Does any of these sentences entail the other one?
My last name is Jones.
My father's last name was Jones.
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No. Consider the case of a married woman who took her husband's name (as is still commonplace), her last name is Jones, but her father's last name was Smith
Traditionally in Western society, the first statement would only entail the second for men or unmarried women, and then only if born within wedlock. Nowadays it's much more complicated as men might change their surname for various reasons, women might not, children born out of wedlock might take their father's surname anyway, and children born within wedlock might take a double-barrelled surname instead of their father's
It also definitely fails to hold in many other cultures as the last name is frequently not inherited, at least not in a simple patrilineal fashion
For example, the father of a Spanish person whose last name is Diaz might not have the name Diaz at all, instead Diaz will be the mother's paternal surname. Each person in the family has a given name followed by their paternal surname then their maternal surname (although these two surnames are sometimes reversed, with the reverse order being the norm in the related Portuguese) and each parent passes their paternal surname down to their child in their respective surname. I.e. using the example on wikipedia, the son of Ángela López Sáenz and Tomás Portillo Blanco would be Pedro Portillo López
Likewise, in East Asia (or Hungary) family names appear before the given name, and so the last name is actually the given name so there would be no reason to expect anyone's last name to be the same as their father's
There are also a few cultures where patronymics are the norm such as Iceland where ones last name is the name of the father with a suffix meaning son or daughter so, whilst my last name being Jónsson wouldn't tell you anything about my father's last name, it would tell you that his given name is Jón
Lastly, there are a few cultures around the world that don't use surnames at all (especially in Indonesia) and only use a single given name. Obviously in this case, the notion of a last name is not very meaningful at all
Names are surprisingly complicated, and it's very easy to make incorrect assumptions about them based on your own cultural context (in this case, that someone has a last name, and that it is inherited from the father). There is a good (and surprisingly short) video by Tom Scott summarising some of these issues from the point of view of designing web forms which can be found here
That said, in a Bayesian sense, taking the first statement as a prior does increase the likelihood of the latter (especially if speaking to someone who is culturally Western European), although certainly not to certainty (as would be required for entailment)