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Studia Logica

, Volume 35, Issue 3, pp 249–255 | Cite as

Projective and inductive generation of abstract logics

  • Stephen L. Bloom
Article

Abstract

An abstract logic 〈A, C〉 consists of a finitary algebraA and a closure systemC onA. C induces two other closure systems onA, CP andCI, by projective and inductive generation respectively. The various relations amongC, CP andCI are determined. The special case thatC is the standard equational closure system on monadic terms is studied in detail. The behavior of Boolean logics with respect to projective and inductive generation is determined.

Keywords

Mathematical Logic Closure System Boolean Logic Inductive Generation Computational Linguistic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    D.J. Brown andR. Suszko,Abstract logics,Dissertationes Mathematicae, Vol. 102 (1973) pp. 5–41.Google Scholar
  2. [2]
    G. Gratzer,Universal algebra, Princeton (1968).Google Scholar
  3. [3]
    S. L. Bloom andD. J. Brown,Classical abstract logics,Dissertationes Mathematicae, Vol. 102 (1973) pp. 43–52.Google Scholar
  4. [4]
    H. Rasiowa andR. Sikorski,The mathematics of metamathematics Warsaw (1963).Google Scholar

Copyright information

© Warszawa 1976

Authors and Affiliations

  • Stephen L. Bloom
    • 1
    • 2
  1. 1.Mathematical Sciences DepartmentIBM T.J. Watson Research CenterYorktown Heights
  2. 2.Department of MathematicsStevens Institute of TechnologyHoboken

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