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On the Structure of Natural Deduction Derivations for “Generally”

  • Leonardo B. VanaEmail author
  • Paulo A. S. Veloso
  • Sheila R. M. Veloso
Chapter
Part of the Trends in Logic book series (TREN, volume 39)

Abstract

Logics for ‘generally’ were introduced as extensions of First-Order Logic (FOL) for handling assertions with vague notions (e.g., ‘generally,’ ‘most,’ and ‘several’) expressed by formulas with generalized quantifiers. Deductive systems have been developed for such logics. Here, we characterize the structure of derivations in natural deduction style for filter logic. This characterization extends the familiar one for FOL.

Keywords

Logics for ‘generally’ Generalized quantifiers Vague notions Natural deduction Derivation structure Normalization Minimum formula Minimum segment 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Leonardo B. Vana
    • 1
    Email author
  • Paulo A. S. Veloso
    • 2
  • Sheila R. M. Veloso
    • 3
  1. 1.Institute of MathematicsUniversidade Federal Fluminense (UFF)NiteróiBrazil
  2. 2.Systems and Computer Engineering Program, COPPEUniversidade Federal do Rio de Janeiro (UFRJ)Rio de JaneiroBrazil
  3. 3.Department of Systems and Computer EngineeringUniversidade Estadual do Rio de Janeiro (UERJ)Rio de JaneiroBrazil

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