da Costa and Tarski meet Goguen and Carnap: a novel approach for ontological heterogeneity based on consequence systems
arXiv:2602.15158v1 Announce Type: new 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 app
arXiv:2602.15158v1 Announce Type: new 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.
Executive Summary
This article proposes a novel approach to ontological heterogeneity, dubbed da Costian-Tarskianism, which combines Carnapian-Goguenism with the concept of consequence systems. Building on the work of Kutz, Mossakowski, and Lücke (2010), Carnielli et al. (2008), and Citkin and Muravitsky (2022), the authors introduce the notion of an extended consequence system and development graph to facilitate the integration of ontologies. The approach has significant implications for applied ontology, enabling the development of more robust and flexible frameworks for knowledge representation and reasoning. While the article provides a comprehensive overview of the theoretical foundations and technical details, further research is needed to fully assess the practical applications and real-world impact of this innovative approach.
Key Points
- ▸ The introduction of da Costian-Tarskianism as a novel approach to ontological heterogeneity
- ▸ The extension of consequence systems with ontological axioms to create extended consequence systems
- ▸ The development of extended development graphs for relating ontologies through morphisms and other operations
Merits
Strength in theoretical foundations
The article builds on well-established theories of Carnapian-Goguenism and consequence systems, providing a solid foundation for the proposed approach
Flexibility and adaptability
The extended consequence system and development graph enable the integration of diverse ontologies and facilitate the development of more robust and flexible frameworks for knowledge representation and reasoning
Demerits
Limited empirical validation
The article focuses primarily on theoretical development, and further research is needed to assess the practical applications and real-world impact of da Costian-Tarskianism
Technical complexity
The proposed approach involves advanced mathematical and logical concepts, which may pose a barrier to adoption and implementation by non-technical stakeholders
Expert Commentary
While da Costian-Tarskianism shows promise as a novel approach to ontological heterogeneity, further research is needed to fully assess its practical applications and real-world impact. The technical complexity of the proposed approach may pose a barrier to adoption and implementation by non-technical stakeholders. Nevertheless, the article provides a comprehensive overview of the theoretical foundations and technical details, and the potential benefits of da Costian-Tarskianism make it an area worthy of further exploration.
Recommendations
- ✓ Future research should focus on empirical validation and case studies to assess the practical applications and real-world impact of da Costian-Tarskianism
- ✓ Development of tools and methodologies to facilitate the adoption and implementation of da Costian-Tarskianism by non-technical stakeholders
