Abstract Logical Constants


A possibility of defining logical constants within abstract logical frameworks is discussed, in relation to abstract definition of logical consequence. We propose using duals as a general method of applying the idea of invariance under replacement as a criterion for logicality.

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  1. 1.

    Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001)

    Google Scholar 

  2. 2.

    Bonnay, D., Westerståhl, D.: Consequence mining. J. Philos. Log. 41, 671–709 (2012)

    Article  Google Scholar 

  3. 3.

    García Matos, M., Väänänen, J.: Abstract model theory as a framework for universal logic. In: Beziau, J.-Y. (ed.) Logica Universalis: Towards a General Theory of Logic, 2nd edn, pp. 19–33. Birkhäuser, Basel (2007)

    Google Scholar 

  4. 4.

    Shoesmith, D.J., Smiley, T.J.: Multiple-conclusion Logic. Cambridge University Press, Cambridge (1978)

    Google Scholar 

  5. 5.

    Šikić, Z.: Singular consequence relations and order relations. Grazer Math. Ber. 304, 118–127 (1989)

    MathSciNet  MATH  Google Scholar 

Download references

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Corresponding author

Correspondence to Tin Perkov.

Additional information

This work has been supported by Croatian Science Foundation (HRZZ) under the Project UIP-05-2017-9219. The paper was awarded the 1st Georgius Benignus Logic Prize (Croatia) and was presented at the universal logic contest at UNILOG 2018 in Vichy. I am grateful to Srećko Kovač for valuable comments and a correction.

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Perkov, T. Abstract Logical Constants. Log. Univers. 12, 341–350 (2018). https://doi.org/10.1007/s11787-018-0206-7

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Mathematics Subject Classification

  • 03C95


  • Logical constants
  • Abstract logic
  • Logical consequence