Grafting modalities onto substructural implication systems

Marcello D'agostino, Dov M. Gabbay, Alessandra Russo

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We investigate the semantics of the logical systems obtained by introducing the modalities □ and ◇ into the family of substructural implication logics (including relevantΓlinear and intuitionistic implication). ThenΓin the spirit of the LDS (Labelled Deductive Systems) methodologyΓwe "import" this semantics into the classical proof system KE. This leads to the formulation of a uniform labelled refutation system for the new logics which is a natural extension of a system for substructural implication developed by the first two authors in a previous paper.

Original languageEnglish
Pages (from-to)65-102
Number of pages38
JournalStudia Logica
Issue number1
StatePublished - 1997
Externally publishedYes


  • Kripke semanticsΓlabelled deductive systemsΓKE system


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