Studia Logica

, Volume 33, Issue 4, pp 349–357 | Cite as

A note on direct products and ultraproducts of logical matrices

  • Jan Zygmunt


In this contribution we shall characterize matrix consequence operation determined by a direct product and an ultraproduct of a family of logical matrices. As an application we shall describe finite consequence operations with the help of ultrapowers.


Mathematical Logic Matrix Consequence Direct Product Computational Linguistic Consequence Operation 
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  1. [1]
    S. Jaśkowski,Recherches sur le système de la logique intuitioniste,Actes du Congrès International de Philosophie Scientifique VI.Philosophie des Mathématiques. Actualités Scientifiques et Industrielles 393 (1936), pp. 58–61.Google Scholar
  2. [2]
    J. Kalicki,On Tarski's method,Comptes Rendus Séances de la Société des Sciences et des Lettres de Varsovie, Classe III (1946).Google Scholar
  3. [3]
    J. Łoś andR. Suszko,Remarks on sentential logics,Indagationes Mathematicae 20 (1958), pp. 177–183.Google Scholar
  4. [4]
    H. Rasiowa,O pewnym fragmencie implikacyjnego rachunku zdań,Studia Logica 3 (1955), pp. 208–222.CrossRefGoogle Scholar
  5. [5]
    S. J. Surma,Method of natural deduction in equivalential and equivalential-negational propositional calculus,Universitas Iagellonica Acta Scientarum Litterarumque, CCLXV,Schedae Logicae 6 (1971), pp. 55–68.Google Scholar
  6. [6]
    R. Wójcicki,Some remarks on the consequence operation in sentential logics,Fundamenta Mathematicae 58 (1970), pp. 289–297.Google Scholar
  7. [7]
    R. Wójcicki,The logic stronger then Łukasiewicz's three valued sentential calculus. The notion of degree of maximality versus the notion of degree of completeness,Studia Logica 33.2 (1974), pp. 201–214.Google Scholar
  8. [8]
    Z. Zawirski,Geneza i rozwój logiki intuicjonistycznej,Kwartalnik Filozoficzny 16 (1946), pp. 165–222.Google Scholar
  9. [9]
    J. Zygmunt,Direct products of consequence operations,Bulletin of the Section of Logic, Polish Academy of Sciences, Institute of Philosophy and Sociology 1.4 (1972), pp. 61–63.Google Scholar

Copyright information

© Warszawa 1974

Authors and Affiliations

  • Jan Zygmunt
    • 1
  1. 1.The Section of LogicPolish Academy of SciencesWrocław

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