A Syntactic Approach to Closure Operation

Marek Nowak

doi:10.18778/0138-0680.46.3.4.04

Authors

Marek Nowak Department of Logic, University of Lodz Lindleya 3/5, 90-131 Lódź, Poland Author

DOI:

https://doi.org/10.18778/0138-0680.46.3.4.04

Keywords:

closure operation, closure system, rule of inference

Abstract

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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