da Costa and Tarski meet Goguen and Carnap: a novel approach for ontological heterogeneity based on consequence systems

Abstract

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.

Figures (3)

• Figure 1: Heterogeneous refinement from $O_1$ to $O_2$.
• Figure 2: Heterogeneous connection of $O_1$ and $O_2$.
• Figure 3: Heterogeneous connection of $O_1$ and $O_2$, with "preparation". Note the original input ontologies may pass through many steps prior to connecting, resulting in final ontologies $O_1^f$ and $O_2^f$.

Theorems & Definitions (34)

• Definition 2.1: Consequence operator or relation
• Definition 2.2: Signature
• Definition 2.3: Language of a signature
• Definition 2.4: Signature morphism
• Definition 2.5: Category of signatures
• Definition 2.6
• Definition 2.7: Consequence System
• Definition 2.8: Compact Consequence System
• Definition 2.9: Quasi-consequence System
• Definition 2.10