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A unification of the basic logics of Sambin and Visser

Ardeshir, M ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1093/jigpal/jzs002
  3. Publisher: 2012
  4. Abstract:
  5. In logical literature, the phrase 'basic logic' refers to at least three different logical systems. The first one, basic propositional logic, BPL was introduced by Albert Visser in 1981. This logic is a subintuitionistic logic that can be obtained from intuitionistic logic by weakening of modus ponens. The second logical system with the name 'basic logic', is the system B that was introduced by G. Sambin and G. Battilotti in 1997. The goal of this logical system is to provide a common foundation for all usual non-modal logics. The third one is called 'basic logic' by P. Hajek in the field of Fuzzy Logic. We show that the two systems BPL and B do not have a direct relationship (i.e. none of them can be obtained from the other as an extension), however, we introduce the logic U, that provides a common base for these two logical systems such that both of them can be obtained as extensions of U
  6. Keywords:
  7. Sambin's basic logic ; Subintuitionistic logics ; Substructural logics ; Visser's basic logic
  8. Source: Logic Journal of the IGPL ; Volume 20, Issue 6 , 2012 , Pages 1202-1213 ; 13670751 (ISSN)
  9. URL: http://jigpal.oxfordjournals.org/content/20/6/1202