Generalizing Fuzzy Logic Probabilistic Inferences

TL;DR

This paper generalizes Boole's linear probability constraints to a broader class of boolean symmetric functions, enabling more flexible probabilistic reasoning with propositional formulas.

Contribution

It introduces a new class of linear constraints for probabilities based on symmetric boolean functions, extending Boole's original framework.

Findings

Generalizes Boole's probability constraints to symmetric boolean functions

Provides a method for probabilistic inference with complex propositional relations

Enhances the theoretical foundation for probabilistic logic reasoning

Abstract

Linear representations for a subclass of boolean symmetric functions selected by a parity condition are shown to constitute a generalization of the linear constraints on probabilities introduced by Boole. These linear constraints are necessary to compute probabilities of events with relations between the. arbitrarily specified with propositional calculus boolean formulas.