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.


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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