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18
Logic and databases: a deductive approach
 ACM Computing Surveys
, 1984
"... The purpose of this paper is to show that logic provides a convenient formalism for studying classical database problems. There are two main parts to the paper, devoted respectively to conventional databases and deductive databases. In the first part, we focus on query languages, integrity modeling ..."
Abstract

Cited by 151 (2 self)
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The purpose of this paper is to show that logic provides a convenient formalism for studying classical database problems. There are two main parts to the paper, devoted respectively to conventional databases and deductive databases. In the first part, we focus on query languages, integrity modeling and maintenance, query optimization, and data
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 52 (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 ...
Tractable Databases: How to Make Propositional Unit Resolution Complete through Compilation
, 1994
"... We present procedures to compile any propositional clausal database \Sigma into a logically equivalent "compiled" database \Sigma ? such that, for any clause C, \Sigma j= C if and only if there is a unit refutation of \Sigma ? [ :C. It follows that once the compilation process is compl ..."
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Cited by 41 (5 self)
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We present procedures to compile any propositional clausal database \Sigma into a logically equivalent "compiled" database \Sigma ? such that, for any clause C, \Sigma j= C if and only if there is a unit refutation of \Sigma ? [ :C. It follows that once the compilation process is complete any query about the logical consequences of \Sigma can be correctly answered in time linear in the sum of the sizes of \Sigma ? and the query. The compiled database \Sigma ? is for all but one of the procedures a subset of the set P I (\Sigma) of prime implicates of \Sigma, but \Sigma ? can be exponentially smaller than P I (\Sigma). Of independent interest, we prove the equivalence of unitrefutability with two restrictions of resolution, and provide a new sufficient condition for unit refutation completeness, thus identifying a new class of tractable theories, one which is of interest to abduction problems as well. Finally, we apply the results to the design of a complete LTMS. 1 INTRODUCT...
Consequencefinding based on ordered linear resolution
 In proc of IJCAI
, 1991
"... Since linear resolution with clause ordering is incomplete for consequencefinding, it has been used mainly for prooffinding. In this paper, we reevaluate consequencefinding. Firstly, consequencefinding is generalized to the problem in which only interesting clauses having a certain property (ca ..."
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Cited by 15 (0 self)
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Since linear resolution with clause ordering is incomplete for consequencefinding, it has been used mainly for prooffinding. In this paper, we reevaluate consequencefinding. Firstly, consequencefinding is generalized to the problem in which only interesting clauses having a certain property (called characteristic clauses) should be found. Then, we show how adding a skip rule to ordered linear resolution makes it complete for consequencefinding in this general sense. Compared with setofsupport resolution, the proposed method generates fewer clauses to find such a subset of consequences. In the propositional case, this is an elegant tool for computing the prime implicants/implicates. The importance of the results lies in their applicability to a wide class of AI problems including procedures for nonmonotonic and abductive reasoning and truth maintenance systems. 1
Clause Trees: a Tool for Understanding and Implementing Resolution in Automated Reasoning
 ARTIFICIAL INTELLIGENCE
"... A new methodology/data structure, the clause tree, is developed for automated reasoning based on resolution in first order logic. A clause tree T on a set S of clauses is a 4tuple <N,E,L,M>, where N is a set of nodes, divided into clause nodes and atom nodes, E is a set of edges, each of whic ..."
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Cited by 7 (6 self)
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A new methodology/data structure, the clause tree, is developed for automated reasoning based on resolution in first order logic. A clause tree T on a set S of clauses is a 4tuple <N,E,L,M>, where N is a set of nodes, divided into clause nodes and atom nodes, E is a set of edges, each of which joins a clause node to an atom node, L is a labeling of N E which assigns to each clause node a clause of S, to each atom node an instance of an atom of some clause of S, and to each edge either + or . The edge joining a clause node to an atom node is labeled by the sign of the corresponding literal in the clause. A resolution is represented by unifying two atom nodes of different clause trees which represent complementary literals. The merge of two identical literals is represented by placing the path joining the two corresponding atom nodes into the set M of chosen merge paths. The tail of the merge path becomes a closed leaf, while the head remains an open leaf which can be resolved on. Th...
An Abductive Approach to Disjunctive Logic Programming
 JOURNAL OF LOGIC PROGRAMMING
, 2000
"... ..."
ACTP: A Configurable TheoremProver
 Data & Knowledge Engineering
, 1994
"... There has been a considerable amount of research into the provision of explicit representation of control regimes for resolutionbased theorem provers. ..."
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Cited by 3 (2 self)
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There has been a considerable amount of research into the provision of explicit representation of control regimes for resolutionbased theorem provers.
Strategies for focusing structurebased theorem proving
, 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 1 (0 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 while minimizing the number of inferences done within each subtheory and the number of messages sent between subtheories. We do so 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 our algorithms. 1