaches for the systematization of ontological relations, based on the integration of their mathematical properties, cognitive foundations, and semantic nature. Relations are considered as sets of tuples of a given arity that define links between elements. Relation algebra helps to understand the semantic patterns underlying these connections and to generalize the rules of their composition. The study examines fundamental relations formed by generalizing image-based cognitive schemas and derived relations based on them. Synthetic and meta-relations (relations between relations) are also considered. Special attention is given to the logical composition of relations and the properties of this process. The paper highlights the connection between basic relations, which emerge from the generalization of sensory experience, and relations artificially synthesized using axiomatic definitions at the ontology level and formal logic-based composition. The proposed taxonomy is aimed at organizing sets of relations to support the construction of universal and consistent ontologies applicable across various domains.
References
Russell, B. (2020). Principles of mathematics. Routledge.
Tarski, A. (1994). Introduction to Logic and to the Methodology of the Deductive Sciences (Vol. 24). Oxford university press.
Herre, H., Heller, B., Burek, P., Hoehndorf, R., Loebe, F., & Michalek, H. (2006). General formal ontology (GFO). Part I: Basic Principles. Onto-Med Report, 8.
Lakoff, G., & Johnson, M. (2008). Metaphors we live by. University of Chicago press.
Johnson, M. (2013). The body in the mind: The bodily basis of meaning, imagination, and reason. University of Chicago press.
Hoffman, D. D., Singh, M., & Prakash, C. (2015). The interface theory of perception. Psychonomic bulletin & review, 22, 1480-1506.
Sowa, J. F. (2000). Knowledge Representation: Logical, Philosophical, and Computational Foundations. Brooks/Cole.
Hayes, P. J. (1989). Naive physics I: Ontology for liquids. In Readings in qualitative reasoning about physical systems (pp. 484-502).
Baader, F., Horrocks, I., & Sattler, U. (2008). Description logics. Foundations of Artificial Intelligence, 3, 135-179.
Guarino, N., & Welty, C. (2002). Evaluating ontological decisions with OntoClean. Communications of the ACM, 45(2), 61-65.
