:: Workshop – Bayesianism II: Foundations and Applications ::

Invited Talk 1 (wednesday às 14h00)
The Order–Theoretic Foundation Of Probability Theory.
Kevin Knuth (SUNY – Albany).

Abstract:
In this talk I will present a new foundation of probability theory that encompasses and generalizes both the Kolmogorov and the Cox formulations. In this picture probability is a bi-valuation defined on a lattice of statements that quantifies the degree to which one statement implies another. The sum rule is a constraint equation that ensures that valuations are assigned so as to not violate associativity of the lattice join and meet. I then derive that there are actually two product rules: one is a constraint equation which arises from associativity of the direct products of lattices, and the other a constraint equation derived from associativity of changes of context. The generality of this formalism enables one to derive the traditionally assumed condition of additivity in measure theory, as well introduce a general notion of product. Further application of this new formalism to number theory and quantum mechanics will also be discussed.

Promotion and Support:
			CAPES-Proex Pós–graduação em Estatística-USP