More On Modal Logics and Deduction

Öztürk I. Ö., Gyenis Z., Molnar Z.

BULLETIN OF THE SECTION OF LOGIC, cilt.0, sa.0, ss.0-1, 2026 (ESCI, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 0 Sayı: 0
  • Basım Tarihi: 2026
  • Dergi Adı: BULLETIN OF THE SECTION OF LOGIC
  • Derginin Tarandığı İndeksler: Scopus, Emerging Sources Citation Index (ESCI), MathSciNet, Philosopher's Index, zbMATH, Directory of Open Access Journals
  • Sayfa Sayıları: ss.0-1
  • Yozgat Bozok Üniversitesi Adresli: Evet

Özet


We study the relation between additivity and deduction theorems in the
algebraic semantics of congruential modal logic. Additivity of the modal operator
is well-known to imply the local deduction-detachment theorem. Our main theme
is that deduction properties of modal logic persist far beyond the additive setting.
We introduce the notion of a strongly non-additive variety, and then we prove that
there are continuum many strongly non-additive minimal discriminator varieties
of Boolean frames; equivalently, continuum many strongly non-additive maximal
congruential modal logics with deduction-detachment theorem. Moreover, every
normal modal logic can be transformed, in an injective way, into a strongly non-
additive one while preserving the (local) deduction theorem. Finally, we show that
neither the class of congruential modal logics with the local deduction theorem nor
its complement is elementary.