Marcelino, Sérgio; Rivieccio, Umberto Locally tabular \(\neq \) locally finite. (English) Zbl 1420.03023 Log. Univers. 11, No. 3, 383-400 (2017). Summary: 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. Cited in 2 Documents MSC: 03B22 Abstract deductive systems 03G27 Abstract algebraic logic Keywords:locally tabular; locally finite; selfextensional logics; matrix semantics PDFBibTeX XMLCite \textit{S. Marcelino} and \textit{U. Rivieccio}, Log. Univers. 11, No. 3, 383--400 (2017; Zbl 1420.03023) Full Text: DOI References: [1] Albuquerque, H., Prenosil, A., Rivieccio, U.: An algebraic view of super-Belnap logics. Submitted · Zbl 1417.03175 [2] Blok, W.J., Pigozzi, D.: Algebraizable logics. Mem. Am. Math. Soc., 396, A.M.S., Providence, (1989) · Zbl 0664.03042 [3] Bou, F., Rivieccio, U.: The logic of distributive bilattices. Log. J. I.G.P.L 19(1), 183-216 (2011) · Zbl 1214.03056 [4] Burris, S., Sankappanavar, H.P.: A course in Universal Algebra. The Millennium edition, 1981, Berlin, Springer (2000) · Zbl 0478.08001 [5] Caleiro, C., Marcelino, S., Rivieccio, U.: Characterizing finite-valuedness. Submitted. http://sqig.math.ist.utl.pt/pub/MarcelinoS/17-CMR-finval.pdf · Zbl 1444.03106 [6] Chagrov, A., Zakharyaschev, M.: Modal Logic, Oxford Logic Guides, vol. 19. Oxford University Press, Oxford (1997) · Zbl 0871.03007 [7] Czelakowski, J.: Protoalgebraic logics, Trends in Logic-Studia Logica Library, 10. Kluwer Academic Publishers, Dordrecht (2001) · Zbl 0984.03002 [8] Font, J.M., Jansana, R.: A General Algebraic Semantics for Sentential Logics. Lecture Notes in Logic, vol. 7, 2nd edn. Springer, Berlin (2009) · Zbl 0865.03054 [9] Font, J.M., Jansana, R., Pigozzi, D.: On the closure properties of the class of full G-models of a deductive system. Stud. Log. 83(1-3), 215-278 (2006) · Zbl 1106.03060 · doi:10.1007/s11225-006-8304-6 [10] Hájek, P.: Metamathematics of fuzzy logic, Trends in Logic-Studia Logica Library, 4. Kluwer Academic Publishers, Dordrecht (1998) · Zbl 0937.03030 · doi:10.1007/978-94-011-5300-3 [11] Rivieccio, U.: An infinity of super-Belnap logics. J. Appl. Non Class. Log. 22(4), 319-335 (2012) · Zbl 1398.03112 · doi:10.1080/11663081.2012.737154 [12] Shoesmith, D.J., Smiley, T.J.: Deducibility and many-valuedness. J. Symb. Log. 36(4), 610-622 (1971) · Zbl 0253.02015 · doi:10.2307/2272465 [13] Wójcicki, R.: Theory of Logical Calculi. Basic Theory of Consequence Operations, Synthese Library, vol. 199. Reidel, Dordrecht (1988) · Zbl 0682.03001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.