Generalizing inference rules in a coherence-based probabilistic default reasoning

In this paper we first recall some notions and results on the coherence-based probabilistic treatment of uncertainty. Then, we deepen some probabilistic aspects in nonmonotonic reasoning, by generalizing OR, CM, and Cut rules. We also illustrate the degradation of these inference rules when the number of premises increases. Finally, we show that the lower bounds obtained when applying OR and Quasi-Conjunction inference rules coincide, respectively, with Hamacher and Lukasiewicz t-norms; the upper bounds in both rules coincide with Hamacher t-conorm.

► A review is given of the coherence-based approach to probability.
► Generalizations are given of OR, CM and Cut rules, with more than two premises.
► The degradation of OR, CM and Cut rules is illustrated, when premises increase.
► Upper bounds in OR and Quasi Conjunction (QC) rules coincide with Hamacher t-conorm.
► Lower bounds in OR and QC rules coincide with Hamacher and Lukasiewicz t-norms.