Complements and different lattice structures in a logic of action

Abstract

H. J. Genrich (1973) developed a precise calculus suited formally to deal with plans, demands, and consummating actions referred to, in short, by the term 'accomplishments' as far as they are characterized by a relationship of fulfilment, i.e.: accomplishments (or actions etc.) fulfil, or meet, plans or requirements. The calculus is applicable to that extent in which these elements, i.e. accomplishments (plans, demands, actions etc.) can be considered to figure on the same level of abstraction and can, for the sake of formal analysis, be combined or even equated, respectively. Interpreting an action as a set of nonsequential, not strictly sequential, processes, "i.e. as a partially ordered set of elementary actions (acts, events, steps)" Genrich (1973) introduced the concept ola plan structure "as a set of mutually alternative actions" amounting to a hierarchical structure of the possible executions of the respective plans. Basically, a set of predicate terms A? referring to accomplishments, actions, plans, tasks, demands etc. is assumed to be given. Therefore, these terms, by presupposition, refer both to actions and to requirements of action, e.g. plans, respectively. The substantive philosophical problems occurring in equating these different factors of an action process are not to be discussed here. For practical reasons of admitting of a formal analysis, this presupposition of formally equating actions and require? ments etc. is taken for granted in this paper. To be more precise, the At should be supplemented by arguments for individual constants designat? ing the agents a?\ we would, then, have complete statements of the form [Ai]ah e.g. [AJ02 etc. However, assuming the simplest case that all action statements refer to the same agent, this more complicated notation may be dispensed with for the time being. If needed, it might easily be reintroduced. The basic relationship is the relation of fulfilment or satisfaction: Ai<A2 may designate that the consummation, or performance, of the