Abstract
We investigate the possibility of extending the non-functionally complete logic of a collection of Boolean connectives by the addition of further Boolean connectives that make the resulting set of connectives functionally complete. More precisely, we will be interested in checking whether an axiomatization for Classical Propositional Logic may be produced by merging Hilbert-style calculi for two disjoint incomplete fragments of it. We will prove that the answer to that problem is a negative one, unless one of the components includes only top-like connectives.
This research was done under the scope of R&D Unit 50008, financed by the applicable financial framework (FCT/MEC through national funds and when applicable co-funded by FEDER/PT2020), and is part of the MoSH initiative of SQIG at Instituto de Telecomunicações. Sérgio Marcelino acknowledges the FCT postdoc grant SFRH/BPD/76513/2011. João Marcos acknowledges partial support by CNPq and by the Humboldt Foundation.
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Caleiro, C., Marcelino, S., Marcos, J. (2017). Merging Fragments of Classical Logic. In: Dixon, C., Finger, M. (eds) Frontiers of Combining Systems. FroCoS 2017. Lecture Notes in Computer Science(), vol 10483. Springer, Cham. https://doi.org/10.1007/978-3-319-66167-4_17
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DOI: https://doi.org/10.1007/978-3-319-66167-4_17
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