A unification of the basic logics of Sambin and Visser

作者：Ardeshir Mohammad^*; Vaezian Vahid

来源：Logic Journal of the IGPL, 2012, 20(6): 1202-1213.

DOI：10.1093/jigpal/jzs002

• Subintuitionistic logics
• substructural logics
• Sambin%26apos
• s basic logic
• Visser%26apos
• s basic logic

In logical literature, the phrase %26apos;basic logic%26apos; 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 %26apos;basic logic%26apos;, 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 %26apos;basic logic%26apos; 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.

• 出版日期2012-12