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Involution Narrowing Algebra

Abstract

The narrowing algebra formalism underlying CLP(intervals) consists of lattice-ordered monoids of monotone contractions on the lattice of states; these are generated by the canonical idempotent operators of the primitive relations of the constraint system used for the problem. This mathematical structure has some similarities with that of some classical operator rings, even though the underlying states form a non-Boolean lattice instead of a linear space. In this paper we show that in the restricted case of certain binary interval convex primitives, there is a broken symmetry which can be restored by generalizing the state lattice to produce an involution on the important fragment of the narrowing algebra. This involution allows some basic theorems of classical *-rings to be ported into this domain.

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Older, W.J. Involution Narrowing Algebra. Constraints 2, 113–130 (1997). https://doi.org/10.1023/A:1009701608825

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  • DOI: https://doi.org/10.1023/A:1009701608825

  • constraints
  • narrowing algebra
  • lattice operators
  • interval convexity
  • row convexity
  • involution