da Costa and Tarski meet Goguen and Carnap: a novel approach for ontological heterogeneity based on consequence systems
This work addresses the problem of integrating diverse ontologies in applied ontology, though it appears incremental as it builds on existing frameworks like Carnapian-Goguenism and consequence systems.
The paper tackles ontological heterogeneity by introducing a novel approach based on consequence systems, extending them with ontological axioms and defining extended development graphs to relate ontologies through morphisms and operations like fibring and splitting.
This paper presents a novel approach for ontological heterogeneity that draws heavily from Carnapian-Goguenism, as presented by Kutz, Mossakowski and Lücke (2010). The approach is provisionally designated da Costian-Tarskianism, named after da Costa's Principle of Tolerance in Mathematics and after Alfred Tarski's work on the concept of a consequence operator. The approach is based on the machinery of consequence systems, as developed by Carnielli et al. (2008) and Citkin and Muravitsky (2022), and it introduces the idea of an extended consequence system, which is a consequence system extended with ontological axioms. The paper also defines the concept of an extended development graph, which is a graph structure that allows ontologies to be related via morphisms of extended consequence systems, and additionally via other operations such as fibring and splitting. Finally, we discuss the implications of this approach for the field of applied ontology and suggest directions for future research.