A Program to Compute G¨odel-L¨ob Fixpoints

Abstract
odel-L¨ ob computability logic (GL). In order to make things relatively self-contained, I sketch the essential ideas of GL, and discuss the significance of its fixpoint theorem. Then I give the algorithm embodied in the program in a little more detail. It should be emphasized that nothing new is presented here — all the theory and methodology are due to others. The main interest is, in a sense, psychological. The approach taken here has been declared in the literature, more than once, to be of theoretical interest only, being too unwieldly in practice. Experimentation shows this is not so provided formulas are not too complicated. A copy of the program can be obtained by ftp from venus.gc.cuny.edu. It is in the subdirectory “/pub/fitting,” under the name “glfixpt.pro.” Log on as “anonymous” and use your full e-mail address as password. If there are difficulties with ftp, send e-mail to the author at mlflc@cunyvm.cuny.edu. The Prolog code is standard, and should run under any implementation, though minor modifications may be necessary for some systems. These modifications are described in the last section, and also in the program itself.
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