A false statement can cause a reasoner’s beliefs to become more accurate.
Suppose for example that Alice believes falsely that there is an invisible dragon in her garage, but then Bob tells her falsely that all dragons, invisible or not, cannot tolerate the smell of motor oil. Alice decides to believe that, notes that there is a big puddle of motor oil in the center of her garage (because her car leaks oil) and stops believing there is an invisible dragon in her garage.
But by your definition of deception, what Bob told Alice just now is not deceptive because it made Alice’s beliefs more accurate, which is all that matters by your definition.
It would be reasonable for Alice to want Bob never to lie to her even when the lie would make her beliefs more accurate, but there is no way for Alice to specify that desire with your formalism. And no way to for Alice to specify the opposite desire, namely, the fact that a lie would be okay with her as long as it makes her beliefs more accurate. And I cannot see a way to improve your definition to allow her to specify that desire.
In summary, although there might be some application, some special circumstance that you did not describe and that I have been unable to imagine, in which it suffices, your definition does not capture all the nuances of deception in human affairs, and I cannot see a way to make it do so without starting over.
But that is not surprising because formalizing things that matter to humans is really hard. Mathematics progresses mainly by focusing on things that are easy to formalize and resigning itself to having only the most tenuous connection to most of the things humans care about.
A false statement can cause a reasoner’s beliefs to become more accurate.
Suppose for example that Alice believes falsely that there is an invisible dragon in her garage, but then Bob tells her falsely that all dragons, invisible or not, cannot tolerate the smell of motor oil. Alice decides to believe that, notes that there is a big puddle of motor oil in the center of her garage (because her car leaks oil) and stops believing there is an invisible dragon in her garage.
But by your definition of deception, what Bob told Alice just now is not deceptive because it made Alice’s beliefs more accurate, which is all that matters by your definition.
It would be reasonable for Alice to want Bob never to lie to her even when the lie would make her beliefs more accurate, but there is no way for Alice to specify that desire with your formalism. And no way to for Alice to specify the opposite desire, namely, the fact that a lie would be okay with her as long as it makes her beliefs more accurate. And I cannot see a way to improve your definition to allow her to specify that desire.
In summary, although there might be some application, some special circumstance that you did not describe and that I have been unable to imagine, in which it suffices, your definition does not capture all the nuances of deception in human affairs, and I cannot see a way to make it do so without starting over.
But that is not surprising because formalizing things that matter to humans is really hard. Mathematics progresses mainly by focusing on things that are easy to formalize and resigning itself to having only the most tenuous connection to most of the things humans care about.