Studia Logica

, Volume 88, Issue 3, pp 405–429 | Cite as

Suszko’s Thesis, Inferential Many-valuedness, and the Notion of a Logical System



According to Suszko’s Thesis, there are but two logical values, true and false. In this paper, R. Suszko’s, G. Malinowski’s, and M. Tsuji’s analyses of logical twovaluedness are critically discussed. Another analysis is presented, which favors a notion of a logical system as encompassing possibly more than one consequence relation.

[A] fundamental problem concerning many-valuedness is to know what it really is.

[13, p. 281]


Suszko’s Thesis inferential many-valuedness many-valued logic bivaluations algebraic values logical truth values. 


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  1. 1.
    Belnap, N. D., ‘How a computer should think’, in G. Ryle (ed.), Contemporary Aspects of Philosophy, Oriel Press Ltd., Stocksfield, 1977, pp. 30–55.Google Scholar
  2. 2.
    Belnap, N. D., ‘A useful four-valued logic, in J. M. Dunn and G. Epstein (eds.), Modern Uses of Multiple-Valued Logic, D. Reidel Publishing Company, Dordrecht, 1977, 8–37.Google Scholar
  3. 3.
    van Benthem J. (1984) ‘Possible Worlds Semantics, a Research Program that Cannot Fail?’. Studia Logica 43, 379–393CrossRefGoogle Scholar
  4. 4.
    Béziau, J.-Y., Universal Logic, in T. Childers and O. Majer (eds.), Proceedings Logica’ 94, Czech Academy of Sciences, Prague, 1994, pp. 73–93.Google Scholar
  5. 5.
    Béziau, J.-Y., ‘What is Many-Valued Logic?’, in Proceedings of the 27th International Symposium on Multiple-Valued Logic, IEEE Computer Society Press, Los Alamitos/Cal., 1997, pp. 117–121.Google Scholar
  6. 6.
    Béziau, J.-Y., ‘Recherches sur la logique abstraite: les logiques normales’, Acta Universitatis Wratislaviensis no. 2023, Logika 18 (1998), 105–114.Google Scholar
  7. 7.
    Blamey S., and L. Humberstone (1991) ‘A Perspective on Modal Sequent Logic’. Publications of the Research Institute for Mathematical Sciences, Kyoto University 27, 763–782CrossRefGoogle Scholar
  8. 8.
    Brown B., and P. Schotch (1999) ‘Logic and Aggregation’. Journal of Philosophical Logic 28, 265–287CrossRefGoogle Scholar
  9. 9.
    Caleiro C., Carnielli W., Coniglio M., and Marcos J. (2005). ‘Two’s company: “The humbug of many logical values"’. In: Beziau J.-Y. (eds). Logica Universalis. Birkhäuser, Basel, pp. 169–189Google Scholar
  10. 10.
    Caleiro, C., W. Carnielli, M. Coniglio, and J. Marcos, ‘Suszko’s Thesis and dyadic semantics’, preprint,
  11. 11.
    Caleiro, C., W. Carnielli, M. Coniglio, and J. Marcos, ‘Dyadic semantics for many-valued logics’, preprint,
  12. 12.
    Cook R. (2005) What’s wrong with tonk (?)’. Journal of Philosophical Logic 34, 217–226CrossRefGoogle Scholar
  13. 13.
    da Costa N., Béziau J.-Y., and Bueno O. (1996) ‘Malinowski and Suszko on manyvalued logics: On the reduction of many-valuedness to two-valuedness’. Modern Logic 6, 272–299Google Scholar
  14. 14.
    Curry H.B. (1963). Foundations of Mathematical Logic. McGraw-Hill, New YorkGoogle Scholar
  15. 15.
    Czelakowski J. (2001). Protoalgebraic Logics. Kluwer Academic Publishers, DordrechtCrossRefGoogle Scholar
  16. 16.
    Devyatkin, L., ‘Non-classical definitions of logical consequence’ (in Russian), Smirnov’s Readings in Logic. Fifth Conference, Moscow (2007), 26–27.Google Scholar
  17. 17.
    Dunn J.M. (1976) ‘Intuitive semantics for first-degree entailment and ‘coupled trees". Philosophical Studies 29, 149–168CrossRefGoogle Scholar
  18. 18.
    Dunn J.M. (2000) ‘Partiality and its dual’. Studia Logica 66, 5–40CrossRefGoogle Scholar
  19. 19.
    Frankowski S. (2004) ‘Formalization of a plausible inference’. Bulletin of the Section of Logic 33, 41–52Google Scholar
  20. 20.
    Frankowski S. (2004) ‘p-consequence versus q-consequence’. Bulletin of the Section of Logic 33, 197–207Google Scholar
  21. 21.
    Gottwald S. (1989). Mehrwertige Logik. Eine Einführung in Theorie und Anwendungen. Akademie-Verlag, BerlinGoogle Scholar
  22. 22.
    Gottwald S. (2001). A Treatise on Many-valued Logic. Research Studies Press, BaldockGoogle Scholar
  23. 23.
    Jennings R., and Schotch P. (1984) ‘The Preservation of Coherence’. Studia Logica 43, 89–106CrossRefGoogle Scholar
  24. 24.
    Malinowski G. (1990) ‘Q-Consequence Operation’. Reports on Mathematical Logic 24, 49–59Google Scholar
  25. 25.
    Malinowski G. (1990) ‘Towards the Concept of Logical Many-Valuedness’. Folia Philosophica 7, 97–103Google Scholar
  26. 26.
    Malinowski G. (1993). Many-valued Logics. Clarendon Press, OxfordGoogle Scholar
  27. 27.
    Malinowski G. (1994) ‘Inferential Many-Valuedness’. In: Jan Woleński (eds). Philosophical Logic in Poland. Kluwer Academic Publishers, Dordrecht, pp. 75–84CrossRefGoogle Scholar
  28. 28.
    Malinowski G. (2001) ‘Inferential Paraconsistency’. Logic and Logical Philosophy 8, 83–89CrossRefGoogle Scholar
  29. 29.
    Malinowski G. (2004) ‘Inferential Intensionality’. Studia Logica 76, 3–16CrossRefGoogle Scholar
  30. 30.
    Muskens R. (1999) ‘On Partial and Paraconsistent Logics’. Notre Dame Journal of Formal Logic 40, 352–374CrossRefGoogle Scholar
  31. 31.
    Rescher N. (1969). Many-Valued Logic. McGraw-Hill, New YorkGoogle Scholar
  32. 32.
    Routley R. (1975) Universal Semantics?’. Journal of Philosophical Logic 4, 327–356CrossRefGoogle Scholar
  33. 33.
    Schröter K. (1955) ‘Methoden zur Axiomatisierung beliebiger Aussagen- und Prädikatenkalküle’. Zeitschrift für mathematische Logik und Grundlagen der Mathematik 1, 241–251CrossRefGoogle Scholar
  34. 34.
    Scott D. (1973) Background to Formalization’. In: Leblanc H. (eds) Truth, Syntax and Modality. North-Holland, Amsterdam, pp. 244–273CrossRefGoogle Scholar
  35. 35.
    Shramko Y., Dunn J.M., and Takenaka T. (2001) ‘The trilattice of constructive truth values’. Journal of Logic and Computation 11, 761–788CrossRefGoogle Scholar
  36. 36.
    Shramko Y., and Wansing H. (2005) ‘Some useful 16-valued logics: how a computer network should think’. Journal of Philosophical Logic 34, 121–153CrossRefGoogle Scholar
  37. 37.
    Shramko Y., and Wansing H. (2005) ‘The Logic of Computer Networks’ (in Russian). Logical Studies (Moscow) 12, 119–145Google Scholar
  38. 38.
    Shramko Y., and Wansing H. (2006) ‘Hypercontradictions, generalized truth values, and logics of truth and falsehood’. Journal of Logic, Language and Information 15, 403–424CrossRefGoogle Scholar
  39. 39.
    Suszko R. (1977) ‘The Fregean axiom and Polish mathematical logic in the 1920’s’. Studia Logica 36, 373–380CrossRefGoogle Scholar
  40. 40.
    Tsuji M. (1998) ‘Many-valued logics and Suszko’s Thesis revisited’. Studia Logica 60, 299–309CrossRefGoogle Scholar
  41. 41.
    Urquhart A. (1973) ‘An interpretation of many-valued logic’. Zeitschrift für mathematische Logik und Grundlagen der Mathematik 19, 111–114CrossRefGoogle Scholar
  42. 42.
    Wansing H. (2006) ‘Connectives stranger than tonk’. Journal of Philosophical Logic 35, 653–660CrossRefGoogle Scholar
  43. 43.
    Wansing, H., and Y. Shramko, ‘Harmonious many-valued propositional logics and the logic of computer networks’, to appear in C. Dégremont, L. Keiff and H. Rückert (eds.), Festschrift dedicated to Shahid Rahman, College Publications, London, 2008.Google Scholar
  44. 44.
    Wójcicki R. (1970) ‘Some Remarks on the Consequence Operation in Sentential Logics’. Fundamenta Mathematicae 68, 269–279Google Scholar
  45. 45.
    Wójcicki R. (1988). Theory of Logical Calculi: Basic Theory of Consequence Operations. Kluwer Academic Publishers, DordrechtCrossRefGoogle Scholar

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© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Institute of PhilosophyDresden University of TechnologyDresdenGermany
  2. 2.Department of PhilosophyState Pedagogical UniversityKrivoi RogUkraine

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