Constructive theories through a modal lens

We present a uniform proof-theoretic proof of the Gödel–McKinsey–Tarski embedding for a class of first-order intuitionistic theories. This is achieved by adapting to the case of modal logic the methods of proof analysis in order to convert axioms into rules of inference of a suitable sequent calculu...

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Veröffentlicht in:Logic journal of the IGPL 2023-12
1. Verfasser: Tesi, Matteo
Format: Artikel
Sprache:eng
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Zusammenfassung:We present a uniform proof-theoretic proof of the Gödel–McKinsey–Tarski embedding for a class of first-order intuitionistic theories. This is achieved by adapting to the case of modal logic the methods of proof analysis in order to convert axioms into rules of inference of a suitable sequent calculus. The soundness and the faithfulness of the embedding are proved by induction on the height of the derivations in the augmented calculi. Finally, we define an extension of the modal system for which the result holds with respect to geometric intuitionistic.
ISSN:1367-0751
1368-9894
DOI:10.1093/jigpal/jzad029