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Contraction-Free Sequent Calculi for Intuitionistic Logic
  • R. Dyckhoff
  • Mathematics, Computer Science
  • J. Symb. Log.
  • 1 September 1992
TLDR
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
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LJQ: A Strongly Focused Calculus for Intuitionistic Logic
TLDR
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
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Proof analysis in intermediate logics
TLDR
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
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Exponentiable morphisms, partial products and pullback complements
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 ofExpand
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GEOMETRISATION OF FIRST-ORDER LOGIC
TLDR
We show that every infinitary first-order theory, suitably restricted, has a geometric conservative extension, hence the title. Expand
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A Note on Harmony
TLDR
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
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Permutability of Proofs in Intuitionistic Sequent Calculi
TLDR
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
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Admissibility of Structural Rules for Contraction-Free Systems of Intuitionistic Logic
TLDR
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
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