A Classification of Logics over FLew and Almost Maximal Logics

  • Hiroakira Ono
  • Masaki Ueda
Part of the Synthese Library book series (SYLI, volume 320)


Let FL ew be the logic obtained from the intuitionistic propositional logic by deleting contraction rule if we formulate it in a sequent system. Sometimes, this logic is called intuitionistic affine logic. The class of logics over FL ew , i.e. logics stronger than or equal to FL ew , includes many interesting logics, e.g., intermediate logics, Łukasiewicz’s many-valued logics, Grišin’s logic and product logic, etc. (See, e.g., Cignoli et al., 2000; Grišin, 1976; Hájek, 1998.) The study of logics over FL ew , will enable us to discuss these different kinds of logics within a uniform framework (see Ono and Komori, 1985; Ono, 1999 for the detail).


Classical Logic Residuated Lattice Intuitionistic Logic Heyting Algebra Product Logic 
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Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Hiroakira Ono
    • 1
  • Masaki Ueda
    • 2
  1. 1.School of Information ScienceJAISTIshikawaJapan
  2. 2.Japan Patent OfficeTokyoJapan

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