General normal forms for any additive logic

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Khaled M. K. M. I.

Studia Scientiarum Mathematicarum Hungarica, vol.54, no.3, pp.394-409, 2017 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 3
  • Publication Date: 2017
  • Doi Number: 10.1556/012.2017.54.3.1372
  • Journal Name: Studia Scientiarum Mathematicarum Hungarica
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.394-409
  • Keywords: Additive Logics, Normal Forms, Partial Connectives
  • Istanbul Medipol University Affiliated: No


In this article, we define general normal forms for any logic that has propositional part and whose non-propositional connectives distribute over finite disjunctions. We do not require the non-propositional connectives to be closed on the set of formulas, so our normal forms cover logics with partial connectives too. We also show that most of the known normal forms in the literature are in fact particular cases of our general forms. These general normal forms are natural improvement of the distributive normal forms of J. Hintikka [6] and their modal analogues, e.g. [1] and [4].