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- 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.
- 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.
- All sorts of other Circumscriptions
described in [Costello, 1997], to be described in detail here
- .Model Preference: We can extend the above types of
circumscription to the more general notion of model preference.
- Various concepts of first order logic, including:
- conservative extension
- translation between theories
- interpolation theorems
- Model theory: We need to understand the
semantics of first order logic, its ``backend.'' Important
concepts include: (See [Hodges, 1997])
- restrictions of models to languages
- Second Order Logic: This is often used to express
circumscription policies/minimality conditions. They can often be
viewed as schema.
- 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.
- Kripke semantics
- Bisimulations: good for comparing temporal/game/modal models.
Some tools are more how we structure and use the logic. These
- Contexts. See [McCarthy, 1993]. Contexts can be used to organize
information, and contain our common sense informatic situation.
- use of the ab predicate
- lots more to add here!
Thu Feb 22 17:21:49 PST 2001