Nonmonotonic Probabilistic Logics between Model-Theoretic Probabilistic Logic and Probabilistic Logic under Coherence

TL;DR

This paper introduces new probabilistic logics that bridge the gap between model-theoretic probabilistic entailment and probabilistic entailment under coherence, enhancing reasoning capabilities especially with zero-event conditioning.

Contribution

It presents probabilistic generalizations of classical default entailment notions that are intermediate in strength, addressing probabilistic inconsistencies and enabling belief revision.

Findings

New formalisms are weaker than model-theoretic probabilistic entailment.

Formalisms are stronger than probabilistic entailment under coherence.

Applicable for handling zero-event conditioning and belief revision.

Abstract

Recently, it has been shown that probabilistic entailment under coherence is weaker than model-theoretic probabilistic entailment. Moreover, probabilistic entailment under coherence is a generalization of default entailment in System P. In this paper, we continue this line of research by presenting probabilistic generalizations of more sophisticated notions of classical default entailment that lie between model-theoretic probabilistic entailment and probabilistic entailment under coherence. That is, the new formalisms properly generalize their counterparts in classical default reasoning, they are weaker than model-theoretic probabilistic entailment, and they are stronger than probabilistic entailment under coherence. The new formalisms are useful especially for handling probabilistic inconsistencies related to conditioning on zero events. They can also be applied for probabilistic belief revision. More generally, in the same spirit as a similar previous paper, this paper sheds light on exciting new formalisms for probabilistic reasoning beyond the well-known standard ones.