The Distributivity on Bi-Approximation Semantics

Authors: Tomoyuki Suzuki
Publication year: 2016
Publication type: Článek v odborném periodiku
Periodical: Notre Dame Journal of Formal Logic
Projects: Mathematical Fuzzy Logic in Computer Science
Bibliographic citation: SUZUKI, Tomoyuki. The Distributivity on Bi-Approximation Semantics. Notre Dame Journal of Formal Logic. 2016, 57(3), 411-430. ISSN 0029-4527. E-ISSN 1939-0726. Dostupné z: http://projecteuclid.org/euclid.ndjfl/1461157795
ID: 461469
Online record: View online record

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.