Circumscription, closed world assumption, default logic

Closed world assumption (CWA):
- Unless an atomic sentence is known to be true, it can be assumed to be false.
- arbitrary atomic sentence is assumed to be false by default, unless specified to be true
- Act as if KB has complete knowledge, so it's either in KB+ or it's not
- KB = KB+ union negative_literals
- KB+ is consistent if KB |=c a but not KB |=c ~a
- KB |=cd a ; where cd means domain closure, no objects exists other than named constants

Circumscription
- strategy is to minimize abnormality (Ab) (minimal entailment), so as few abnormal individuals as possible
- Let Ab be a predicate to handle abnormal cases where defaults don't apply
- Vx [Bird(x) ^ ~AbFly(x) => Flies(x)] if x is a bird and x is not abnormal flier, then it flies; all NORMAL birds fly
- generalization of CWA

Default logic
- KB = where F is a set of first-order-sentences, D is a set of default rules which specifies which assumptions can be made and when
- default rule is Bird(x):Flies(x)/Flies(x), so if we have Bird(x) and ~Flies(x) then assume Flies(x), can be written as Bird(x)=>Flies(x)
- extension - sentences that constitute a reasonable set of beliefs given a default theory