Small steps in dynamics of information
Fernando Raymundo Velazquez-Quesada

Abstract:
This dissertation presents a logical framework for representing small steps in dynamics of information.

Classical Epistemic Logic with possible worlds models is one of the most widely used frameworks for representing and reasoning about agents’ information.
Its dynamic counterpart, Dynamic Epistemic Logic, allows us to represent and reason about actions that change this information, like ‘hard’ announcements
that make us discard completely the possibilities where the announced proposition is not true, of ‘soft’ announcements where we simply consider the
announced proposition very likely to be the case, but nevertheless we do not eliminate the situations in which it does not hold.

However, agents represented in the epistemic logic framework are omniscient: their information is closed under logical consequence. This property, useful 
in some applications, is a very strong idealization in some others: it is often argued that, because of it, epistemic logic is not an adequate tool for
reasoning about the information of ‘real’ agents with bounded abilities. More importantly, omniscience makes irrelevant the small steps that we non-ideal
agents perform every day in our life, like change in awareness, introspection and, especially, inference.

In this dissertation, we extend the classical epistemic logic framework in order to represent, besides the omniscient epistemic logic notion of information,
other finer notions that do not need to have strong closure properties and, in particular, do not need to be closed under logical consequence. We explore
different definitions for notions like awareness (Chapters 3 and 4), explicit knowledge (Chapters 2, 4 and 5) and explicit beliefs (Chapter 5), discussing
some of their properties.

More importantly, we provide definitions for finer actions that affect these finer notions of information. We introduce actions representing changes in
awareness (Chapters 3 and 4), knowledge-based (i.e., truth-preserving) inference (Chapters 2, 4 and 5) and belief-based (non-truth-preserving) inference 
(Chapter 5). We also present non-omniscient versions of the already studied acts of ‘hard’ and ‘soft’ announcement (Chapters 2 and 4 for the first, Chapter 
5 for the second). In all cases we define the action, present its basic properties, and provide a sound and complete axiom system.

The developed framework has a wide range of connections and applications. In particular, we discuss the relation of the several acts of inference we
define with known forms of reasoning, like deduction, default and abductive reasoning (Chapter 6). For applications, we make a few suggestions of how
our framework might provide a useful tool that gives new perspective in fields like Linguistics, Cognitive Science and Game Theory (Chapter 7).

We conclude by mentioning further interesting questions and extensions that deserve additional investigation (Chapter 8).