Women In Logic (@womeninlogic.bsky.social)

Sequent Images of Normal Derivations and Natural Deduction Images of Derivations without M-cuts - Journal of Logic, Language and Information A standard sequent system (the system $$\mathcal{L}\mathcal{J}$$ L J ), a standard natural deduction system (the system $$\mathcal{N}\mathcal{J}$$ N J ) and an extended natural deduction system (the system $$\mathcal{N}\mathcal{E}$$ N E ) will be considered. The $$\mathcal{L}\mathcal{J}$$ L J -images of $$\mathcal{N}\mathcal{J}$$ N J -derivations and $$\mathcal{N}\mathcal{E}$$ N E -derivations ( $$\mathcal {GLJ}$$ GLJ -derivations and $$\mathcal {PLJ}$$ PLJ -derivations) and the $$\mathcal{N}\mathcal{E}$$ N E -images of $$\mathcal{N}\mathcal{J}$$ N J -derivations ( $$\mathcal {ENE}$$ ENE -derivations) will be presented. It will be shown that $$\mathcal {PLJ}$$ PLJ -derivations and $$\mathcal {GLJ}$$ GLJ -derivations have special cuts, nde-cuts and nd-cuts, respectively. Nd-cuts corresponding to maximum segments of $$\mathcal{N}\mathcal{J}$$ N J -derivations (ndam-cuts) and nde-cuts corresponding to maximum segments of $$\mathcal{N}\mathcal{E}$$ N E -derivations (ndeam-cuts) will be studied. It will be shown that (A) an $$\mathcal{N}\mathcal{J}$$ N J -derivation is normal iff its $$\mathcal{N}\mathcal{E}$$ N E -image is normal iff its $$\mathcal{L}\mathcal{J}$$ L J -image has no ndam-cuts; (B) an $$\mathcal {GLJ}$$ GLJ -derivation has no ndam-cuts iff its $$\mathcal{N}\mathcal{J}$$ N J -image is normal iff its $$\mathcal{N}\mathcal{E}$$ N E -image is normal; and (C) an $$\mathcal {ENE}$$ ENE -derivation is normal iff its $$\mathcal{N}\mathcal{J}$$ N J -image is normal iff its $$\mathcal{L}\mathcal{J}$$ L J -image has no ndeam-cuts. https://link.springer.com/article/10.1007/s10849-025-09435-x?utm_source=springer_etoc&utm_medium=email&utm_campaign=CONR_10849_AWA1_GL_DTEC_054CI_TOC-280925&utm_content=etoc_springer_20250928