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Is the usage of 'would have been' correct in this sentence below?

The only time I believe we exchanged physical pleasantries would have been at the 70th birthday dinner hosted in honour of your mother-in-law, Erelu Ojuolape Ojora at The Eko Hotel and Suites in Lagos some years back.

Read more at: http://www.vanguardngr.com/2016/04/candid-letter-senate-president/

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Yes, to me that usage is fine. In that context, "would have been" is substantially identical to "was," except that "would have been" typically is meant to convey a connotation that the speaker is trying to remember/has to think about when it was, as opposed to knowing definitively when it was (here, also indicated by speaker's use of "The only time I believe...").

In a different context, "would have been" of course means that what comes after is speculative/uncertain, and a trace of that is present in the connotation. A more express statement of this concept would be "I don't believe I've met him, but if I have it would have been at your mother-in-law's 70th birthday dinner."

Incidentally, I find the phrase "physical pleasantries" strange. Pleasantries are relatively content-free phrases like "It is nice to meet you," "How are you," &c. These are also described as "phatic," I am informed by another post. Anyway, since "pleasantries" are usually verbal (but may be written), "exchanged physical pleasantries" sounds to me like a euphemism for some type of casual sexual activity. I suppose that a handshake or brief hug could be said to be "exchanging physical pleasantries," but I have never heard this phrase used before.