Pluralistic Perspectives on Logic and Formal Philosophy

The project within the competition ''International Academic Cooperation of HSE University''.

Leaders of the team: Elena Dragalina-Chernaya, Fabio Bertato, Itala d’Ottoviano

Project Manager: Tatiana Khromova

Implementation period: 2024-2026

About the project

A joint project of the International Laboratory for Logic, Linguistics and Formal Philosophy of the Higher School of Economics and the Center for Logic, Epistemology and History of Science (University of Campinas, Brazil) unites Russian and Brazilian logicians-philosophers and logicians-mathematicians in solving metamathematical and methodological difficulties caused by the pluralism of logical systems.

Logical pluralism raises the classic question of the demarcation of the disciplinary boundaries of logic in a new way, problematizing the uniqueness of its role in relation to other sciences, which has traditionally been explained by its a priori and universal normativity. The recognition of the fundamental multiplicity of correct logical systems forces us to reconsider this tradition, rethinking the foundations of logic and other formal sciences. 

The key areas of our research are related to the analysis of relations between various formal systems in the pluralistic universe of modern logic that unites them, the construction of translations between them and their combinations, and the clarification of the interrelation of proof-theoretic, model-theoretic, and algorithmic properties of non-classical logical systems.

The development of combined logics with operators obeying the rules of various logical systems is of interest to philosophy and computer science, combining into a single coherent system of reasoning concerning knowledge, necessity, obligations, actions, time. The pluralistic approach to rational agency also includes a comparison of the deductive and expressive power of various logical systems in modeling reasoning and decision-making by communities of limited rational agents based on incomplete, contradictory and contextually dependent information.

Research objectives:

• development of new methods for analyzing and comparing model-theoretic and proof-theoretic properties of logical systems based on a combination of different approaches to their interpretation (as structures, algebras, categories, sets of inference rules, etc.);
• research of algorithmic properties of non-well-founded deductive systems, identification of the influence of various characteristics of formal systems on their algorithmic properties;
• development of multi-dimensional, multi-agent and multi-modal logics in the perspective of pluralism of logical systems;
• identification of new implicit connections between intuitionistic and modal systems, in particular, the construction of translations of intuitionistic epistemic logic into classical logic with two modalities interpreted as knowledge and verification;
• development of new approaches to the disciplinary demarcation of logic using the conceptual apparatus of formal ontology and formal epistemology.

The project is attended by young researchers, including undergraduate, graduate and postgraduate students of philosophical and mathematical programs. The results of the project will be tested at theoretical seminars and international scientific conferences, and will be reflected in a series of publications in highly rated journals.  Within the framework of the project, it is planned to hold annual Russian-Brazilian workshops on the problem of logical pluralism, as well as Russian-Brazilian schools of logic and formal philosophy, which will unite and develop the already established traditions of logic schools by the International Laboratory for Logic, Linguistics and Formal Philosophy at the Higher School of Economics and the Center for Logic, Epistemology and History of Science at the University of Campinas.

The Scientific Team of the Project