## Compilation for Critically Constrained Knowledge Bases (1996)

Venue: | In Proc. of the 13 th National Conference on Artificial Intelligence (AAAI’96 |

Citations: | 18 - 0 self |

### BibTeX

@INPROCEEDINGS{Schrag96compilationfor,

author = {Robert Schrag},

title = {Compilation for Critically Constrained Knowledge Bases},

booktitle = {In Proc. of the 13 th National Conference on Artificial Intelligence (AAAI’96},

year = {1996},

pages = {510--515}

}

### OpenURL

### Abstract

We show that many "critically constrained" Random 3SAT knowledge bases (KBs) can be compiled into disjunctive normal form easily by using a variant of the "Davis-Putnam" proof procedure. From these compiled KBs we can answer all queries about entailment of conjunctive normal formulas, also easily --- compared to a "bruteforce " approach to approximate knowledge compilation into unit clauses for the same KBs. We exploit this fact to develop an aggressive hybrid approach which attempts to compile a KB exactly until a given resource limit is reached, then falls back to approximate compilation into unit clauses. The resulting approach handles all of the critically constrained Random 3SAT KBs with average savings of an order of magnitude over the brute-force approach. Introduction Consider the task of reasoning from a propositional knowledge base (KB) F which is expressed as a conjunctive normal formula (CNF). We are given other, query CNFs Q 1 ; Q 2 ; : : : ; QN and asked, for each Q i ,...

### Citations

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Citation Context ...nstrained" KBs from Random3SAT as a benchmark. First, we introduce an exact KC approach based on the very effective "Davis-Putnam" proof procedure for determining propositional satisfia=-=bility, or DP (Davis & Putnam 1960-=-, Davis, Logemann, & Loveland 1962). We modify DP to collect a prime implicant cover --- a disjunctive normal formula (DNF) equivalent to the input KB, which serves as FC . On the many KBs which are e... |

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Citation Context ...ry processing; and fallback query processing for approximate KC, when the compiled bounds are not sufficient. In each of these operations, we use a Lisp version of the "tableau" implementati=-=on of DP (Crawford & Auton 1993-=-), which we have modified slightly to produce the variants we have described. We performed all our experiments on a Sun SPARC-5 workstation using Allegro Common Lisp, measuring execution times with th... |

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Citation Context ...as not received much attention. The former problem --- where the input and the output have the same normal form --- is important for circuit design, where it is known as "2-level logic minimizati=-=on" (Quine 1952-=-, McCluskey 1956, Tison 1967, Coudert 1994). Algorithms for solving the latter problem which interests us seem to be directed primarily toward tasks in automated reasoning (Slagle, Chang, & Lee 1970, ... |

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Citation Context ...ved much attention. The former problem --- where the input and the output have the same normal form --- is important for circuit design, where it is known as "2-level logic minimization" (Qu=-=ine 1952, McCluskey 1956-=-, Tison 1967, Coudert 1994). Algorithms for solving the latter problem which interests us seem to be directed primarily toward tasks in automated reasoning (Slagle, Chang, & Lee 1970, Rymon 1994, Jack... |

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Citation Context ... general, neither bound is equivalent to the KB itself, which is why this compilation approach is called "approximate." Propositional reasoning with these Horn clause CNFs can be done in lin=-=ear time (Dowling & Gallier 1984-=-). To answer a query about a clause C in approximate KC, we use the following procedure. (A CNF query follows from a KB F iff every one of its clauses follows from F.) KC-query(C;F lb ; F ub ; F) 1 if... |

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Citation Context ...o admit only 7 solutions. Using DPPI on this subgraph would produce a small prime implicant cover. Recognizing criticality generally without performing work much like exact KC may be impossible. See (=-=Dechter & Pearl 1992-=-) for a discussion of some related problems. We show that compiling critically constrained KBs aggressively can make fast, exact KC possible and that the fallback approach of bootstrapped approximate ... |

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Citation Context ...on. The former problem --- where the input and the output have the same normal form --- is important for circuit design, where it is known as "2-level logic minimization" (Quine 1952, McClus=-=key 1956, Tison 1967-=-, Coudert 1994). Algorithms for solving the latter problem which interests us seem to be directed primarily toward tasks in automated reasoning (Slagle, Chang, & Lee 1970, Rymon 1994, Jackson & Pais 1... |

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Citation Context ...ny of these Random 3SAT KBs depends on their being critically constrained. The problem of prime implicant generation is co-NP-hard; the total number of prime implicants can be \Omega\Gamma8 n = p n) (=-=Chandra & Markowsky 1978-=-); an irredundant cover can include as many as 2 n prime implicants. A full search by our DPPI algorithm must visit at least as many leaves as are contained in the union of irredundant covers of minim... |

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Citation Context ...lgorithms for solving the latter problem which interests us seem to be directed primarily toward tasks in automated reasoning (Slagle, Chang, & Lee 1970, Rymon 1994, Jackson & Pais 1990, Sochor 1991, =-=Madre & Coudert 1991-=-, Castell & Cayrol 1996). Among the cited algorithms, only that of Castell and Cayrol has been shown to be feasible for generating the prime implicants for many of our critically constrained Random 3S... |

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Citation Context ...1956, Tison 1967, Coudert 1994). Algorithms for solving the latter problem which interests us seem to be directed primarily toward tasks in automated reasoning (Slagle, Chang, & Lee 1970, Rymon 1994, =-=Jackson & Pais 1990-=-, Sochor 1991, Madre & Coudert 1991, Castell & Cayrol 1996). Among the cited algorithms, only that of Castell and Cayrol has been shown to be feasible for generating the prime implicants for many of o... |

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2 |
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(Show Context)
Citation Context ...s have many solutions which typically are easy to find; KC for such KBs may be unnecessary --- or even counter-productive, if a KC approach must enumerate all of their many observed prime implicates (=-=Schrag & Crawford 1996). KBs which ar-=-e "over-constrained" (i.e., inconsistent) are uninteresting for most practical purposes --- they entail any query. Thus, we may argue that KC is most useful when KBs are "critically con... |

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1 |
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Citation Context ...the latter problem which interests us seem to be directed primarily toward tasks in automated reasoning (Slagle, Chang, & Lee 1970, Rymon 1994, Jackson & Pais 1990, Sochor 1991, Madre & Coudert 1991, =-=Castell & Cayrol 1996-=-). Among the cited algorithms, only that of Castell and Cayrol has been shown to be feasible for generating the prime implicants for many of our critically constrained Random 3SAT KBs. All of these al... |

1 |
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Citation Context ..., McCluskey 1956, Tison 1967, Coudert 1994). Algorithms for solving the latter problem which interests us seem to be directed primarily toward tasks in automated reasoning (Slagle, Chang, & Lee 1970, =-=Rymon 1994-=-, Jackson & Pais 1990, Sochor 1991, Madre & Coudert 1991, Castell & Cayrol 1996). Among the cited algorithms, only that of Castell and Cayrol has been shown to be feasible for generating the prime imp... |

1 |
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Citation Context ...dert 1994). Algorithms for solving the latter problem which interests us seem to be directed primarily toward tasks in automated reasoning (Slagle, Chang, & Lee 1970, Rymon 1994, Jackson & Pais 1990, =-=Sochor 1991-=-, Madre & Coudert 1991, Castell & Cayrol 1996). Among the cited algorithms, only that of Castell and Cayrol has been shown to be feasible for generating the prime implicants for many of our critically... |

1 | KUIE Layout: An interval-based graphical constraint system - Schrag - 1990 |

1 | 1996b. Search in SAT/CSP: Phase Transitions, Abstraction, and Compilation - Schrag |