The whole point of alt is to make your site accessible. If the image is important for your site (for example, a link posted by someone, mentioned in the text, etc.), you want everyone to know what it is and what is there. Bullet points and blank images do not meet these criteria, so you can simply leave them without alt s. Bullets in the "supposed" javascript menu are executed both in CSS and in the layout, so if you feel like jumping through several hoops, you can still get your code to check whether you consider it worthy.
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