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A syntactic approach to closure operation. (English) Zbl 1423.06019

Summary: In the paper, tracing the traditional Hilbert-style syntactic account of logics, a syntactic characteristic of a closure operation defined on a complete lattice follows. The approach is based on observation that the role of rule of inference for a given consequence operation may be played by an ordinary binary relation on the complete lattice on which the closure operation is defined.

MSC:

06B23 Complete lattices, completions
06A15 Galois correspondences, closure operators (in relation to ordered sets)
03G10 Logical aspects of lattices and related structures
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References:

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