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Dynamic Programming Algorithms as Products of Weighted Logic Programs

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Logic Programming (ICLP 2008)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5366))

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Abstract

Weighted logic programming, a generalization of bottom-up logic programming, is a successful framework for specifying dynamic programming algorithms. In this setting, proofs correspond to the algorithm’s output space, such as a path through a graph or a grammatical derivation, and are given a weighted score, often interpreted as a probability, that depends on the score of the base axioms used in the proof. The desired output is a function over all possible proofs, such as a sum of scores or an optimal score. We describe the PRODUCT transformation, which can merge two weighted logic programs into a new one. The resulting program optimizes a product of proof scores from the original programs, constituting a scoring function known in machine learning as a “product of experts.” Through the addition of intuitive constraining side conditions, we show that several important dynamic programming algorithms can be derived by applying PRODUCT to weighted logic programs corresponding to simpler weighted logic programs.

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Author information

Authors and Affiliations

  1. School of Computer Science, Carnegie Mellon University, USA

    Shay B. Cohen, Robert J. Simmons & Noah A. Smith

Authors
  1. Shay B. Cohen
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  2. Robert J. Simmons
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  3. Noah A. Smith
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Editor information

Editors and Affiliations

  1. Clayton School of Information Technology, Monash University, Australia

    Maria Garcia de la Banda

  2. Department of Computer Science, New Mexico State University, NM 88003, Las Cruces, USA

    Enrico Pontelli

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Cohen, S.B., Simmons, R.J., Smith, N.A. (2008). Dynamic Programming Algorithms as Products of Weighted Logic Programs. In: Garcia de la Banda, M., Pontelli, E. (eds) Logic Programming. ICLP 2008. Lecture Notes in Computer Science, vol 5366. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89982-2_18

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  • DOI: https://doi.org/10.1007/978-3-540-89982-2_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89981-5

  • Online ISBN: 978-3-540-89982-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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