Ronald E. Prather
Abstract
In a number of books and articles [1,2], Lorenzen has developed a general kind of calculus for deriving character strings inductively, using finite systems of clauses, reminiscent of those that appear in logic programming. At the same time, these clauses are remarkably similar to the productions that appear in the multiple antecedent canonical systems of Post [3], as used originally to derive a computational basis for the formal notion of an algorithm. However, the interpretation is quite different in the case of the Lorenzen Calculus, where each successively derived word is a member of the theory, rather than (as in the case of Post, Turing [4], or Chomsky [5] productions) simply a "way station" on the route to a single generated "terminal" word. We intend to make a clear distinction between these two approaches at an appropriate point in the development, but it is well that a tentative appreciation of this fundamental difference be understood at the outset.
- Lorenzen, P., Einfuhrung in die operative Logik und Mathematik, Springer-Verlag, Berlin, 1955.Google Scholar
Cross Ref
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- Turing, A., On Computable Numbers, with an Application to the Entscheidungs Problem, Proc. London Math. Soc., 2--42, 1936.Google Scholar
- Chomsky, N., On Certain Formal Properties of Grammars, Inform and Control, 2, 1959.Google Scholar
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- Salomaa, A., Formal Languages, Academic Press, New York, 1973. Google ScholarDigital Library
- Prather, R., Elements of Discrete Mathematics, Houghton Mifflin, Boston, 1986. Google ScholarDigital Library
- Prather, R., The Relation of Lorenzen Calculus to Logic Programming and Formal Language Theory, submitted to Jour. of Logic Programming.Google Scholar
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- Brainerd, W. and Landweber, L., Theory of Computation. John Wiley and Sons, New York, 1974. Google ScholarDigital Library
- Prather, R., The Lorenzen Calculus as a Logic Programming Language, submitted to Fourth Annual Logic in Computer Science Symposium, Asilomar, California, June 1989.Google Scholar
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