Abstract
Frame semantics for negation on the Australian Plan accommodates many different negations, but it falls short on accommodating subminimal negation when the language contains conjunction and disjunction. In this paper, I will present a multi-relational frame semantics –multi-incompatibility frame semantics– that can accommodate subminimal negation. I will first argue that multi-incompatibility frames are in accordance with the philosophical motivations behind negation on the Australian Plan, namely its modal and exclusion-expressing nature. Then, I will prove the soundness and completeness results of a subminimal logic that consists of the multi-incompatibility semantics and a proof system with operational rules that characterize subminimal negation, conjunction and disjunction. Lastly, I will prove some key correspondence theorems that relate frame conditions to certain principles that are associated with stronger negations, which will give rise to a new kite of negations that includes subminimal negation.
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Acknowledgements
I would like to thank the participants of the UC Davis LLeMMMa reading group, especially to Adam Sennet, Hanti Lin, G.J. Mattey, I-Sen Chen and Da Fan, for their feedback on earlier drafts of this paper. I would also like to thank two anonymous referees of this journal, and the audiences of AAL 2021 and GSCL XXII conferences for their comments. Additionally, I am grateful to Lauren Emerick and Jordan Bell for their editorial input. Special thanks to Rohan French who patiently worked through many different drafts of this paper and provided essential guidance.
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Tabakci, S.K. Subminimal Negation on the Australian Plan. J Philos Logic 51, 1119–1139 (2022). https://doi.org/10.1007/s10992-022-09661-9
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DOI: https://doi.org/10.1007/s10992-022-09661-9