We propose a perspective on knowledge compilation which calls for analyzing
different compilation approaches according to two key dimensions: the
succinctness of the target compilation language, and the class of queries and
transformations that the language supports in polytime. We then provide a
knowledge compilation map, which analyzes a large number of existing target
compilation languages according to their succinctness and their polytime
transformations and queries. We argue that such analysis is necessary for
placing new compilation approaches within the context of existing ones. We also
go beyond classical, flat target compilation languages based on CNF and DNF,
and consider a richer, nested class based on directed acyclic graphs (such as
OBDDs), which we show to include a relatively large number of target
compilation languages
Independence -- the study of what is relevant to a given problem of reasoning -- has received an increasing attention from the AI community. In this paper, we consider two basic forms of independence, namely, a syntactic one and a semantic one. We show features and drawbacks of them. In particular, while the syntactic form of independence is computationally easy to check, there are cases in which things that intuitively are not relevant are not recognized as such. We also consider the problem of forgetting, i.e., distilling from a knowledge base only the part that is relevant to the set of queries constructed from a subset of the alphabet. While such process is computationally hard, it allows for a simplification of subsequent reasoning, and can thus be viewed as a form of compilation: once the relevant part of a knowledge base has been extracted, all reasoning tasks to be performed can be simplified.
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