The AI Arsenal

1. Domain Circumscription: We want to be able to minimize objects in a domain. In more general terms, we prefer models without unnecessary objects, to keep our world uncluttered.
2. Formula Circumscription: Not only would be want to prefer models with overall smaller domains, but perhaps models where certain formulas have minimal extensions. An example is preferring models with the fewest abs in them.
3. All sorts of other Circumscriptions described in [Costello, 1997], to be described in detail here later!
4. .Model Preference: We can extend the above types of circumscription to the more general notion of model preference.
5. Various concepts of first order logic, including:
   1. conservative extension
   2. translation between theories
   3. interpolation theorems
6. Model theory: We need to understand the semantics of first order logic, its ``backend.'' Important concepts include: (See [Hodges, 1997])
   1. homomorphisms
   2. isomorphism
   3. embedding
   4. restrictions of models to languages
7. Second Order Logic: This is often used to express circumscription policies/minimality conditions. They can often be viewed as schema.
8. Set Theory: Some intuitive formalization without paradoxes is needed, without too much mathematical drudgery. [McCarthy, 1996] gives a formalization in set theory of the checkerboard problem. Another reason we need set theory is that it is the underlying basis for model theory, which is definitely required.

   It would be nice to have a ``common sense'' version of set theory.

9. Kripke semantics
10. Bisimulations: good for comparing temporal/game/modal models.

Some tools are more how we structure and use the logic. These include:

1. Contexts. See [McCarthy, 1993]. Contexts can be used to organize information, and contain our common sense informatic situation.
2. use of the ab predicate
3. lots more to add here!