Access Restriction

Author Darwiche, Adnan
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2001
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Boolean functions ♦ Knowledge compilation ♦ Model-based diagnosis ♦ Propositional logic ♦ Satisfiability
Abstract Knowledge compilation has been emerging recently as a new direction of research for dealing with the computational intractability of general propositional reasoning. According to this approach, the reasoning process is split into two phases: an off-line compilation phase and an on-line query-answering phase. In the off-line phase, the propositional theory is compiled into some target language, which is typically a tractable one. In the on-line phase, the compiled target is used to efficiently answer a (potentially) exponential number of queries. The main motivation behind knowledge compilation is to push as much of the computational overhead as possible into the off-line phase, in order to amortize that overhead over all on-line queries. Another motivation behind compilation is to produce very simple on-line reasoning systems, which can be embedded cost-effectively into primitive computational platforms, such as those found in consumer electronics.One of the key aspects of any compilation approach is the target language into which the propositional theory is compiled. Previous target languages included Horn theories, prime implicates/implicants and ordered binary decision diagrams (OBDDs). We propose in this paper a new target compilation language, known as decomposable negation normal form (DNNF), and present a number of its properties that make it of interest to the broad community. Specifically, we show that DNNF is universal; supports a rich set of polynomial--time logical operations; is more space-efficient than OBDDs; and is very simple as far as its structure and algorithms are concerned. Moreover, we present an algorithm for converting any propositional theory in clausal form into a DNNF and show that if the clausal form has a bounded treewidth, then its DNNF compilation has a linear size and can be computed in linear time (treewidth is a graph-theoretic parameter that measures the connectivity of the clausal form). We also propose two techniques for approximating the DNNF compilation of a theory when the size of such compilation is too large to be practical. One of the techniques generates a sound but incomplete compilation, while the other generates a complete but unsound compilation. Together, these approximations bound the exact compilation from below and above in terms of their ability to answer clausal entailment queries. Finally, we show that the class of polynomial--time DNNF operations is rich enough to support relatively complex AI applications, by proposing a specific framework for compiling model-based diagnosis systems.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2001-07-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 48
Issue Number 4
Page Count 40
Starting Page 608
Ending Page 647

Open content in new tab

   Open content in new tab
Source: ACM Digital Library