Gentzen's sequent calculus LJ, and its variants such as G3, are (as is well known) convenient as a basis for automating proof search for IPC (intuitionistic propositional calculus).Expand

LJQ is a focused sequent calculus for intuitionistic logic, with a simple restriction on the first premisss of the usual left introduction rule for implication.Expand

Using labelled formulae, a cut-free sequent calculus for intuitionistic propositional logic is presented, together with an easy cut-admissibility proof; both extend to cover, in a uniform fashion, all intermediate logics characterised by frames satisfying conditions expressible by one or more geometric implications.Expand

In a category K with finite limits, the exponentiability of a morphisms s is (rather easily) characterised in terms of K admitting partial products (essentially those of Pasynkov) over s; and that of… Expand

In the proof-theoretic semantics approach to meaning, harmony, requiring a balance between introduction-rules (I-rules) and elimination rules (E- rules) within a meaning conferring natural-deduction proof-system, is a central notion.Expand

We prove a folklore theorem, that two derivations in a cut-free sequent calculus for intuitionistic propositional logic (based on Kleene's G3) are inter-permutable (using a set of basic reduction rules) iff they determine the same natural deduction.Expand

We give a direct proof of admissibility of cut and contraction for the contraction-free sequent calculus G4ip for intuitionistic propositional logic and for a corresponding multi-succedent calculus.Expand