A Geometric Presentation of Probabilistic Satisfiability

TL;DR

This paper introduces a geometric framework for probabilistic satisfiability by extending truth values and clause evaluations through linear operators, providing a new perspective on probabilistic logic.

Contribution

It presents a novel geometric approach to probabilistic satisfiability using linear extensions of truth values and clause evaluations.

Findings

Linear operators extend expected truth values over probability distributions.

Probabilistic satisfiability can be analyzed using linear maps.

The approach accommodates multiple truth values.

Abstract

By considering probability distributions over the set of assignments the expected truth values assignment to propositional variables are extended through linear operators, and the expected truth values of the clauses at any given conjunctive form are also extended through linear maps. The probabilistic satisfiability problems are discussed in terms of the introduced linear extensions. The case of multiple truth values is also discussed.