Stephen Cole Kleene. Permutabilities of inferences in Gentzen's calculi LK and LJ. Memoirs of the American Mathematical Society, 10, 1952.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....every step that a Turing machine takes during some computation. Clearly, such proofs are not of particular use in the expression of mathematically interesting proofs. They will serve us, however, as a convenient device for representing and reasoning about computation. 2. 8 Additional readings In [Kle52], Kleene presents a detailed analysis of permutability of inference rules for classical and intuitionistic sequent systems similar to those presented here. In [Mil91] Miller argues that proof theory should be considered a rich and appropriate setting for justifying declarative programming. The ....

Stephen Cole Kleene. Permutabilities of inferences in Gentzen's calculi LK and LJ. Memoirs of the American Mathematical Society, 10, 1952.

....and simply into the structure of the proof. A second approach requires that all right hand rules should be done simultaneously. Although it is difficult to deal with simultaneous rule application in the sequent calculus, we can employ permutations of inference rules within the sequent calculus [Kle52]. That is, we can require that if two or more right introduction rules can be use to derive a given sequent, then all possible orders of applying those right introduction rules can be obtained from any other order simply by permuting right introduction inferences. Using this second approach, we ....

Stephen Cole Kleene. Permutabilities of inferences in gentzen's calculi LK and LJ. Memoirs of the American Mathematical Society, 10, 1952.

....operational semantics of the logic as a programming language. A second choice requires that all possible introductions on the right can be done simultaneously. Although the sequent calculus cannot deal directly with simultaneous rule application, reference to permutabilities of inference rules [16] can indirectly address simultaneity. That is, we can require that if two or more right introduction rules can be used to derive a given sequent, then all possible orders of applying those right introduction rules can, in fact, be done and the resulting proofs are all equal modulo permutations of ....

Stephen Cole Kleene. Permutabilities of inferences in Gentzen's calculi LK and LJ. Memoirs of the American Mathematical Society, 10, 1952.

....every step that a Turing machine takes during some computation. Clearly, such proofs are not of particular use in the expression of mathematically interesting proofs. They will serve us, however, as a convenient device for representing and reasoning about computation. 3. 8 Additional readings In [Kle52], Kleene presents a detailed analysis of permutability of inference rules for classical and intuitionistic sequent systems similar to those presented here. In [Mil91] Miller argues that proof theory should be considered a rich and appropriate setting for justifying declarative programming. The ....

Stephen Cole Kleene. Permutabilities of inferences in Gentzen's calculi LK and LJ. Memoirs of the American Mathematical Society, 10, 1952.

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