The distributivity on bi-approximation semantics.

*(English)*Zbl 1436.03317Summary: In this paper, we give a possible characterization of the distributivity on bi-approximation semantics. To this end, we introduce new notions of special elements on polarities and show that the distributivity is first-order definable on bi-approximation semantics. In addition, we investigate the dual representation of those structures and compare them with bi-approximation semantics for intuitionistic logic. We also discuss that two different methods to validate the distributivity – by the splitters and by the adjointness – can be explicated with the help of the axiom of choice as well.

##### MSC:

03G10 | Logical aspects of lattices and related structures |

03G25 | Other algebras related to logic |

03G27 | Abstract algebraic logic |

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\textit{T. Suzuki}, Notre Dame J. Formal Logic 57, No. 3, 411--430 (2016; Zbl 1436.03317)

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