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57
Towards understanding and harnessing the potential of clause learning
 Journal of Artificial Intelligence Research
, 2004
"... Efficient implementations of DPLL with the addition of clause learning are the fastest complete Boolean satisfiability solvers and can handle many significant realworld problems, such as verification, planning and design. Despite its importance, little is known of the ultimate strengths and limitat ..."
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Cited by 96 (12 self)
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Efficient implementations of DPLL with the addition of clause learning are the fastest complete Boolean satisfiability solvers and can handle many significant realworld problems, such as verification, planning and design. Despite its importance, little is known of the ultimate strengths and limitations of the technique. This paper presents the first precise characterization of clause learning as a proof system (CL), and begins the task of understanding its power by relating it to the wellstudied resolution proof system. In particular, we show that with a new learning scheme, CL can provide exponentially shorter proofs than many proper refinements of general resolution (RES) satisfying a natural property. These include regular and DavisPutnam resolution, which are already known to be much stronger than ordinary DPLL. We also show that a slight variant of CL with unlimited restarts is as powerful as RES itself. Translating these analytical results to practice, however, presents a challenge because of the nondeterministic nature of clause learning algorithms. We propose a novel way of exploiting the underlying problem structure, in the form of a high level problem description such as a graph or PDDL specification, to guide clause learning algorithms toward faster solutions. We show that this leads to exponential speedups on grid and randomized pebbling problems, as well as substantial improvements on certain ordering formulas. 1.
Propositional Independence: FormulaVariable Independence and Forgetting
 Journal of Artificial Intelligence Research
, 2003
"... 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, ..."
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Cited by 86 (13 self)
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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 simpli  cation 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 simpli ed.
PartitionBased Logical Reasoning for FirstOrder and Propositional Theories
 Artificial Intelligence
, 2000
"... In this paper we provide algorithms for reasoning with partitions of related logical axioms in propositional and firstorder logic (FOL). We also provide a greedy algorithm that automatically decomposes a set of logical axioms into partitions. Our motivation is twofold. First, we are concerned with ..."
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Cited by 60 (9 self)
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In this paper we provide algorithms for reasoning with partitions of related logical axioms in propositional and firstorder logic (FOL). We also provide a greedy algorithm that automatically decomposes a set of logical axioms into partitions. Our motivation is twofold. First, we are concerned with how to reason e#ectively with multiple knowledge bases that have overlap in content. Second, we are concerned with improving the e#ciency of reasoning over a set of logical axioms by partitioning the set with respect to some detectable structure, and reasoning over individual partitions. Many of the reasoning procedures we present are based on the idea of passing messages between partitions. We present algorithms for reasoning using forward messagepassing and using backward messagepassing with partitions of logical axioms. Associated with each partition is a reasoning procedure. We characterize a class of reasoning procedures that ensures completeness and soundness of our messagepassing ...
Factored planning
 In IJCAI’03
, 2003
"... We present a generalpurpose method for dynamically factoring a planning domain, whose structure is then exploited by our generic planning method to find sound and complete plans. The planning algorithm’s time complexity scales linearly with the size of the domain, and at worst exponentially with th ..."
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Cited by 52 (7 self)
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We present a generalpurpose method for dynamically factoring a planning domain, whose structure is then exploited by our generic planning method to find sound and complete plans. The planning algorithm’s time complexity scales linearly with the size of the domain, and at worst exponentially with the size of the largest subdomain and interaction between subdomains. The factorization procedure divides a planning domain into subdomains that are organized in a tree structure such that interaction between neighboring subdomains in the tree is minimized. The combined planning algorithm is sound and complete, and we demonstrate it on a representative planning domain. The algorithm appears to scale to very large problems regardless of the black box planner used. 1
Practical PartitionBased Theorem Proving for Large Knowledge Bases
, 2003
"... Query answering over commonsense knowledge bases typically employs a firstorder logic theorem prover. While firstorder inference is intractable in general, provers can often be handtuned to answer queries with reasonable performance in practice. ..."
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Cited by 31 (4 self)
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Query answering over commonsense knowledge bases typically employs a firstorder logic theorem prover. While firstorder inference is intractable in general, provers can often be handtuned to answer queries with reasonable performance in practice.
Theorem proving with structured theories (full report
, 2001
"... Motivated by the problem of query answering over multiple structured commonsense theories, we exploit graphbased techniques to improve the efficiency of theorem proving for structured theories. Theories are organized into subtheories that are minimally connected by the literals they share. We prese ..."
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Cited by 27 (6 self)
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Motivated by the problem of query answering over multiple structured commonsense theories, we exploit graphbased techniques to improve the efficiency of theorem proving for structured theories. Theories are organized into subtheories that are minimally connected by the literals they share. We present messagepassing algorithms that reason over these theories using consequence finding, specializing our algorithms for the case of firstorder resolution, and for batch and concurrent theorem proving. We provide an algorithm that restricts the interaction between subtheories by exploiting the polarity of literals. We attempt to minimize the reasoning within each individual partition by exploiting existing algorithms for focused incremental and general consequence finding. Finally, we propose an algorithm that compiles each subtheory into one in a reduced sublanguage. We have proven the soundness and completeness of all of these algorithms. 1
Partitionbased Decision Heuristics for Image Computation using SAT and BDDs
 in Proceedings of the 2001 IEEE/ACM international conference on Computeraided design (ICCAD
, 2001
"... Methods based on Boolean satisfiability (SAT) typically use a Conjunctive Normal Form (CNF) representation of the Boolean formula, and exploit the structure of the given problem through use of various decision heuristics and implication methods. In this paper, we propose a new decision heuristic ..."
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Cited by 27 (1 self)
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Methods based on Boolean satisfiability (SAT) typically use a Conjunctive Normal Form (CNF) representation of the Boolean formula, and exploit the structure of the given problem through use of various decision heuristics and implication methods. In this paper, we propose a new decision heuristic based on separatorset induced partitioning of the underlying CNF graph. It targets those variables whose choice generates clause partitions with disjoint variable supports. This can potentially improve performance of SAT applications by decomposing the problem dynamically within the search. In the context of a recently proposed image computation method combining SAT and BDDs, this results in simpler BDD subproblems. We provide algorithms for CNF partitioning – one based on a clausevariable dependency matrix, and another based on standard hypergraph partitioning techniques, and also for the use of partitioning information in decision heuristics for SAT. We demonstrate the effectiveness of our proposed partitionbased heuristic with practical results for reachability analysis of benchmark sequential circuits. 1.
A ModelBased Diagnosis Framework for Distributed Systems
, 2002
"... We present a distributed modelbased diagnostics architecture for embedded diagnostics. We extend the traditional modelbased definition of diagnosis to a distributed diagnosis definition, in which we have a collection of distributed components whose interconnectivity is described by a directed ..."
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Cited by 24 (0 self)
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We present a distributed modelbased diagnostics architecture for embedded diagnostics. We extend the traditional modelbased definition of diagnosis to a distributed diagnosis definition, in which we have a collection of distributed components whose interconnectivity is described by a directed graph.
A Scalable Approach for Partitioning OWL Knowledge Bases
 In: 2nd Int. Workshop on Scalable Semantic Web Knowledge Base Systems (SSWS2006
, 2006
"... Abstract. We describe an approach to partitioning a large OWL ABox with respect to a TBox so that specific kinds of reasoning can be performed separately on each partition and the results trivially combined in order to achieve complete answers. The main features of our approach include: a reasonable ..."
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Cited by 21 (1 self)
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Abstract. We describe an approach to partitioning a large OWL ABox with respect to a TBox so that specific kinds of reasoning can be performed separately on each partition and the results trivially combined in order to achieve complete answers. The main features of our approach include: a reasonable tradeoff between the complexity of the task and the granularity of partitioning; worstcase polynomial time complexity; and the ability to handle problems that are too large for main memory. In addition, we show promising experimental results on both the Lehigh University Benchmark data and the real world FOAF data. This work could contribute to the development of scalable Semantic Web systems that need to deal with large amounts of data. 1
Distributed reasoning in a peertopeer setting
 In de Mántaras
, 2004
"... Abstract. In a peertopeer inference system, each peer can reason locally but can also solicit some of its acquaintances, which are peers sharing part of its vocabulary. In this paper, we consider peertopeer inference systems in which the local theory of each peer is a set of propositional clauses ..."
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Cited by 20 (7 self)
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Abstract. In a peertopeer inference system, each peer can reason locally but can also solicit some of its acquaintances, which are peers sharing part of its vocabulary. In this paper, we consider peertopeer inference systems in which the local theory of each peer is a set of propositional clauses defined upon a local vocabulary. An important characteristic of peertopeer inference systems is that the global theory (the union of all peer theories) is not known (as opposed to partitionbased reasoning systems). The contribution of this paper is twofold. We provide the first consequence finding algorithm in a peertopeer setting: it is anytime and computes consequences gradually from the solicited peer to peers that are more and more distant. We exhibit a sufficient condition on the acquaintance graph of the peertopeer inference system for guaranteeing the completeness of this algorithm. We also present first experimental results that are promising. 1