| Rachel Ben-Eliyahu. A hierarchy of tractable subsets for computing stable models. Journal of Artificial Intelligence Research, 5:27--52, 1996. |
....how, by relaxing one constraint, previously linear complexity is increased to intractability. 1 Introduction Computation of the stable semantics has become a salient activity in several areas of artificial intelligence including truth maintenance systems, default logic, and autoepistemic logic [1]. The complexity of logic programming semantics, however, is a huge deterrent [15] In fact, identifying whether or not a stable model exists, in general, is NP complete [12] 5] For some classes of logic programs, however, such as for stratified programs [14] the problem is linear. In this ....
....at most one subgoal. A unit uni rule program (UU) is both unit and uni rule. Likewise, a unit uni appearance program (UA) is unit and uni appearance. The algorithms we present to compute the stable and well founded semantics for these classes operate on their dependency digraphs as in [10] and [1]. The algorithms are closely related to one another in that each deals with the acyclic and the cyclic sections of the digraph, separately. The syntactic restrictions on these classes of programs induce obvious properties on their corresponding digraphs. The two classes we present for which ....
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Rachel Ben-Eliyahu. A hierarchy of tractable subsets for computing stable models. Journal of Artificial Intelligence Research, 5:27--52, 1996.
....not be obtained from Brewka s well founded semantics (see page 35 in [2] On the other hand, reasoning under our semantics is intractable in the general case while it can be done in polynomial time under Brewka s semantics. However, based on recent results of computations of stable models, e.g. [3], it is possible to locate a reasonably broad tractable subclass of our prioritized logic programs so that the applicable range of our method can be identified. Detailed work concerning the computational analysis about our PLPs and DPLPs was presented in [9] The prioritized logic programs ....
R. Ben-Eliyahu, A hierarchy of tractable subsets for computing stable models. Journal of Artificial Intelligence Research, 6 1996 27--52.
.... set semantics can be reduced to the stable model semantics of logic programs [4] without increasing the computational cost [5] Although the computation for stable model semantics is still intractable generally, Ben Eliyahu has recently identified the tractable subclass for computing stable models [1] and Niemela and Simons further implemented some efficient algorithms to compute stable model semantics [16] Hence, these results are obviously applicable in the implementation of our approach. Example 12 The light power domain revisited. We slightly modify the causal relations in Example 7 by ....
R. Ben-Eliyahu, A hierarchy of tractable subsets for computing stable models. Journal of Artificial Intelligence Research, 6 1996 27--52.
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