Abstract: The inference problem for propositional circumscription is known to
be highly intractable and, in fact, harder than the inference problem for classi-
cal propositional logic. More precisely, in its full generality this problem is P - 2
complete, which means that it has the same inherent computational complexity
as the satisfiability problem for quantified Boolean formulas with two alternations
(universal-existential) of quantifiers. We use Schaefer?s framework of generalized
satisfiability problems to study the family of all restricted cases of the inference
problem for propositional circumscription. Our main result yields a complete clas-
sification of the ?truly hard? ( P -complete) and the ?easier? cases of this problem
2
(reducible to the inference problem for classical propositional logic). Specifically,
we establish a dichotomy theorem which asserts that each such restricted case either
is P -complete or is in coNP. Moreover, we provide efficiently checkable criteria
2
that tell apart the ?truly hard? cases from the ?easier? ones. We show our results both
when the formulas involved are and are not allowed to contain constants. The present
work complements a recent paper by the same authors, where a complete classifi-
cation into hard and easy cases of the model-checking problem in circumscription
was established.