Abstract
We outline the rather complicated history of attempts at axiomatizing Jaśkowski’s discussive logic \(\mathbf {D_2}\) and show that some clarity can be had by paying close attention to the language we work with. We then examine the problem of axiomatizing \(\mathbf {D_2}\) in languages involving discussive conjunctions. Specifically, we show that recent attempts by Ciuciura are mistaken. Finally, we present an axiomatization of \(\mathbf {D_2}\) in the language Jaśkowski suggested in his second paper on discussive logic, by following a remark of da Costa and Dubikajtis. We also deal with an interesting variant of \(\mathbf {D_2}\), introduced by Ciuciura, in which negation is also taken to be discussive.
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Acknowledgements
The first author was a Postdoctoral Fellow for Research Abroad of JSPS at the time of submission, and now a Postdoctoral Research Fellow of JSPS. The second author was supported by FWF Grant P25417-G15 (LOGFRADIG). We would like to thank the referees for their helpful comments and suggestions which substantially improved the paper.
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Presented by Heinrich Wansing
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Omori, H., Alama , J. Axiomatizing Jaśkowski’s Discussive Logic \(\mathbf {D_2}\). Stud Logica 106, 1163–1180 (2018). https://doi.org/10.1007/s11225-017-9780-6
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DOI: https://doi.org/10.1007/s11225-017-9780-6