Remarks on logics for probability, with an eye toward universal constructions (Part II)

Abstract: The use of logic to reason about probability has a long tradition in science, and any ambition of surveying past work in a single talk would be ill-advised. Instead, in this light, informal, leisurely talk, I attempt to highlight selected fundamental issues that arise in the field. For example, starting from the logical side: Is "The coin probably lands heads" a sentence in classical logic? Or is it a modal sentence? Can we attach any meaning to the sentence "It is likely that the coin probably lands heads"? And how do we infer one such sentence from another? By the end of the talk, I hope to manage to indicate that convincing answers to these and other related questions are available. These answers pertain to logic and algebra, but in turn suggest new questions in probability theory that are not traditionally associated with that field; for example, is there a "free", or most general, assignment of probabilities to the sentence "The coin lands heads”?

logic

Audience: researchers in the topic

Nonclassical Logic Webinar