Knowledge compilation and theory approximation

@article{Selman1996KnowledgeCA,
  title={Knowledge compilation and theory approximation},
  author={Bart Selman and Henry A. Kautz},
  journal={J. ACM},
  year={1996},
  volume={43},
  pages={193-224}
}
Computational efficiency is a central concern in the design of knowledge representation systems. In order to obtain efficient systems, it has been suggested that one should limit the form of the statements in the knowledge base or use an incomplete inference mechanism. The former approach is often too restrictive for practical applications, whereas the latter leads to uncertainty about exactly what can and cannot be inferred from the knowledge base. We present a third alternative, in which… 

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References

SHOWING 1-10 OF 152 REFERENCES
An Empirical Evaluation of Knowledge Compilation by Theory Approximation
TLDR
This study suggests that knowledge compilation may indeed be a practical approach for dealing with intractability in knowledge representation systems.
Knowledge Compilation using Horn Approximations
TLDR
This work introduces a knowledge compilation method that allows the user to enter statements in a general, unrestricted representation language, which the system compiles into a restricted language that allows for efficient inference.
A General Framework for Knowledge Compilation
TLDR
This work presents a third alternative, in which knowledge given in a general representation language is translated (compiled) into a tractable form — allowing for efficient subsequent query answering.
An Analysis of Approximate Knowledge Compilation
TLDR
This paper provides general characterizations of the L U B that are independent of the target language; analyzes the properties of the Generate-LUB algor i thm of Selman and Kautz, proving its correctness for any target language closed under subsumption; and generalizes the procedure to arbi t rary target languages.
Making Believers out of Computers
Vivid Knowledge and Tractable Reasoning: Preliminary Report
TLDR
This work explores the use of \vivid" forms for knowledge, in which determining the truth of a sentence is on the order of a database retrieval, and shows that some forms of incomplete knowledge can still be handled eeciently if the authors extend a vivid KB in a natural way.
Learning Useful Horn Approximations
TLDR
A learning process is presented that uses observed queries to estimate the query distribution, and then uses these estimates to hill-climb, eeciently, in the space of size-bounded Horn approximations, until reaching one that is, with provably high probability, eeectively at a local optimum.
Exploiting Locality in a TMS
TLDR
A new approach for exploiting Truth Maintenance Systems (TMS) is presented which makes them simpler to use without necessarily incurring a substantial performance penalty.
Computers and Intractability: A Guide to the Theory of NP-Completeness
Horn formulae play a prominent role in artificial intelligence and logic programming. In this paper we investigate the problem of optimal compression of propositional Horn production rule knowledge
...
...