Quantifiers as Adjoint in Probability

TL;DR

This paper generalizes classical deterministic quantifiers to probabilistic ones within the Kleisli category of the Giry monad, enabling the handling of nondeterminism in a categorical framework.

Contribution

It introduces a novel categorical approach to probabilistic quantifiers by extending the deterministic case using the Giry monad, bridging logic and probability theory.

Findings

Probabilistic quantifiers are modeled as adjoints in the Giry monad category.

The approach incorporates nondeterminism into logical quantification.

Provides a categorical foundation for probabilistic logic.

Abstract

Using the Kleisi category of the Giry monad the deterministic existential and universal quantifiers are generalized to incorporate nondeterminism. These probabilistic quantifiers are quantified over the points of the category which are probability measures.