An Analysis of Approximate Knowledge Compilation

Knowledge compilat ion is the process by which an in i t ia l theory w i th respect to which inference is intractable is transformed into one or more "approximate" or equivalent theories w i th respect to which inference can be performed efficiently. Selman and Kautz introduced Horn lowest upper bound (LUB) approximations in [SK91], and generalized them in [KS91; SK95] to a number of target languages other than Horn. In this paper, we analyze the problem of knowledge compilat ion for arbi trary clausal target languages, generalizing in several ways previous results. We provide general characterizations of the L U B that are independent of the target language; analyze the properties of the Generate-LUB algor i thm of Selman and Kautz, proving its correctness for any target language closed under subsumption (including a wide fami ly of languages which guarantee polynomial size approximations); and generalize the procedure to arbi t rary target languages. We also examine some computat ional aspects of these procedures and the quality of Horn approximations.