Until the words, "we are officially in a relationship" are spoken, can someone you are seeing date around?

Until the words, we are officially in a relationship are spoken, can someone you are seeing date around?

If you have been seeing/dating someone, yet you've not defined your relationship as being solely wanting to exclusively see each other, IN YOUR OPINION, can they/you date/sleep around until there is an official title or do you think at a certain point, it should be obvious to someone you're seeing routinely that they should not be seeing other people?

Until the words, "we are officially in a relationship" are spoken, can someone you are seeing date around?
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