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Parititionbased logical reasoning
 In Proc. KR ’2000
, 2000
"... We investigate the problem of reasoning with partitions of related logical axioms. Our motivation is twofold. First, we are concerned with how to reason effectively with multiple knowledge bases that have overlap in content. Second, and more fundamentally, we are concerned with how to exploit struc ..."
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Cited by 57 (15 self)
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We investigate the problem of reasoning with partitions of related logical axioms. Our motivation is twofold. First, we are concerned with how to reason effectively with multiple knowledge bases that have overlap in content. Second, and more fundamentally, we are concerned with how to exploit structure inherent in a set of logical axioms to induce a partitioning of the axioms that will lead to an improvement in the efficiency of reasoning. To this end, we provide algorithms for reasoning with partitions of axioms in propositional and firstorder logic. Craig’s interpolation theorem serves as a key to proving completeness of these algorithms. We analyze the computational benefit of our algorithms and detect those parameters of a partitioning that influence the efficiency of computation. These parameters are the number of symbols shared by a pair of partitions, the size of each partition, and the topology of the partitioning. Finally, we provide a greedy algorithm that automatically decomposes a given theory into partitions, exploiting the parameters that influence the efficiency of computation. 1
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 57 (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 ...
Formal Methods in Knowledge Engineering
 The Knowledge Engineering Review
, 1995
"... This paper presents a general discussion of the role of formal methods in Knowledge Engineering. We give an historical account of the development of the field of Knowledge Engineering towards the use of formal methods. Subsequently, we discuss the pro's and cons of formal methods. We do this ..."
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Cited by 5 (0 self)
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This paper presents a general discussion of the role of formal methods in Knowledge Engineering. We give an historical account of the development of the field of Knowledge Engineering towards the use of formal methods. Subsequently, we discuss the pro's and cons of formal methods. We do this by summarising the proclaimed advantages, and by arguing against some of the commonly heard objections against formal methods. We briefly summarise the current state of the art and discuss the most important directions that future research in this field should take. This paper presents a general setting for the other contributions in this issue of the Journal, which each deal with a specific issue in more detail. 1 Historical growth of Knowledge Engineering towards Formal Methods Although the history of KBS technology and Knowledge Engineering (KE) is well documented in a number of places in the literature ( e.g. [42, ch.2]), in this section we will give an account of the development of K...
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
Approximate Reasoning for Contextual Databases
 Proceedings of the Eighth IEEE International Conference on Tools with Artificial Intelligence (ICTAI96
, 1996
"... Contextual reasoning has been proposed as a tool for solving the problem of generality in AI and for effectively handling huge knowledge bases, while approximate reasoning has been developed to overcome the computational barrier of classical deduction. This paper combines these approaches to provide ..."
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Cited by 1 (1 self)
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Contextual reasoning has been proposed as a tool for solving the problem of generality in AI and for effectively handling huge knowledge bases, while approximate reasoning has been developed to overcome the computational barrier of classical deduction. This paper combines these approaches to provide an intuitive representation of knowledge and an effective deduction. Its semantics and a tableau calculus are presented. The key computational features are discussed.
unknown title
"... We investigate the problem of reasoning with partitions of related logical axioms. Our motivation is twofold. First, we are concerned with how to reason effectively with multiple knowledge bases that have overlap in content. Second, and more fundamentally, we are concerned with how to exploit struc ..."
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We investigate the problem of reasoning with partitions of related logical axioms. Our motivation is twofold. First, we are concerned with how to reason effectively with multiple knowledge bases that have overlap in content. Second, and more fundamentally, we are concerned with how to exploit structure inherent in a set of logical axioms to induce a partitioning of the axioms that will lead to an improvement in the efficiency of reasoning. To this end, we provide algorithms for reasoning with partitions of axioms in propositional and firstorder logic. Craig’s interpolation theorem serves as a key to proving completeness of these algorithms. We analyze the computational benefit of our algorithms and detect those parameters of a partitioning that influence the efficiency of computation. These parameters are the number of symbols shared by a pair of partitions, the size of each partition, and the topology of the partitioning. Finally, we provide a greedy algorithm that automatically decomposes a given theory into partitions, exploiting the parameters that influence the efficiency of computation. 1
PartitionBased Logical Reasoning for FirstOrder and Propositional Theories
"... 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 ..."
Abstract
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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 effectively with multiple knowledge bases that have overlap in content. Second, we are concerned with improving the efficiency 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 (data driven) messagepassing and using backward (query driven) 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 algorithms. We also provide a specialized algorithm for propositional satisfiability checking with partitions. Craig’s interpolation theorem serves as a key to proving soundness and completeness of these algorithms. An analysis of these algorithms emphasizes parameters of partitionings that influence the efficiency of computation. These parameters are the number of symbols shared by a pair of partitions, the size (number of symbols) of each partition, and the topology of the partitioning. We provide a principled way for automatically decomposing a given theory into partitions. We provide a greedy algorithm that instantiates this method while exploiting the parameters that influence the efficiency of computation.
unknown title
"... We investigate the problem of reasoning with partitions of related logical axioms. Our motivation is twofold. First, we are concerned with how to reason effectively with multiple knowledge bases that have overlap in content. Second, and more fundamentally, we are concerned with how to exploit struc ..."
Abstract
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We investigate the problem of reasoning with partitions of related logical axioms. Our motivation is twofold. First, we are concerned with how to reason effectively with multiple knowledge bases that have overlap in content. Second, and more fundamentally, we are concerned with how to exploit structure inherent in a set of logical axioms to induce a partitioning of the axioms that will lead to an improvement in the efficiency of reasoning. To this end, we provide algorithms for reasoning with partitions of axioms in propositional and firstorder logic. Craig’s interpolation theorem serves as a key to proving completeness of these algorithms. We analyze the computational benefit of our algorithms and detect those parameters of a partitioning that influence the efficiency of computation. These parameters are the number of symbols shared by a pair of partitions, the size of each partition, and the topology of the partitioning. Finally, we provide a greedy algorithm that automatically decomposes a given theory into partitions, exploiting the parameters that influence the efficiency of computation. 1