Characterizing and Reasoning about Probabilistic and Non-Probabilistic Expectation

Title: Characterizing and Reasoning about Probabilistic and Non-Probabilistic Expectation

Research Question: How can we characterize and reason about expectation in various representations of uncertainty, including probability, sets of probability measures, belief functions, and possibility measures?

Methodology: The researchers introduced a propositional logic for reasoning about expectation, where the semantics depend on the underlying representation of uncertainty. They provided sound and complete axiomatizations for the logic in the case that the underlying representation is probability, sets of probability measures, belief functions, and possibility measures. They compared the expressiveness of this logic to the corresponding logic for reasoning about likelihood in the case of sets of probability measures, and showed that it is more expressive. They also demonstrated that satisifiability for these logics is NP-complete, no harder than satisifiability for propositional logic.

Results: The researchers found that the logic for reasoning about expectation is more expressive than the corresponding logic for reasoning about likelihood in the case of sets of probability measures. They also showed that the logic is equi-expressive in the case of probability, belief, and possibility.

Implications: This research provides a unified approach to reasoning about expectation in various representations of uncertainty. It also has implications for the field of artificial intelligence, as it contributes to the development of knowledge representation formalisms and methods for uncertainty reasoning.

Keywords: Expectation, probability theory, Dempster-Shafer belief functions, possibility measures, propositional logic, uncertainty, probability measures, belief functions, NP-complete, satisifiability, artificial intelligence, knowledge representation

Link to Article: https://arxiv.org/abs/0312037v2 Authors: arXiv ID: 0312037v2