Algorithmic information dynamics of formal theories

• Grant number: 23/05593-1
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: October 29, 2023
• End date: October 20, 2024
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Itala Maria Loffredo D'Ottaviano
• Grantee: Felipe Sobreira Abrahão
• Supervisor: Hector Zenil
• Host Institution: Centro de Lógica, Epistemologia e História da Ciência (CLE). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: Oxford Immune Algorithmics (OIA), England
• Associated to the scholarship: 21/14501-8 - Algorithmic-informational systemics: toward a formal theory from mutually self-organizing partial structures, BP.PD

Abstract

Complex systems science is one of the most challenging fields to develop overarching theories at the same time that its immediate applications are evinced in several areas of knowledge, including biology, physics, cybernetics, artificial intelligence, sociology, and cognitive science. Although computability theory and information theory play a foundational role in such an interdisciplinary field to which mathematical definitions and theorems from both these theories have been contributing, the well-known properties displayed by complex systems, such as evolution, emergence, and self-organization, have not been yet known to be in turn related to mathematical logic. From a transdisciplinary approach, based on algorithmic information dynamics and model-theoretic systemics from quasi-truth theory, we aim to demonstrate that this in fact holds true. Formally, we aim to establish mathematical definitions and theorems that demonstrate sufficient conditions for interacting formal systems giving rise to the constitution of a (eigen)structure in the asymptotic limit that remains invariant under any subjective transformation that an arbitrarily chosen formal theory can define. In addition to contributing to foundational mathematics and logic, our research bridges the gap between abstract theories in complexity science and applications to society. (AU)