On Two Forms of Bureaucracy in Derivations
Kai BrÂ¨ nnler1 and StÂ´phane Lengrand2 u e
Institut fÂ¨r angewandte Mathematik und Informatik u NeubrÂ¨ckstr. 10, CH 3012 Bern, Switzerland u 2 PPS, UniversitÂ´ genus Paris 7, France e
Abstract. We call irrelevant information in derivations bureaucracy. An example of much(prenominal) irrelevant information is the order between devil full-strength inference rules that trivially permute. Building on ideas by Guglielmi, we post both forms of bureaucracy that occur in the calculus of structures (and, in fact, in every non-trivial terminus rewriting derivation). We develop term calculi that provide derivations that do not contain this bureaucracy. We also prepare a normalisation procedure that removes bureaucracy from derivations and ?nd that in a certain sense the normalisation process is a process of cut elimination.
Consider the following two certaintys in a sequent system for neoclassic logical system: Â¯ A, B, A, C Â¯?C A, B, A Â¯ A ? B, A ? C Â¯ A, B, A, C Â¯ A ? B, A, C Â¯ A ? B, A ? C
Clearly, these two proofs are essentially the same, and we prefer not to distinguish them. more(prenominal) to the point, the sequent calculus forces us to choose an order of two rule applications that we do not command to choose because it is not relevant.
Let us call bureaucracy this fact that a proof-theoretic formalism forces us to distinguish morally identical proofs. produce nets, introduced by Girard  for linear logic, are a less bureaucratic formalism than the sequent calculus. They have also been developed for classical logic, for example by Robinson  and by Lamarche and StraÃburger . Proof nets have the deservingness that they do not distinguish between proofs such as the above. However, establishing the correctness of a proof net generally requires checking a global criterion which is more algorithmic than deductive. The notion of logical implication step is lost when moving from the sequent calculus to proof nets. Let us informally call a formalism...If you want to get a full essay, order it on our website: Ordercustompaper.com
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