Rational beliefs are sensitive to truth and logic. Truth is what beliefs aim at; logic tells us how beliefs must cohere. Other mental states (emotions, desires, etc) inherit this sensitivity, insofar as they interact with rational belief. So if we radically revise our views on truth and logic our theory of rational minds will have to change too.
One way that this can happen is if we adopt a nonclassical logic or semantics—giving up the assumption that the law of excluded middle always holds; or that contradictions are never true. Another way it can happen is if—even holding fixed a classical backdrop—there is simply no fact of the matter whether a given proposition is true or false.
So what’s life like in this setting? What patterns of belief are rationally coherent? How should we update these beliefs when we receive evidence? How should we act, when our uncertainty about outcomes is due to vagueness rather than mere ignorance?
This website reports my work on how rationality adapts when classical assumptions are dropped. My other projects, full CV details, and the like can be found here.