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On the structure of modal and tense operators on a boolean algebra

Authors :
Bezhanishvili, Guram
Kornell, Andre
Publication Year :
2023

Abstract

We study the poset NO(B) of necessity operators on a boolean algebra B. We show that NO(B) is a meet-semilattice that need not be distributive. However, when B is complete, NO(B) is necessarily a frame, which is spatial iff B is atomic. In that case, NO(B) is a locally Stone frame. Dual results hold for the poset PO(B) of possibility operators. We also obtain similar results for the posets TNO(B) and TPO(B) of tense necessity and possibility operators on B. Our main tool is Jonsson-Tarski duality, by which such operators correspond to continuous and interior relations on the Stone space of B.<br />Comment: 18 pages

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2308.08664
Document Type :
Working Paper