This is the main statement of my current (2010-2013) project on imperative logic. See also Cognitivism about imperatives; Conditional commands; Preposcription semantics and KDDc4; The transformational approach to imperative consequence; and Permissives and epistemic modals,
Abstract: An argument is usually said to be valid iff it is truth-preserving – iff it cannot be that all its premises are true and its conclusion false. But imperatives (it is normally thought) are not truth-apt. They are not in the business of saying how the world is, and therefore cannot either succeed or fail in doing so. To solve this problem, we need to find a new criterion of validity, and I aim to propose such a criterion.
Parsons, Josh. 2013. “Command and Consequence.” Philosophical Studies 164 (1): 61–92. doi:10.1007/s11098-013-0094-x.