From Logic to Practice by Gabriele Lolli Marco Panza & Giorgio Venturi

Author:Gabriele Lolli, Marco Panza & Giorgio Venturi
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

32To be more precise, we should say that the model contemplated here is something like a realizability model.

33Roughly speaking, the idea is that the reduction steps for detours involving logical connectives are defined on open proofs and not closed ones (cf. Schroeder-Heister 2006, §§3.1, 3.2). Moreover, as was said on p. 145, no new detours are created by mathematical rules. It remains to analyze the permutations between logical and mathematical rules, but we will see this on p. 150. It should be noticed that putting open proofs on the same level as closed ones, at least with respect to their semantic role, is far from trivial. Usually, in proof-theoretical semantics, the priority is given to closed proofs because the semantic key concept is that of validity, rather than that of computation, as it is in the case under analysis (cf. Schroeder-Heister 2006, §3.3; Schroeder-Heister 2014, §§2.2.2, 2.2.3).

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