Measuring inaccuracy of uncertain doxastic states in many-valued logical systems

I will propose an alternative philosophical approach to the representation of uncertain doxastic states. I will argue that the current account of measuring inaccuracy of uncertain doxastic states is inadequate for Belnap's four-valued logic. Specifically, a situation can be found in which either an inaccuracy measure returns a completely wrong result or an agent's inaccuracy score is inadequate relative to the mistake in her doxastic attitude. This will motivate an alternative representation of uncertain doxastic states based on ordered pairs. I will describe a possible inaccuracy measure that is suitable for ordered pairs, and I will show that it has all the qualities that are required for an inaccuracy measure to be legitimate. Finally, I will introduce conditions of rationality for uncertain doxastic states represented by ordered pairs.