Geodesic
A Syntactic Approach to Closure Operation
Bulletin of the Section of Logic, Tome 46 (2017) no. 3-4.

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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.
Keywords: closure operation, closure system, rule of inference 
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     author = {Nowak, Marek},
     title = {A {Syntactic} {Approach} to {Closure} {Operation}},
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     url = {http://geodesic.mathdoc.fr/item/BSL_2017_46_3-4_a0/}
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Nowak, Marek. A Syntactic Approach to Closure Operation. Bulletin of the Section of Logic, Tome 46 (2017) no. 3-4. http://geodesic.mathdoc.fr/item/BSL_2017_46_3-4_a0/