T. Eiter et G. Gottlob, THE COMPLEXITY OF NESTED COUNTERFACTUALS AND ITERATED KNOWLEDGE-BASE REVISIONS, Journal of computer and system sciences, 53(3), 1996, pp. 497-512
Citations number
39
Categorie Soggetti
System Science","Computer Science Hardware & Architecture","Computer Science Theory & Methods
We consider the computational complexity of evaluating nested counterf
actuals over a propositional knowledge base. A counterfactual p > q is
a conditional query with the meaning ''If p would be true in the know
ledge base, would it then hold that also q is true,'' which is differe
nt from material implication p double right arrow q. A nested counterf
actual is a counterfactual statement where the premise p or the conclu
sion q is a counterfactual. Statements of the form p(1) > (p(2) ... (p
(n) > q) ...) intuitively correspond to conditional queries involving
a sequence of revisions. We show that evaluating such statements is Pi
(2)(P)- complete and that this task becomes PSPACE-complete if negatio
n is allowed in a nesting of this form. We also consider nesting a cou
nterfactual in the premise, i.e., (p > q) > r, and show that evaluatin
g such statements is Pi(4)(P)-complete, thus most likely much harder t
han evaluating p > (q > r). Finally, we also address iterated nestings
in the premise and the mix of nestings in the premise and the conclus
ion. (C) 1996 Academic Press, Inc.