On the path to the truth Logical & computational aspects of learning

In this dissertation, we study various perspectives on learning and its relation to knowledge and belief within a formal approach. We mostly focus on inductive inference (or, inductive learning), namely the process of inferring general conclusions from incoming information. Our work is based in two areas that, independently, study dynamics of information, Dynamic Epistemic Logic (DEL) and Formal Learning Theory (FLT). In particular, our aim is to further develop the connection between DEL and FLT initiated by Nina Gierasimczuk (2009, 2010).
In Part I (Chapter 3 and Chapter 4) of the thesis we use the DEL approach to investigate information dynamics arising from incoming observations or from incoming truthful announcements using subset space semantics. First, we obtain two novel logics that formalize various learning theoretic notions in the spirit of FLT. Then, we introduce a new logic that formalizes the process of information gathering via arbitrary public announcements in scenarios with multiple learners.~We solve the long standing open question of finding a recursive axiomatization for a strong version of Arbitrary Public Announcement Logic (APAL) and for its variant Group Announcement Logic (GAL).
In Part II (Chapter 5 and Chapter 6), we focus completely on the learning model of finite identification in FLT. By using tools in combinatorics and recursion theory, we provide a fine-grained theoretical analysis of the structural and computational differences between finite identification with positive data and finite identification with complete data.