Wow, that's interesting. So we can do vector arithmetic and the results make sense as a form of embedding/concept logic. Addition seems to work like "and" / set intersection. Subtraction works like set difference ("T\S", also literally written "T-S", i.e. "without"), which logically says "T, but not S", or in terms of predicate calculus, "T(x) & not S(x)".
Perhaps there is also some unitary vector operation which directly corresponds to negation (not Sally)? Perhaps multiplying the vector by -1? Or would (-1)S rather pick out "the opposite of Sally in conceptual space" instead of "not / anyone but, Sally"? And what about logical disjunction (union)? One could go further here, and ask whether there is an analog to logical quantifiers. Then there is of course the question whether there is anything in vector logic which would correspond to relations, binary predicates, like R(x, y), not just unitary ones, etc.
Perhaps there is also some unitary vector operation which directly corresponds to negation (not Sally)? Perhaps multiplying the vector by -1? Or would (-1)S rather pick out "the opposite of Sally in conceptual space" instead of "not / anyone but, Sally"? And what about logical disjunction (union)? One could go further here, and ask whether there is an analog to logical quantifiers. Then there is of course the question whether there is anything in vector logic which would correspond to relations, binary predicates, like R(x, y), not just unitary ones, etc.
(Sorry for rambling, I'm thinking out loud here.)