A Constructive Logic with Classical Proofs and Refutations

We study a conservative extension of classical propositional logic distinguishing between four modes of statement: a proposition may be affirmed or denied, and it may be strong or classical. Proofs of strong propositions must be constructive in some sense, whereas proofs of classical propositions pr...

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Bibliographic Details
Published in:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 1 - 13
Main Authors: Barenbaum, Pablo, Freund, Teodoro
Format: Conference Proceeding
Language:English
Published: IEEE 29.06.2021
Subjects:
Calculus
Cognition
Computational modeling
Computer science
Encoding
Focusing
Semantics
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Summary:We study a conservative extension of classical propositional logic distinguishing between four modes of statement: a proposition may be affirmed or denied, and it may be strong or classical. Proofs of strong propositions must be constructive in some sense, whereas proofs of classical propositions proceed by contradiction. The system, in natural deduction style, is shown to be sound and complete with respect to a Kripke semantics. We develop the system from the perspective of the propositions-as-types correspondence by deriving a term assignment system with confluent reduction. The proof of strong normalization relies on a translation to System F with Mendler-style recursion.
DOI:10.1109/LICS52264.2021.9470649