General normal forms for any additive logic

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Khaled M. K. M. I.

Studia Scientiarum Mathematicarum Hungarica, cilt.54, sa.3, ss.394-409, 2017 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 54 Sayı: 3
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1556/012.2017.54.3.1372
  • Dergi Adı: Studia Scientiarum Mathematicarum Hungarica
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.394-409
  • Anahtar Kelimeler: Additive Logics, Normal Forms, Partial Connectives
  • İstanbul Medipol Üniversitesi Adresli: Hayır

Özet

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].