LIRa session: Tim French

Speaker: Tim French (The University of Western Australia)

Date and Time: Wednesday, March 27th 2024, 16:30-18:00
(PLEASE NOTE the unusual day of the week)

Venue: ILLC seminar room F1.15 in Science Park 107 and online.

Title: Aleatoric Reasoning: The World as an Urn of Marbles

Abstract. Imagine the world, and all that we experience as being capriciously random like an urn of marbles. There is no causality or meaning; just random chance. Will it rain today? We draw a marble from the urn and if it is blue, it will rain. Will it snow today? We draw three marbles from the urn and if they are all blue it will snow.

Such a world can be succinctly modelled by a domain of marbles (a probability space), and a set of Boolean predicates defined over the domain of marbles. By providing a language where complex propositions are defined over the set of predicate atoms, correlation emerges and reason may be applied. This is not ontological reason, or scientific causality, but rather the pure epistemic bias that comes from observation. This language provides a simple model of belief and knowledge: an agent’s beliefs are given by the probability space of marbles in an urn, conditioned on experience; and an agent’s knowledge is communicated a priori, as the form of equivalences among complex propositions, creating correspondences among the world’s inherent randomness.

In this talk we will discuss and present and language for building complex propositions from these aleatoric atoms, and define a logic of identity among the propositions. We will demonstrate some basic applications of the logic, including some interesting proof theoretic and expressivity results. We will then explore the process of learning in an aleatoric world, using some convenient mathematical results to show how conditioning can be applied when observations correspond to complex aleatoric propositions. This allows agents to refine their beliefs according to experience and knowledge, and gain a meaningful understanding of the aleatoric world.