Constructive canonicity in non-classical logics. (English) Zbl 0949.03019

From the text: We deal with the completeness aspect of the Sahlqvist theorem, i.e. we use a new technique which is able to prove canonicity without any previous or simultaneous reduction of the second-order one. We also extend the result in such a way that it applies to intermediate logics, to logics with the difference connective and to intuitionistic modalities. Another aspect of the proof we present here is its constructive character. We get a constructive analogue of Stone’s representation theorem for a large class of varieties of distributive lattices with further operators.


03B45 Modal logic (including the logic of norms)
03B55 Intermediate logics
06D20 Heyting algebras (lattice-theoretic aspects)
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