On A priori Belief Updates in the Epistemic Analysis of Distributed Systems

Abstract

This thesis is at the intersection of three very different fields: philosophy, epistemic logic and distributed systems. Logic and philosophy share a very long tradition, at least since Aristotle’s syllogisms. While the ties between logic and distributed systems are more recent, the epistemic modelling of distributed systems has proved to be extremely fruitful both in the design of distributed algorithms and in the formalization of distributed tasks. Philosophy and distributed systems have rarely been seen together, even though, unsurprisingly, there are many philosophical questions arising from the distributed field, especially related to the role of agency of artificial agents and of their (attributed) epistemic states. The core of this thesis is to relate the three fields in conjunction to give some initial answers to the question: What is the role of a priori knowledge in distributed systems? This question really requires the three fields combined to give an answer: distributed systems are the arena in which the question is posed, a priori knowledge is a philosophical notion and knowledge in distributed systems is formalized naturally by epistemic logic. In this thesis, we will address this and related questions from the combined perspective of the three fields. This thesis proves that explicitly modelling a priori knowledge in distributed systems provides a number of novel insights, as it happened for the modelling of other epistemic notions: indeed, we provide a formal account that relates a recent interpretation of the a priori vs. a posteriori distinction to the process of designing distributed systems. On this philosophical groundwork we build up a family of logics that relax some of the common a priori assumptions in distributed systems. Finally, we provide the tools to perform a priori updates using Dynamic Epistemic Logic, allowing to change the a priori knowledge of agents dynamically. In particular, we introduce two distinct a priori update mechanisms, one representing the intervention of the system designer, and the other representing the ability of agents in self-adapting systems to adapt autonomously to unexpected behavior. The fruitfulness of the approach however is not limited to distributed systems only: the inquiry raises some crucial philosophical questions related to e.g. ethics and creativity, deeply linked to explainable artificial intelligence topics; at the same time it urges the development of new logic tools that can sharpen our formal understanding of (meta-level) reasoning.