We proposed a novel framework for the representation of goals and other mental-like attitudes in terms of degree of expected outcomes, where an outcome is an order of possible alternatives. The sequences of alternatives is modelled by a non-classical (substructural) operator. In this paper we provide a modal logic based axiomatisation of the intuition they propose, and we discuss some variants (in particular for the notion of social intention, intentions that are compliant with norms). Given that the outcome operator is substructural, we first propose a novel sequence semantics (a generalisation of possible world semantics) to model the outcome operator, and we prove that the axiomatisation is sound and complete with respect to the new semantics.