Logica Universalis

, 5:319 | Cite as

The Logic with Truth and Falsehood Operators from a Point of View of Universal Logic

Article
First Online:
Received:
Accepted:

Abstract

The logic with independent truth and falsehood operators TFL is proposed. In TFL(→) standard truth-conditions for the implication are adopted. Nevertheless the laws of classical logic are not valid. In this language more then 107 different binary connectives can be defined. So this logic can be treated as universal logic relatively to the class of sentential logics.

Mathematics Subject Classification (2010)

Primary 03B22 Secondary 03B45 03B52 

Keywords

Truth operator falsehood operator truth logic universal logic 
This is a preview of subscription content, log in to check access.

References

  1. 1.
    Béziau, J.-Y.: What is a Logic? Plenary talk. The Sixth Smirnovs Readings in Logic, Moscow (2009) (in Russian)Google Scholar
  2. 2.
    Dunn J.M.: Partiality and its Dual. Stud. Log. 65, 5–40 (2000)MathSciNetCrossRefGoogle Scholar
  3. 3.
    D’Ottaviano, I.M.L., da Costa, N.C.A.: Sur un probleme de Jaskowski. Comptes Rendus de l’Acadmie des Sciences. Paris, vol. 270, Serie A, pp. 1349–1351 (1970)Google Scholar
  4. 4.
    Pavlov S.A.: Logic FL4 with Falsehood Operator. MultiValued Log. 5, 125–138 (2000)MATHGoogle Scholar
  5. 5.
    Pavlov, S.A.: Semantics with Only One Bedeutung: Rethinking Frege’s Semantics, XXII World Congress of Philosophy. Rethinking Philosophy Today. Seoul, Korea (Abstract) (2008)Google Scholar
  6. 6.
    Pawlow, S.A.: Einige nichttraditionelle Ideen in der Logik. In: Philosophie und Naturwissenschaften in Vergangenheit und Gegenwart. Heft 5: Philosophische Probleme der Logik, Berlin. S. 33–40 (1978)Google Scholar
  7. 7.
    von Wright, G.H.: Truth-Logics, Logique et Analyse, vol. 120, Nouvelle Serie, pp. 311–334 (1987)Google Scholar

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Institute of Philosophy RASMoscowRussia

Personalised recommendations