Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

In this example, we call ψ = Bird (parrot) ∨ Bird (sparrow) a formula and X
is a distinguished variable [2]. We can now formalize circumscription as
follows.
CIR (KB: Bird)
= KB ∧ [ ∀ ψ KB (ψ) ∧ (∀ X ψ (X) → Bird (X) )]
→∀ X ( Bird (X) →ψ (X))
where KB denotes the set of the given pieces of knowledge, connected by
AND operator; KB (ψ) denotes a knowledge base, where every occurrence of
Bird is replaced by ψ [10].
It is to be noted that ψ has been quantified in the circumscription
schema above, thereby making it a second order formula.
The semantic interpretation that circumscription constructs a minimal
follows directly from the last example. We, for instance, found that
∀ X Bird (X) → (X = parrot ∨ X = sparrow),
which is equivalent to
∀ X (( ¬ X = parrot ∨ X = sparrow) → ¬ Bird (X)).
The last expression implicates there exists no interpretation of Bird(X), where
X is not a parrot or sparrow.
7.10 Auto-epistemic Logic
The word ‘auto-epistemic’ means reflection upon self-knowledge [9].
Developed by Moore in the early 80’s this logic attempts to derive inferences
based on the belief of the speaker. For instance, consider the sentence: “Are the
Olympics going to be held in Japan next year?" The answer to this: No,
otherwise I must have heard about it. Now, suppose, the next morning I found
in the newspaper that the Olympics will be held in Japan next year. Now, my
answer to the above question will be: yes. But it is to be noted that my longterm
knowledge that ‘if something is going to be held in my neighborhood,
then I will know about it” is still valid.