Sara Ugolini – A logico-algebraic perspective on (non-classical) probability theory

Logic Supergroup — Online Colloquium, March 11, 2021

Sara Ugolini (Barcelona) – A logico-algebraic perspective on (non-classical) probability theory

Algebraic logic and probability theory have had a deep connection from the start: in fact, in the work of George Boole, what we now call Boolean algebras provided a first common abstraction of the notions of logical statement as well as of probabilistic event. In this talk we will see how a notion of probability map has been defined on well-known ordered structures, such as lattice ordered groups, MV-algebras and other residuated structures connected to substructural logics. In particular, we are interested in the probability theory of so-called “many-valued events”: events that can result to be neither true nor false, but true to some degree. The algebraic approach has proven to be powerful in this context, and it has shown interesting connections to measure theory. In this framework, we will also see how Łukasiewicz logic can be used to define a logic for probabilistic reasoning on both classical and many-valued events.