Studia Logica

, Volume 51, Issue 2, pp 249–277 | Cite as

The logic of linear tolerance

  • Giorgie Dzhaparidze


A nonempty sequence 〈T1,...,Tn〉 of theories is tolerant, if there are consistent theories T 1 + ,..., T n + such that for each 1 ≤i ≤n, T i + is an extension of Ti in the same language and, if i ≤n, T i + interprets T i+1 + . We consider a propositional language with the modality ◊, the arity of which is not fixed, and axiomatically define in this language the decidable logics TOL and TOLω. It is shown that TOL (resp. TOLω) yields exactly the schemata of PA-provable (resp. true) arithmetical sentences, if ◊(A1,..., An) is understood as (a formalization of) “〈 PA+A1, ..., PA+An〉 is tolerant”.


Mathematical Logic Computational Linguistic Decidable Logic Consistent Theory Propositional Language 
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Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • Giorgie Dzhaparidze
    • 1
  1. 1.Institute of PhilosophyGeorgian Academy of SciencesTbilisiGeorgia

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