St Germain en Laye, November 13th 2024.
This chapter of “a guided tour of Artificial Intelligence research” written by Thierry DENEUX, Didier DUBOIS, and Henri PRADE, deals with uncertainty representation in AI.
1. Uncertainty Representation Frameworks:
- Probability Theory: The most widely known framework for handling uncertainty. It models uncertainty in terms of probability distributions and focuses on quantifying the likelihood of events.
- Possibility Theory: An alternative to probability theory that deals with uncertainty in terms of possibility rather than probability. It is often used when data is incomplete or vague.
2. Challenges of Representing Uncertainty:
- The passage highlights that one of the main challenges in AI and knowledge representation is how to represent and reason about uncertainty in a meaningful way.
- Both probability theory and possibility theory address uncertainty, but they do so from different perspectives:
- Probability theory focuses on the likelihood of an event occurring.
- Possibility theory focuses on how plausible an event is, regardless of its likelihood.
3. Related Topics:
- Rough Sets: A formalism used to deal with vagueness and granularity in data. Rough sets do not require a precise definition of objects and can work with imprecise or incomplete information.
- Fuzzy Sets: Extend classical set theory to handle the concept of partial membership. Unlike traditional sets where an element either belongs or does not belong, fuzzy sets allow for a gradual degree of membership, useful for modeling vagueness.
- These concepts are tied to the idea of granularity in representations (the level of detail or precision of the representation), and gradualness in predicates (how natural language terms like « tall, » « large, » or « likely » can be represented in a mathematical model).
4. Other Frameworks:
- Formal Concept Analysis: A method for data analysis that structures information into formal concepts and hierarchies, aiming to uncover implicit knowledge.
- Conditional Events and Ranking Functions: Approaches for reasoning about uncertain or incomplete information by ranking possibilities or conditioning on new evidence.
- Possibilistic Logic: A form of logic that integrates possibility theory with logical reasoning, allowing reasoning under uncertainty.
Read chapter on Representations of Uncertainty in Artificial Intelligence: Probability and Possibility by Springer: https://link.springer.com/chapter/10.1007/978-3-030-06164-7_3
#AI #ArtificialIntelligence #Uncertainty #Springer #Nexyad
