I think Djikstra would not be bothered by this. His arguments tend to be that even with such a search process it's the very providence of formal language to give someone the power to guide that search.
In other words, you'd need formal language to be able to specify what you truly want, then would "translate" it to natural language to execute the search, the processor would search for the proper formal language expression, and then you would verify.
Or you could just skip all the intermediate steps.
It's the developers of agents like Siri and Cortana, not the users, who need formal language.
Anyway I don't think we're disagreeing with each other: there is always going to be a place for formal languages, they won't ever go away and be "replaced" with natural language interfaces, it's just that Jane Random will be more than happy to speak some gibberish to her computer and let the machine figure things out.
Oh but we are: I don't think Jane Random will ever reach so far into that direction until her desires become vastly simplified. So in a Wall-e style future then yes, but in one where people still do things creatively there will always be need for formality.
In other words, you'd need formal language to be able to specify what you truly want, then would "translate" it to natural language to execute the search, the processor would search for the proper formal language expression, and then you would verify.
Or you could just skip all the intermediate steps.