Notre Dame Journal of Formal Logic

The Distributivity on Bi-Approximation Semantics

Tomoyuki Suzuki

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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.

Article information

Source
Notre Dame J. Formal Logic, Volume 57, Number 3 (2016), 411-430.

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

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1461157795

Digital Object Identifier
doi:10.1215/00294527-3542442

Mathematical Reviews number (MathSciNet)
MR3521490

Zentralblatt MATH identifier
06621299

Subjects
Primary: 03G10: Lattices and related structures [See also 06Bxx] 03G25: Other algebras related to logic [See also 03F45, 06D20, 06E25, 06F35]
Secondary: 03G27: Abstract algebraic logic

Keywords
lattice-based logics relational semantics canonicity

Citation

Suzuki, Tomoyuki. The Distributivity on Bi-Approximation Semantics. Notre Dame J. Formal Logic 57 (2016), no. 3, 411--430. doi:10.1215/00294527-3542442. https://projecteuclid.org/euclid.ndjfl/1461157795


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