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2016 The Distributivity on Bi-Approximation Semantics
Tomoyuki Suzuki
Notre Dame J. Formal Logic 57(3): 411-430 (2016). DOI: 10.1215/00294527-3542442

Abstract

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.

Citation

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Tomoyuki Suzuki. "The Distributivity on Bi-Approximation Semantics." Notre Dame J. Formal Logic 57 (3) 411 - 430, 2016. https://doi.org/10.1215/00294527-3542442

Information

Received: 23 April 2013; Accepted: 12 May 2014; Published: 2016
First available in Project Euclid: 20 April 2016

zbMATH: 06621299
MathSciNet: MR3521490
Digital Object Identifier: 10.1215/00294527-3542442

Subjects:
Primary: 03G10, 03G25
Secondary: 03G27

Rights: Copyright © 2016 University of Notre Dame

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Vol.57 • No. 3 • 2016
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