5 research outputs found
Checking Trustworthiness of Probabilistic Computations in a Typed Natural Deduction System
In this paper we present the probabilistic typed natural deduction calculus
TPTND, designed to reason about and derive trustworthiness properties of
probabilistic computational processes, like those underlying current AI
applications. Derivability in TPTND is interpreted as the process of extracting
samples of possibly complex outputs with a certain frequency from a given
categorical distribution. We formalize trust for such outputs as a form of
hypothesis testing on the distance between such frequency and the intended
probability. The main advantage of the calculus is to render such notion of
trustworthiness checkable. We present a computational semantics for the terms
over which we reason and then the semantics of TPTND, where logical operators
as well as a Trust operator are defined through introduction and elimination
rules. We illustrate structural and metatheoretical properties, with particular
focus on the ability to establish under which term evolutions and logical rules
applications the notion of trustworhtiness can be preserved