Topological methods of empirical and formal inquiry have emerged in domain theory, formal learning theory, epistemology and philosophy of science. Formal learning theory deals with the question of how an agent should use observations about her environment to arrive at correct and informative conclusions. A central insight of Abramsky, Vickers and Kelly is that verifiable propositions constitute the open sets of a topological space, giving correspondence between topology and formal learning theory. The goal of our work is to present the initial steps of how precisely the topological formalization of empirical inquiry may be generalized in terms of abstract model theory. Institutions constitute the main branch of categorical abstract model theory, which formalizes the notion of a logical system, including syntax, semantics and the satisfaction relation between them. In this framework, following Kelly, we define what is a method, and 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, i.e. invariant through some signature morphism between two signatures in the category of signatures.