Skip to main content
SpringerLink
Log in

Multi-valued Semantics: Why and How

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

According to Suszko’s Thesis, any multi-valued semantics for a logical system can be replaced by an equivalent bivalent one. Moreover: bivalent semantics for families of logics can frequently be developed in a modular way. On the other hand bivalent semantics usually lacks the crucial property of analycity, a property which is guaranteed for the semantics of multi-valued matrices. We show that one can get both modularity and analycity by using the semantic framework of multi-valued non-deterministic matrices. We further show that for using this framework in a constructive way it is best to view “truth-values” as information carriers, or “information-values”.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Avron A.: ‘Simple Consequence relations’. Information and Computation 92, 105–139 (1991)

    Article  Google Scholar 

  2. Avron, A., ‘Non-deterministic Matrices and Modular Semantics of Rules’, in J.-Y. Beziau (ed.), Logica Universalis, Birkhüser Verlag, 2005, pp. 149–167.

  3. Avron, A., ‘Logical Non-determinism as a Tool for Logical Modularity: An Introduction’, in S. Artemov, H. Barringer, A. S. d’Avila Garcez, L. C. Lamb, and J. Woods (eds.), We Will Show Them: Essays in Honor of Dov Gabbay, vol. 1, 105–124, College Publications, 2005.

  4. Avron A.: ‘Non-deterministic Semantics for Logics with a Consistency Operators’. International Journal of Approximate Reasoning 45, 271–287 (2007)

    Article  Google Scholar 

  5. Avron A.: ‘5-valued Non-deterministic Semantics for The Basic Paraconsistent Logic mCi’. Studies in Logic, Grammar and Rhetoric 14, 127–136 (2008)

    Google Scholar 

  6. Avron A., Konikowska B.: ‘Multi-valued Calculi for Logics Based on Nondeterminism’. Journal of the Interest Group in Pure and Applied Logic 10, 365–387 (2005)

    Google Scholar 

  7. Avron A., Lev I.: ‘Non-deterministic Multiple-valued Structures’. Journal of Logic and Computation 15, 241–261 (2005)

    Article  Google Scholar 

  8. Caleiro, C., W. A. Carnielli, M. E. Coniglio, and J. Marcos, ‘Two’s Company: “The Humbug of Many Logical Values”’, in J.-Y. Beziau (ed.), Logica Universalis, Birkhüser Verlag, 2005, pp. 169–189.

  9. Carnielli, W. A., M. E. Coniglio, and J. Marcos, ‘Logics of Formal Inconsistency’, in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd edition, Vol. 14, Kluwer Academic Publishers, 2007, pp. 1–93.

  10. da Costa N.C.A.: ‘On the theory of inconsistent formal systems’. Notre Dame Journal of Formal Logic 15, 497–510 (1974)

    Article  Google Scholar 

  11. da Costa N.C.A., Béziau J.-Y., Bueno O.: ‘Malinowski and Suszko on Many-valued Logics: On the Reductions of Many-valuedness to Two-valuedness’. Modern Logic 6, 272–299 (1974)

    Google Scholar 

  12. da Costa, N. C. A., D. Krause, and O. Bueno, ‘Paraconsistent Logics and Paraconsistency: Technical and Philosophical Developments’, in D. Jacquette (ed.), Philosophy of Logic, North-Holland, 2007, pp. 791–911.

  13. Łoś J., Suszko R.: ‘Remarks on sentential logics’. Indagationes Mathematicae 20, 177–183 (1958)

    Google Scholar 

  14. Malinowski G.: ‘Inferential Many-valuedness’. In: Woleński, J. (eds) Philosophical Logic in Poland, pp. 75–84. Kluwer Academic Publishers, Dordrecht (1994)

    Google Scholar 

  15. Marcos J.: ‘Possible-translations Semantics for Some Weak Classically-based Paraconsistent Logics’. Journal of Applied Non-classical Logics 18, 7–28 (2008)

    Article  Google Scholar 

  16. Scott D.A.: ‘Background to Formalization’. In: Leblanc, H. (eds) Truth, Syntax, and Modality, pp. 244–273. North-Holland, Amsterdam (1973)

    Chapter  Google Scholar 

  17. Shoesmith D.J., Smiley T.J.: ‘Deducibility and Many-valuedness’. Journal of Symbolic Logic 36, 610–622 (1971)

    Article  Google Scholar 

  18. Shoesmith, D. J., and T. J. Smiley, Multiple-Conclusion Logic, Cambridge University Press, 1978.

  19. Suszko R.: ‘The Fregean Axiom and Polish Mathematical Logic in the 1920’s’. Studia Logica 36, 373–380 (1977)

    Article  Google Scholar 

  20. Tsuji M.: ‘Many-valued Logics and Suszko’s Thesis Revisited’. Studia Logica 60, 299–309 (1998)

    Article  Google Scholar 

  21. Urquhart A.: ‘An Interpretation of Many-valued Logic’. Zeitschrift für mathematische Logik und Grundlagen der Mathematik 19, 111–114 (1973)

    Article  Google Scholar 

  22. Urquhart, A., ‘Many-valued logic’, in D. M. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd edition Vol. 2, Kluwer Academic Publishers, 2001, pp. 249–295.

  23. Wansing H., Shramko Y.: ‘Suszko’s Thesis, Inferential Many-valuedness, and the Notion of a Logical System’. Studia Logica 88, 405–429 (2008)

    Article  Google Scholar 

  24. Wójcicki R.: ‘Some Remarks on the Consequence Operation in Sentential Logics’. Fundamenta Mathematicae 68, 269–279 (1970)

    Google Scholar 

  25. Wójcicki, R., Theory of Logical Calculi: Basic Theory of Consequence Operations, Kluwer, 1988.

Download references

Author information

Authors and Affiliations

  1. School of Computer Science, Tel-Aviv University, Ramat Aviv, 69978, Israel

    Arnon Avron

Authors
  1. Arnon Avron
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Arnon Avron.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Avron, A. Multi-valued Semantics: Why and How. Stud Logica 92, 163–182 (2009). https://doi.org/10.1007/s11225-009-9193-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-009-9193-2

Keywords

Search

Navigation