Paracomplete Probabilities

TL;DR

This paper develops a framework for handling probabilities in paracomplete logic systems, introducing a total probability theorem and Bayes' rule adapted to undeterminedness interpreted as missing evidence.

Contribution

It introduces a novel approach to paracomplete probabilities using LFUs, including new theorems and a probability space definition for undeterminedness.

Findings

Proved a total paracomplete probability theorem.

Established a paracomplete Bayes' rule.

Defined a probability space accommodating undeterminedness.

Abstract

This paper presents an advance in the direction of working with probabilities in a paracomplete setting using Logics of Formal Undeterminedness (LFUs). The undeterminedness is interpreted here as missing evidence. A theorem of total paracomplete probability and a paracomplete Bayes' rule have been proved using this setup. We end with a definition of a paracomplete probability space illustrating a way to define probabilities on sets in the presence of undeterminedness.