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

TL;DR

This paper introduces a new ontological heterogeneity framework based on consequence systems, extended with ontological axioms, enabling flexible ontology integration and relation through morphisms and graph operations.

Contribution

It proposes the da Costian-Tarskianism approach, combining consequence systems with ontological axioms and extended development graphs for ontology heterogeneity.

Findings

Defines extended consequence systems with ontological axioms

Introduces extended development graphs for ontology relations

Discusses implications for applied ontology

Abstract

This paper presents a novel approach for ontological heterogeneity that draws heavily from Carnapian-Goguenism, as presented by Kutz, Mossakowski and L\"ucke (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.