If a person did not form the intention of fasting from the night before, can he observe a voluntary fast that day?

It was narrated that Yazid said:

"Salamah told us that the Messenger of Allah said to a man: 'Announce the day of Ashura. Whoever has eaten let him not eat for the rest of the day, and whoever has not eaten, let him fast."'

أَخْبَرَنَا مُحَمَّدُ بْنُ الْمُثَنَّى، قَالَ حَدَّثَنَا يَحْيَى، عَنْ يَزِيدَ، قَالَ حَدَّثَنَا سَلَمَةُ، أَنَّ رَسُولَ اللَّهِ صلى الله عليه وسلم قَالَ لِرَجُلٍ ‏

‏ أَذِّنْ - يَوْمَ عَاشُورَاءَ - مَنْ كَانَ أَكَلَ فَلْيُتِمَّ بَقِيَّةَ يَوْمِهِ وَمَنْ لَمْ يَكُنْ أَكَلَ فَلْيَصُمْ ‏

‏ ‏.‏