Non-monotonic reasoning
Classical consequence
1. Basic properties of classical consequence (reflexivity, cumulative transitivity, monotony)
2. Compactness and maximalizability property
3. Supraclassicality and paraclassicality
4. Uniform substitution
5. How to get more
Additional background assumptions
1. Pivotal-assumptions
2. Default-assumptions (cautious monotony, non-compactness)
Restrictions of the set of models (valuations)
1. Pivotal-valuations (non-compactness, definable sets of valuations)
2. Default-valuations (preferential models, consistency preservation, non-monotonicity, non-transitivity, cautious monotony for well-founded relations on models, not consistency preservation)
Additional background rules
1. Pivotal-rules (neither disjunction in the premisses nor contraposition)
2. Default-rules
Default logic
1. Default rules
2. Default theories
3. Operational semantics (process, extension)
4. General properties (consistency preservation, cautious monotony)
5. Normal default theories (existence of extensions, monotony in defaults, orthogonalitz of extensions)
6. Representation in normal default theories (non-normality required)
7. Semi-normal default theories
8. Proof theory for default logic
9. Joint consistency of justifications
10. Modified extensions
11. Priorities among defaults