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Definite clause programs are canonical (over a suitable domain)

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Abstract

For each first-order languageL with a nonempty Herbrand universe, we construct an algebraC interpreting the function symbols ofL that is a model of the Clark equality theory with languageL and is canonical in the sense that for every definite clause programP in the languageL,T P C ↓ ω is the greatest fixed point ofT P C. The universe of individuals inC is a quotient of the set of terms ofL and is, a fortiori, countable ifL is countable. If ℒ contains at least one function symbol of arity at least 2, then the graphs of partial recursive functions onC, suitably defined, are representable in a natural way as individuals inC.

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Authors and Affiliations

  1. School of Computer and Information Science, Syracuse University, 13244, Syracuse, NY, USA

    Howard A. Blair & Allen L. Brown Jr.

  2. Xerox Webster Research Center, 14580, Webster, NY, USA

    Howard A. Blair & Allen L. Brown Jr.

Authors
  1. Howard A. Blair
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  2. Allen L. Brown Jr.
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Research sponsored in part by U.S. Air Force Contract F30602-85-C-0008.

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Blair, H.A., Brown, A.L. Definite clause programs are canonical (over a suitable domain). Ann Math Artif Intell 1, 1–19 (1990). https://doi.org/10.1007/BF01531067

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