Canonicity results of substructural and lattice-based logics

Review of Symbolic Logic 4 (1):1-42 (2011)

In this paper, we extend the canonicity methodology in Ghilardi & Meloni (1997) to arbitrary lattice expansions, and syntactically describe canonical inequalities for lattice expansions consisting of -meet preserving operations, -multiplicative operations, adjoint pairs, and constants. This approach gives us a uniform account of canonicity for substructural and lattice-based logics. Our method not only covers existing results, but also systematically accounts for many canonical inequalities containing nonsmooth additive and multiplicative uniform operations. Furthermore, we compare our technique with the approach in Dunn et al. (2005) and Gehrke et al. (2005)
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DOI 10.1017/s1755020310000201
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References found in this work BETA

Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2002 - Cambridge University Press.
Modal Logic.Alexander Chagrov - 1997 - Oxford University Press.
Introduction to Higher Order Categorical Logic.J. Lambek & P. J. Scott - 1989 - Journal of Symbolic Logic 54 (3):1113-1114.
Logics Without the Contraction Rule.Hiroakira Ono & Yuichi Komori - 1985 - Journal of Symbolic Logic 50 (1):169-201.

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Complete Additivity and Modal Incompleteness.Wesley H. Holliday & Tadeusz Litak - 2019 - Review of Symbolic Logic 12 (3):487-535.
A Sahlqvist Theorem for Substructural Logic.Tomoyuki Suzuki - 2013 - Review of Symbolic Logic 6 (2):229-253.

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