Towards a Combinatorial Proof Theory

reasonable form of analyticity that can be demanded in Gilp ∗ : for any deriva- tion d, containing both cuts at the sequent and the TND-sequent level, there exists a cut-

We define two type assignment systems called Soft Intuitionistic Logic (SIL) and Intuition- istic Logic with Promotion (PIL) in which we introduce the exponential modality.. of

The proof is obtained by a direct mapping between formal E-strategies and derivations in a cut-free complete sequent calculus for first order intuitionistic logic.. Our approach

Classical logic focuses on truth (hence truth values) Intuitionistic logic focuses on provability (hence proofs) A is true if it is provable. The excluded

For example, intuitionistic logic was developed to rid (classical) logic of certain logical principles and model checking

In the Kripke semantics defined for dual-intuitionistic logic (see [Gor00]), the dual of intuitionistic implication is interpreted as being valid in a possible world if it is valid

To summarize, our prescription for obtaining compact proof certificates is as follows: (1) start from a focused sequent proof; (2) uniquely name every subformula path in

The missing piece to decompose cuts to their atomic form as shown in (9) is the rule s↑, dual to the switch s↓ rule, which allows to move a substructure in positive position outside