Probabilistic Semantics and Defaults

TL;DR

This paper introduces a non-numeric probabilistic formalism called inference graphs for reasoning under uncertainty without relying on numeric probabilities, addressing limitations of existing approaches.

Contribution

It presents a novel non-numeric formalism based on probability theory, conditional independence, and favoring sentences, suitable for default reasoning without numeric probabilities.

Findings

Inference graphs handle nonmonotonic reasoning examples.

Sentences can be verified through semantic experiments.

Formalism avoids numeric probabilities and peculiar side effects.

Abstract

There is much interest in providing probabilistic semantics for defaults but most approaches seem to suffer from one of two problems: either they require numbers, a problem defaults were intended to avoid, or they generate peculiar side effects. Rather than provide semantics for defaults, we address the problem defaults were intended to solve: that of reasoning under uncertainty where numeric probability distributions are not available. We describe a non-numeric formalism called an inference graph based on standard probability theory, conditional independence and sentences of favouring where a favours b - favours(a, b) - p(a|b) > p(a). The formalism seems to handle the examples from the nonmonotonic literature. Most importantly, the sentences of our system can be verified by performing an appropriate experiment in the semantic domain.