This position paper aims at setting a new semantics for multi-modal mu-calculus to represent interactive states where abstract actions may be applied to. A least fixed point formula may be available to denote states allowing interaction. A simple algebraic representation for interactive states can be definable. For communication between human and machinery, a modality is reserved. In applicative task domains, knowledge construction is focused on with respect to interactive action applications through communications. Panel touch behaviour on iDevice as practice, URL references as functions and grammatical rule applications for sequential effects are studied, as knowledge construction technologies. These views coherent with abstract state machine are finally related to recent trends as semiring in algebraic structure and coalgebra for streams as sequential knowledge structures. A refinement of interactive techniques is positioned into a formal approach to multi-modal logic, applicable to some practices.