Abstract
Thirty years ago I formulated a conjecture about a kind of completeness of intuitionistic logic. The framework in which the conjecture was formulated had the form of a semantic approach to a general proof theory (presented at the 4th World Congress of Logic, Methodology and Philosophy of Science at Bucharest 1971 [6]). In the present chapter, I shall reconsider this 30-year old conjecture, which still remains unsettled, but which I continue to think of as a plausible and important supposition. Reconsidering the conjecture, I shall also reconsider and revise the semantic approach in which the conjecture was formulated.
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Notes
- 1.
Prawitz [4]. The elimination rules are there said to be the inverse of the corresponding introduction rules.
- 2.
One may argue that to allow the value to contain new inferences is too liberal, since the justifying operation then produces an argument that goes beyond what was present in the arguments for the premisses. However, this is an angle that is not taken up here.
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Acknowledgments
Work on this chapter was done within the project Interpretation and Meaning, funded by Bank of Sweden Tercentenary Foundation.
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Prawitz, D. (2014). An Approach to General Proof Theory and a Conjecture of a Kind of Completeness of Intuitionistic Logic Revisited. In: Pereira, L., Haeusler, E., de Paiva, V. (eds) Advances in Natural Deduction. Trends in Logic, vol 39. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7548-0_12
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