Home > Meeting Topics and Material > Dr. Kirk Sturtz to speak on ‘Quantifiers as Adjoints in Probability’

Dr. Kirk Sturtz to speak on ‘Quantifiers as Adjoints in Probability’

Time: 5 September, 2pm – 3pm
Location: Bldg. 620, Globemaster Conf Rm
Speaker: Dr. Kirk Sturtz – Universal Mathematics
Title: Quantifiers as Adjoints in Probability

Abstract:
A first-order logic under uncertainty is developed using the Kleisli category of the Giry monad. We start from the basics and show how the deterministic existential and universal quantifiers generalize to incorporate nondeterminism. These probabilistic quantifiers are quantified over the points of the category which are probability measures, and these quantifiers are stable under substitution. With the probabilistic existential quantifier, probabilistic relations (m-ary predicates) can be defined and composed in a manner which generalizes the composition of deterministic relations. This work is directed towards building a mathematical framework for sensor fusion.

Speaker Bio:
Kirk Sturtz received the B.S. in Mechanical Engineering from the University of Toledo, a M.S. in Aerospace Engineering from Iowa State University, and a Ph.D. in Systems Science and Mathematics from Washington University in 1992. He has worked at McDonnell Aircraft Company, Veda Inc., Wright State University, and now for Universal Mathematics. His current interest is in the development of category theoretic methods for probability and its application to layered sensing and fusion.

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