What does the notation ab1, ab2, etc. refer to in predicate logic?

223 Views Asked by At

I'm trying to decipher a set of relations from a John McCarthy paper:

$$ specializes(c1,c2) \land \neg ab1(p,c1,c2) \land ist(c1,p) \supset ist(c2,p) $$

and

$$ specializes(c1,c2) \land \neg ab2(p,c1,c2) \land ist(c2,p) \supset ist(c1,p) $$

The text is fairly clear about what the functions $specializes(\cdot)$ and $ist(\cdot)$ mean, but I have know idea what is meant by $ab1(\cdot)$ and $ab2(\cdot)$. Any ideas?

1

There are 1 best solutions below

1
On BEST ANSWER

I found the answer in another paper by Akman and Surav:

ab is an abnormality predicate to support non­-monotonicity. $$ \forall c_1 \forall c_2 \forall p (c_1 \preceq c_2) \land ist(c1,p) \land \neg ab(p,c1,c2) \to ist(c2,p) $$

Abnormality predicates seem to come from an earlier paper by McCarthy:

A single predicate ab, standing for ``abnormal'' is circumscribed with certain other predicates and functions considered as variables that can be constrained to achieve the circumscription subject to the axioms.

I think McCarthy often assumes you've read all his earlier papers, and therefore you can understand his notation...