Hypothetical Logic of Proofs - Bonelli, Eduardo Augusto (2014)
The logic of proofs is a refinement of modal logic introduced by Artemov in 1995 in which the modality ◻A is revisited as ⟦t⟧A where t is an expression that bears witness to the validity of A. It enjoys arithmetical soundness and completeness and is capable of reflecting its own proofs (⊦A implies ⊦ ⟦t⟧A, for some t). We develop the Hypothetical Logic of Proofs, a reformulation of LP based on judgemental reasoning