This note contains materials for a short introductory course in belief revision theory to be held in Spring 2026 at IUSS Pavia. The main topics to be discussed are the following:
- Formal Preliminaries: A review of classical propositional logic, possible worlds semantics (truth-sets), and the properties of logical consequence relations and operators (including non-monotonicity and cumulative transitivity).
- AGM Postulates: The standard theory of belief revision, focusing on the representation of epistemic states as logically closed belief sets and the rational constraints on revision encoded by the six foundational and two supplementary AGM postulates.
- The Semantic Approach: The construction of concrete belief revision operators using possible worlds and evidence-relative plausibility orderings (satisfying Connectedness, Transitivity, Centeredness, and the Limit Assumption).
- The Representation Theorem: The “bridge” between axioms and constructions, proving that AGM postulates and the plausibility ordering construction are mathematically equivalent (covering both “Soundness” and, for finite languages, “Completeness”).
The material is divided as follows:
- Session 1 (link) contains an introduction to the formal framework of belief revision theory, formal preliminaries (language, consequence operators, belief sets), and the standard AGM axiomatic approach, detailing the foundational postulates, supplementary postulates, and derivative rules.
- Session 2 (link) introduces the semantic construction of the revision operator using possible worlds and plausibility orderings. It includes the formal statement of the Representation Theorem and the full proof of its first half (“Soundness”).
- Session 3 (link) covers the second half of the Representation Theorem (“Completeness”). Assuming a finite language, it details the syntactic-semantic translation (using state descriptions) and proves that any AGM belief revision operator can be perfectly represented by a plausibility ordering.
- Session 4 — TBA.