Interval Notations

It is known that different authors use different notations (slightly different or radically different) for intervals, interval vectors, widths, etc. This difference in notations makes our papers more difficult to read, especially for researchers from other fields. It is therefore desirable to have uniform notations.

The problem of choosing uniform notations is not so easy, because all notations have their drawbacks (e.g., the standard notation $\overline x$ for the upper endpoint of an interval is also used in statistics to denote average, and the sometimes used alternative notation $x^+$ is also used in lattice theory to denote $\max(x,0)$).

Lately, there has been an essential progress is designing a reasonable consistent system of interval notations: namely, the latest book by Kearfott contains notations that, to the viewpoint of several researchers, take into consideration both the desirable features of the previous notations and the critical comments that have been made about these previous notation systems.

Kearfott's notations, together with the other parts of his book, were widely circulated, and Baker Kearfott has taken into consideration suggestions that have been proposed to improve his system. In this sense, Kearfott's notations are not simply one of the possible systems of notations, but they are already the result of the active discussion and compromise within the interval community.

In view of this fact, maybe, we can simply adopt Kearfott's notations (or at least some version of it) as the standard? We can make it an obligatory standard for the Reliable Computing journal (and maybe for our conferences), and a de facto standard for papers published elsewhere (in the sense that we will try to abide by these notations ourselves and, when acting as referees, recommend other authors to abide).

The papers that are already in the "to appear" (or close to final) stage can stay "as is", but the new papers can be made uniform.

We can definitely do that if there is a consensus in the interval community.

The Notations

If you do not have access to Kearfott's book, you can download a
PostScript file with the three pages of Baker Kearfott's book that contain these notations, and three style files that make these notations easier to implement (gd.tex, reptdefs.tex, rs.tex).
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