Generalizations of Liveness and Fairness Properties

The definitions of many known properties of concurrent systems (e.g. liveness, fairness, impartiality, justice) require every action to satisfy some condition. Sometimes the level of actions is too fine and one would like to consider the corresponding conditions for sets of actions.A framework for such treatment is proposed in this paper. The known liveness and fairness properties are generalized and investigated in accordance to the lattice structure of partitions of a set of actions. Partitions are used in order to group actions and form some cruder levels of abstraction