Foundations of logic programming
Foundations of logic programming
Formal languages
Elements of Discrete Mathematics
Elements of Discrete Mathematics
Logic for Problem Solving
Theory of Computation
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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.