One of the major trends in modern logic has been the move from logic to logics. This has created the need to develop general results applicable to enormous families of logical systems, while at the same time accounting for the speciﬁc features of each family member in a modular way. This volume focuses on canonicity and correspondence results for non-classical logics. Canonicity and correspondence are intimately related, and recently, general methodologies for obtaining such results have become very prominent. These methodologies extend the original Sahlqvist canonicity and correspondence theorem from the realm of model theory to the realm of algebra, coalgebra and Stone-type duality. This volume collects a small sample of results in this very vibrant research ﬁeld. The ﬁrst paper, entitled ‘The Canonical FEP Construction’, introduces a novel construction, based on canonical extensions. This construction is used to prove the ﬁnite embeddability property (FEP) for varieties of decreasing residuated lattice-ordered algebras deﬁned by equations from a certain syntactically speciﬁed class. The ﬁnite algebras produces in this way are guaranteed to be internally compact, which is not the case with more traditional FEP constructions. The second paper, ‘Dual characterizations for ﬁnite lattices via correspondence theory for monotone modal logic’,
Journal of Logic and Computation – Oxford University Press
Published: Apr 1, 2017
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