Defaults and Infinitesimals: Defeasible Inference by Nonarchimedean Entropy-Maximization

TL;DR

This paper introduces a novel semantics for defeasible inference using nonarchimedean probability measures with infinitesimals, interpreting defaults as generalized constraints and employing entropy maximization for preferred models.

Contribution

It proposes a new framework combining infinitesimal probabilities, generalized constraints, and entropy maximization to enhance defeasible inference semantics.

Findings

Provides a formal semantics for defeasible inference with infinitesimals.

Integrates generalized conditional constraints into probabilistic reasoning.

Uses entropy maximization to select preferred models.

Abstract

We develop a new semantics for defeasible inference based on extended probability measures allowed to take infinitesimal values, on the interpretation of defaults as generalized conditional probability constraints and on a preferred-model implementation of entropy maximization.