The faithfulness of atomic polymorphism
It is known that the full intuitionistic propositional calculus can be embedded into the atomic polymorphic system Fat, a calculus with only two connectives: the conditional and the second-order universal quantifier. The embedding uses a translation of formulas due to Prawitz and relies on the so-ca...
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| Format: | article |
| Language: | eng |
| Published: |
2021
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| Online Access: | http://hdl.handle.net/10400.2/10489 |
| Country: | Portugal |
| Oai: | oai:repositorioaberto.uab.pt:10400.2/10489 |
| Summary: | It is known that the full intuitionistic propositional calculus can be embedded into the atomic polymorphic system Fat, a calculus with only two connectives: the conditional and the second-order universal quantifier. The embedding uses a translation of formulas due to Prawitz and relies on the so-called property of instantiation overflow. In this paper, we show that the previous embedding is faithful i.e., if a translated formula is derivable in Fat, then the original formula is already derivable in the propositional calculus. |
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