Topological Inquiry in Abstract Model Theory
Formal learning theory poses the question of how an agent
should use observations about its environment to arrive at accurate and
true conclusions. To answer this question, empirical and formal inquiries
have been provided with topological models in Domain Theory,
Formal Learning, Epistemology and Philosophy of Science.
The goal of our work is to present the initial steps of how
precisely the topological formalization of empirical inquiry may be gen-
eralized in terms of abstract model theory. In this framework, following
Genin and Kelly, we define what is a method, as well as verifiability,
refutability, decidability and limiting verifiability of a proposition.
Furthermore, we define what is an abstract empirical problem, and
its solvability. We prove that verifiability, refutability, decidability, and
limiting verifiability of a proposition and solvability of a problem are
invariant under change of notation.
Asterios Gatzounis
Last modified: Wed Oct 16 2024