Abstract
We show that for an arbitrary logic being locally tabular is a strictly weaker property than being locally finite. We describe our hunt for a logic that allows us to separate the two properties, revealing weaker and weaker conditions under which they must coincide, and showing how they are intertwined. We single out several classes of logics where the two notions coincide, including logics that are determined by a finite set of finite matrices, selfextensional logics, algebraizable and equivalential logics. Furthermore, we identify a closure property on models of a logic that, in the presence of local tabularity, is equivalent to local finiteness.
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Work 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 FEDERPT2020) and with the support of EU FP7 Marie Curie PIRSES-GA-2012-318986 project GeTFun: Generalizing Truth-Functionality. The first author also acknowledges the FCT postdoc grant SFRH/BPD/76513/2011.
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Marcelino, S., Rivieccio, U. Locally Tabular \(\ne \) Locally Finite. Log. Univers. 11, 383–400 (2017). https://doi.org/10.1007/s11787-017-0174-3
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DOI: https://doi.org/10.1007/s11787-017-0174-3