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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Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001)
Bonnay, D., Westerståhl, D.: Consequence mining. J. Philos. Log. 41, 671–709 (2012)
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)
Shoesmith, D.J., Smiley, T.J.: Multiple-conclusion Logic. Cambridge University Press, Cambridge (1978)
Šikić, Z.: Singular consequence relations and order relations. Grazer Math. Ber. 304, 118–127 (1989)
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
Mathematics Subject Classification
- Logical constants
- Abstract logic
- Logical consequence