A Syntactic Approach to Closure Operation
DOI:
https://doi.org/10.18778/0138-0680.46.3.4.04Keywords:
closure operation, closure system, rule of inferenceAbstract
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.
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