We address the problem of extending probability from the total choices of an ASP specification to the stable models and, from there, to general events.

Our approach is algebraic in the sense that it relies on an equivalence relation over the set of events and uncertainty is expressed with variables and polynomial expressions.

We frame our work in the context of machine learning and induction of logic problems, the two (current) forms of artificial intelligence.

References:

• https://arxiv.org/abs/1801.00631, Gary Marcus, Deep Learning: A Critical Appraisal, 2018.
• https://arxiv.org/abs/1911.01547, François Chollet, On the Measure of Intelligence, 2019.
• https://arxiv.org/abs/1801.00631, Bengio et al., A Meta-Transfer Objective for Learning to Disentangle Causal Mechanisms, 2019.
• https://arxiv.org/abs/1801.00631, Cropper et al., Turning 30: New Ideas in Inductive Logic Programming, 2020.
• https://doi.org/10.1201/9781003427421, Fabrizio Riguzzi, Foundations of Probabilistic Logic Programming, 2023.