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Boolean Approximation Revisited

  • Peter Schachte
  • Harald Søndergaard
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4612)

Abstract

Most work to date on Boolean approximation assumes that Boolean functions are represented by formulas in conjunctive normal form. That assumption is appropriate for the classical applications of Boolean approximation but potentially limits wider use. We revisit, in a lattice-theoretic setting, so-called envelopes and cores in propositional logic, identifying them with upper and lower closure operators, respectively. This leads to recursive representation-independent characterisations of Boolean approximation for a large class of classes. We show that Boolean development can be applied in a representation-independent setting to develop approximation algorithms for a broad range of Boolean classes, including Horn and Krom functions.

Keywords

Boolean Function Propositional Logic Closure Operator Conjunctive Normal Form Propositional Knowledge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Peter Schachte
    • 1
  • Harald Søndergaard
    • 1
  1. 1.NICTA Victoria Laboratory, Department of Computer Science and Software Engineering, The University of Melbourne, Vic. 3010Australia

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